Yan-Hui Lin

Yan-Fu Li

Enrico Zio

Reliability Assessmentof SystemsSubject to Dependent Degradation Processes and Random Shocks

Keywords: multi-state system, system reliability assessment, degradation, random shocks, dependency, piecewise-deterministic Markov process, Monte Carlo simulation, residual heat removal system

System failures can be induced by internal degradation mechanisms or by external causes.

In this paper, we consider the reliability ofsystems experiencing both degradation and random shock processes. The dependencies between degradation processes and random shocks, and among degradation processes areexplicitly modelled. The degradation processes of system components are modeled by multi-state models (MSMs) and physics-based models (PBMs).The piecewisedeterministic Markov process modeling framework is employed to combine MSMs and PBMs, and for incorporating degradation and random shocks dependencies.The Monte Carlo simulation and finite-volume methodsare used to compute the system reliability. Asubsystem of a residual heat removal system in a nuclear power plant is considered as illustrative case.

FV

Finite-volume

RHRS Residual heat removal system

Notations 𝑲

INTRODUCTION

The evaluation of the system reliability over time is an important and critical task. For example, the reliability of safety systems in nuclear power plants, such as reactor shutdown, emergency core cooling systems and other safety multi-component systems in nuclear industry, need to meet safety requirements imposed by regulation to ensure their operational safety [START_REF] Marseguerra | A multiobjective genetic algorithm approach to the optimization of the technical specifications of a nuclear safety system[END_REF]. The instances when the requirements are not satisfied can be identified byreliability analysis. Reliability improvement actions can, then, be performed by design on maintenance, to avoid possible human and economic losses. In this paper, we investigate the reliability assessment of multi-component systems subject to dependent degradation processes influenced by random shocks. The dependencies pose challenging issues in system reliability modeling and assessment [START_REF] Schöttl | A reliability model of a system with dependent components[END_REF]) (e.g. for microelectromechanical systems, which are complex systems experiencing dependent component failure processes and multiple dependent competing failure processes for each component (Song, et al., 2014b)). System failures can be induced byinternal degradation mechanisms (e.g. wear, fatigue and erosion)orby external causes(e.g. thermal and mechanical shocks) [START_REF] Jiang | Modeling zoned shock effects on stochastic degradation in dependent failure processes[END_REF]. The interactions between these factors needto be considered under certain circumstances, e.g.

whendegradation processes andrandom shocksare s-dependent (e.g. single-event overloadswith safe shock magnitudescan influence the fatigue crack growth of stents by causing instantaneous increase on the crack propagation [START_REF] Keedy | Reliability analysis and customized preventive maintenance policies for stents with stochastic dependent competing risk processes[END_REF]), orthe degradation state of some components in onesystem can influence the degradation dynamics or the remaining useful life of the others(e.g. the degradation of the pre-filtration stations leading to a lower performance level of the sand filter in a water treatment plant [START_REF] Rasmekomen | Maintenance optimization for asset systems with dependent performance degradation[END_REF]). Neglecting these aspects may result in overestimation of system reliability [START_REF] Wang | Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying copulas[END_REF].

In industrial systems, many critical components (e.g. valves and pumps in the nuclear and aerospace industries) are designed to be highly reliable, for which statistical degradation/failure data are often limited. In this case, multi-state models (MSMs) [START_REF] Black | A semi-Markov approach for modelling asset deterioration[END_REF][START_REF] Giorgio | An age-and state-dependent Markov model for degradation processes[END_REF][START_REF] Moghaddass | Multistate degradation and supervised estimation methods for a condition-monitored device[END_REF] and physics-based models (PBMs) [START_REF] Chookah | A probabilistic physics-of-failure model for prognostic health management of structures subject to pitting and corrosion-fatigue[END_REF][START_REF] Daigle | A model-based prognostics approach applied to pneumatic valves[END_REF][START_REF] Wang | Physics-Based Device-Level Power Electronic Circuit Hardware Emulation on FPGA[END_REF] can be used to describe the evolution of degradation in components and systems. A MSM describes the degradation process in a discrete way, supported by material science knowledge (Lin, et al., 2015b) and/or available but limited degradation/failure historical data from field collection or degradation tests [START_REF] Giorgio | An age-and state-dependent Markov model for degradation processes[END_REF]. On the contrary, a PBM gives an integrated mechanistic description of the component life consistent with the underlying real degradation mechanisms under operating conditions [START_REF] Hu | Model-based dynamic power assessment of lithium-ion batteries considering different operating conditions[END_REF], by using physics knowledge modeled by corresponding mathematical equations [START_REF] Chookah | A probabilistic physics-of-failure model for prognostic health management of structures subject to pitting and corrosion-fatigue[END_REF]. In practice, degradation models of different nature have to be applied depending on the available information of the degradation processes. Recently, the piecewise-deterministic Markov process (PDMP) modeling framework has been employed to incorporate PBMs and MSMs, and to treat the dependencies among degradation processes but without considering the influences of random shocks (Lin, et al., 2015a). On the other hand, random shocks can accelerate the degradation processes (e.g. internal thermal shocks and water hammers onto power plant components [START_REF] Salonen | Experience on in-service damage in power plant components[END_REF]).

The reliability of systems experiencing both degradation and random shocks is a problem that has been widely studied [START_REF] Becker | Dynamic reliability under random shocks[END_REF][START_REF] Jiang | Reliability and maintenance modeling for dependent competing failure processes with shifting failure thresholds[END_REF], Lin, et al., 2015b[START_REF] Peng | Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes[END_REF][START_REF] Rafiee | Reliability modeling for dependent competing failure processes with changing degradation rate[END_REF], Song, et al., 2014a, Song, et al., 2014b[START_REF] Wang | Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying copulas[END_REF][START_REF] Yang | Maintenance of multi-state production systems deteriorated by random shocks and production[END_REF].The dependency among these processes leading to failure has posed some challengesto reliability modeling.A literature review is presented below, to position our contributions within the existing works. Previous research has focused on the dependency between one type of degradation processes and random shocks, and among degradation processes themselves. [START_REF] Wang | Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying copulas[END_REF]employed copulasto handle these two types of dependencies; however,sufficient degradation/failure data is required to determine the copula functionsthrough statistical inference.

In this paper, we extend the PDMP modeling framework for system reliability assessment, considering not only the dependencies among degradation processes but also the impacts of random shocks. To the best knowledge of the authors, this is the first work investigating systems with both continuous and multi-state degradation processes, subject to random shocks and considering the dependencies between degradation processes and random shocks, and among degradation processes.

Since the analytical solution is difficult to obtain due to thecomplexity of the system being considered, we employ two numerical approaches to assess system reliability: the Monte Carlo (MC) simulation [START_REF] Marseguerra | Monte Carlo approach to PSA for dynamic process systems[END_REF] and the finite-volume (FV) [START_REF] Cocozza-Thivent | A finite-volume scheme for dynamic reliability models[END_REF] methods.

The remainder of this article is organized as follows. Section 2 provides the assumptions and descriptions of the degradation processes and random shocks. Section 3 presents the extended modelfor systems with degradation and random shock processes, consideringtheir dependencies. The proposed MC simulationand FV methods are presented in Section 4. Section 5 presents an illustrative study taken from a real residual heat removal system (RHRS) operated by Électricité de France (EDF).

The RHRS is used for cooling the reactor during and following shutdown, contributing to safety by removing heat from the core and transferring it to the environment. Specifically, we consider an important subsystem consisting of a pneumatic valve and a centrifugal pump in series. This system setting is widely used, under different conditions, in a variety of domains for fluid delivery (from water supply to spacecraft fueling systems) (Daigle and[START_REF] Daigle | A model-based prognostics approach applied to pneumatic valves[END_REF][START_REF] Daigle | Model-based prognostics with concurrent damage progression processes[END_REF].

Numerical results and analysis are presented in Section 6. Section 7 concludes the work.

ASSUMPTIONS AND MODEL DESCRIPTIONS

We consider a multi-component system. [START_REF] Yeh | Optimal inspection and replacement policies for multi-state deteriorating systems[END_REF] and [START_REF] Zuo | Replacement-repair policy for multi-state deteriorating products under warranty[END_REF]; Markov processes are widely used to describe components degradation processes.

The transition rates between different degradation states are estimated from the degradation and/or failure data from historical field collection. The failure state set of the process𝐾 𝑛 is denoted by 𝓕 𝐾 𝑛 = {0}.

PBMs

We follow the assumptions on PBMs made in [START_REF] Lin | Dynamic Reliability Models for Multiple Dependent Competing Degradation Processes[END_REF]: This assumption is made in [START_REF] Lorton | A methodology for probabilistic model-based prognosis[END_REF] and widely used (Daigle and[START_REF] Daigle | A model-based prognostics approach applied to pneumatic valves[END_REF][START_REF] Daigle | Model-based prognostics with concurrent damage progression processes[END_REF]. Note that higher-order differential equations can be converted into a system of first-order differential equations by introducing extra variables [START_REF] Zwillinger | Handbook of differential equations[END_REF].

 A degradation


Random shocks

Random shocks can influence the degradation processes of the components. The following assumptions are made, similarly to various previous works [START_REF] Jiang | Reliability and maintenance modeling for dependent competing failure processes with shifting failure thresholds[END_REF][START_REF] Peng | Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes[END_REF][START_REF] Rafiee | Reliability modeling for dependent competing failure processes with changing degradation rate[END_REF], Song, et al., 2014a[START_REF] Yang | Maintenance of multi-state production systems deteriorated by random shocks and production[END_REF].

 Random shocks occur in time according to a homogeneous Poisson process {𝑁 𝑡 , 𝑡 ≥ 0}

with constant arrival rate𝜇(Fig. 1), where the random variable 𝑁 𝑡 denotes the number of random shocks occurred until time 𝑡.

 The damages of random shocks aredivided into two types: extreme and cumulative.

 Extreme and cumulative shocks are mutually exclusive.

 Extreme shocksimmediately lead the componentsto failure, whereas cumulative shocks gradually deteriorate the components.

DEPENDENT DEGRADATION PROCESSES AND RANDOM SHOCKS

Dependency between degradation processes and random shocks

Due to the different nature of PBMs and MSMs, the impacts of random shocks on the two groups of components are characterized in different ways.

Impacts on MSMs

In the generic degradation process𝐾 𝑛 ∈ 𝑲, random shocks can cause the process variable𝑌 𝐾 𝑛 𝑡 to step from state 𝑖 to a further degraded state 𝑗 with probability 𝑝 𝑖𝑗 , 𝑖 > 𝑗 [START_REF] Yang | Maintenance of multi-state production systems deteriorated by random shocks and production[END_REF]

Impacts on PBMs

In the generic degradation process𝐿 𝑚 ∈ 𝑳, the 𝑖-th shock becomes extreme if the shock load 𝑊 𝑖 exceeds the maximal material strength 𝐷, otherwise, it can bring an instantaneous random increase 𝑯 𝑖 to 𝑿 𝐿 𝑚 𝑡 (Song, et al., 2014b). The overall degradation level of 𝐿 𝑚 is expressed as follows:

𝑫 𝐿 𝑚 𝑡 = 𝑿 𝐿 𝑚 𝑡 + 𝑯 𝑖 𝑁 𝑐 𝑡 𝑖=1 , 𝑖𝑓 𝑁 ′ 𝑡 ≠ 0 𝑿 𝐿 𝑚 𝑡 , 𝑖𝑓 𝑁 ′ 𝑡 = 0 (1)
where 𝑁 𝑐 (𝑡)is the number of cumulative shocks occurred in the developing 𝐿 𝑚 process before the extreme shock occurs until time 𝑡. The process𝐿 𝑚 leads to failure if 𝑫 𝐿 𝑚 𝑡 reaches the predefined failure state set 𝓕 𝐿 𝑚 or a shock with load larger than 𝐷 occurs. An example of degradation process𝐿 𝑚 considering random shocks is shown in Fig. 3, where 𝑊 𝑖 is the shock load of the 𝑖-th shock occurred

Dependency among degradation processes

Dependencies may exist among degradation processes within each group and between the two groups. The degradation states of the processes of set𝑲may influence the evolution of the continuous variablesof the degradation processes of set𝑳, andthe degradation levels ofthe lattermay influence the transition times and transition directions of the former(the detailed formulations are shown in eqs. ( 2) and ( 3)) (Lin, et al., 2015a).

Let 𝒀 𝑡 = (𝑌 𝐾 1 𝑡 , … , 𝑌 𝐾 𝑁 𝑡 ) ∈ 𝑺 = {0, 1, … , 𝑑 𝑺 } and 𝑿 𝑡 = 𝑿 𝐿 1 𝑡 , … , 𝑿 𝐿 𝑀 𝑡 ∈ ℝ 𝑑 𝐿 .The evolution of 𝒀 𝑡 is governed by the transition rates which depend on the states of the degradation processes in the first group 𝑿 𝑡 and also in the second group 𝒀 𝑡 , as follows:

𝑙𝑖𝑚 ∆𝑡 → 0 𝑃 𝒀(𝑡 + ∆𝑡) = 𝒋 𝑿 𝑡 , 𝒀 𝑡 = 𝒊, 𝜽 𝑲 = 𝜽 𝐾 𝑛 𝑁 𝑛 =1 /∆𝑡 = 𝜆 𝒊 𝒋 | 𝑿 𝑡 , 𝜽 𝑲 , ∀ 𝑡 ≥ 0, 𝒊, 𝒋 ∈ 𝑺, 𝒊 ≠ 𝒋 (2)
The evolution of 𝑿 𝑡 is described by mathematical equations representing the underlying physics and depends on the states of the degradation processes in the second group 𝒀 𝑡 and also in the first group 𝑿 𝑡 , as follows: (3)

𝑿 𝑡 = 𝑿 𝐿 1 𝑡 , … ,

PDMPs for systems subject to degradation dependency and random shocks

Let 𝒁 𝑡 denote the overall degradation process of the system:

𝒁 𝑡 = 𝑿 ′ 𝑡 = 𝑫 𝐿 1 𝑡 , … , 𝑫 𝐿 𝑀 𝑡 , 𝒀 ′ 𝑡 = (𝒀 𝑡 , 𝑁 𝑡 ) ∈ 𝑬 = ℝ 𝑑 𝐿 × 𝑺 ′ (4)
where 𝑬 is a space combining ℝ 𝑑 𝐿 and 𝑺 ′ = 𝑺 × ℕ.Let 𝑇 𝑘 , 𝑘 ∈ ℕ denote the 𝑘-th jump time in𝒀 ′ 𝑡 and 𝒁 𝑘 = 𝒁 𝑇 𝑘 = 𝑿 ′ 𝑇 𝑘 , 𝒀 ′ 𝑇 𝑘 = 𝑿 𝑘 ′ , 𝒀 𝑘 ′ . The evolution of 𝒁 𝑡 between two consecutive jumps of 𝒀 ′ 𝑡 , between which no shock occurs to the system and the degradation state does not change, can be written as follows: The reliability of the system at time 𝑡 is defined as follows:

𝒁 𝑡 = 𝑿 ′ 𝑡
𝑅 𝑡 = 𝑃 𝒁 𝑠 ∉ 𝓕, ∀𝑠 ≤ 𝑡 = ∫ 𝑝 𝑡 (𝑑𝒛) 𝒛∉𝓕 ( 10
)
where 𝓕isthe space of the failure states of the system.

In the general modeling framework, the temporal variability is considered as follows:

(1) the randomness in MSMs could imply the temporal variability of the degradation processes modeled by PBMs, as shown in Figs.

(3) and ( 8); (2) in PBMs, the temporal variability of the degradation variables can be attributed to the time-varying physical variables associated with the underlying degradation mechanisms.

The parameters in the proposed model are mainly divided into three groups: (1) transition rates in multi-state models;

(2) parameters in physics equations of physics-based models and (3) parameters characterizing random shock processes. The values of the first group can be estimated, using degradation and/or failure data from historical field collection or degradation tests, through maximum likelihood estimation for complete or incomplete data [START_REF] Lisnianski | Statistical Analysis of Reliability Data for Multi-state Systems[END_REF][START_REF] Ogurtsova | Estimating transition rates for multistate models from panel data and repeated crosssections[END_REF]; they can also be estimated by domain experts using physics knowledge (e.g. the values of the transition rates in multi-state physics model (Lin, et al., 2015b)) are described by physics equations). For the second group, the laws of physics are used to build the equations describing the development of the underlying degradation mechanisms (e.g. fatigue, wear, corrosion, etc.) [START_REF] Daigle | A model-based prognostics approach applied to pneumatic valves[END_REF];

the related parameter values can be estimated through regression models using degradation and/or failure data. For example, the physics equations of the fatigue cracking of the seal are built according to Paris-Erdogan law [START_REF] Newby | Estimation of Paris-Erdogan law parameters and the influence of environmental factors on crack growth[END_REF], which relates the stress intensity factor range to the crack growth under a fatigue stress regime; the values of the parameters are estimated through least squares regression methods by using data on crack length and cycles. The values of the third group can be estimated using related degradation and/or failure data obtained from historical field collection or shock tests [START_REF] Chan | Accelerated stress testing handbook: Guide for achieving quality products[END_REF], using likelihood-based inference or regression models [START_REF] Ye | A distribution-based systems reliability model under extreme shocks and natural degradation[END_REF]. For example, the Brown-Proschan model is employed to model wear and shock processes of tire treads [START_REF] Ye | A distribution-based systems reliability model under extreme shocks and natural degradation[END_REF], whereby the likelihood function can be derived based on cumulative hazard function and the parameter values are estimated through maximum likelihood estimation.

SYSTEM RELIABILITY ASSESSMENT UNDER DEPENDENT DEGRADATION AND RANDOM SHOCK PROCESSES

The analytical solution of 𝑅 𝑡 is difficult to obtain mainly due to the complex PDMPs used to model the dependent degradation and random shock processes [START_REF] Labeau | A Monte Carlo estimation of the marginal distributions in a problem of probabilistic dynamics[END_REF]. Therefore, we consider the following two approximate methods: the MC simulation method [START_REF] Marseguerra | Monte Carlo approach to PSA for dynamic process systems[END_REF] based on the semi-Markov kernel of 𝒁 𝑛 , 𝑇 𝑛 𝑛≥0 (eq. ( 7)) and the FV method [START_REF] Cocozza-Thivent | A finite-volume scheme for dynamic reliability models[END_REF] based on the Chapman-Kolmogorov equation (eq. ( 9)). They are two widely used approaches for solving PDMPs to evaluate reliability quantities. The FV method approximates the probability density function of PDMPs by discretizing the state space of the continuous variables and the time space. It is a method that can lead to comparable results as the MC simulation method, using less computing time for low dimensional problems [START_REF] Eymard | Comparison of numerical methods for the assessment of production availability of a hybrid system[END_REF].However, it is typically unsuited for high-dimensional problems or problems with complex equations describing the deterministic evolution. Besides, it is relatively more difficult to implement than the MC simulation method.

MC simulation method

The MC simulation method to compute the system reliability at time 𝑡 consists ofreplicating several times the lifeprocess of the system by repeatedly samplingitsholding time and arrival state from the corresponding probability distributions.Each replication continues until the time of system evolution reaches𝑡 or until the system enters a state in the failure set𝓕.The procedure of the MC simulation method is as follows:

Set 𝑁 𝑚𝑎𝑥 (the maximum number of replications) and 𝑘 = 0 (index of replication) Set𝑘′ = 0 (number of replicationsthat end in a systemfailure state)

While𝑘 < 𝑁 𝑚𝑎𝑥 Initialize the system by setting 𝒁 = (𝑿 ′ 0 , 𝒀 ′ 0 )(initial system state), and the time 𝑇 = 0 (initial system time)

Set𝑡 ′ = 0 (state holding time)

While𝑇 < 𝑡

Sample a 𝑡 ′ by using the probability distribution 𝑑𝐹 𝒁 𝑡 Sample an arrival state 𝒚for stochastic process 𝒀 ′ 𝑡 and an arrival state 𝒙 for process 𝑿 ′ 𝑡 by using eq. ( 8)

Set𝑇 = 𝑇 + 𝑡′ If𝑇 ≤ 𝑡 Set 𝒁 = 𝒙, 𝒚 If𝒁 ∈ 𝓕 Set𝑘 ′ = 𝑘 ′ + 1 Break End if
Else(when 𝑇 > 𝑡)

If𝜑 𝒁, 𝑡 + 𝑡 ′ -𝑇 ∈ 𝓕

Set𝑘 ′ = 𝑘 ′ + 1 Break End if

End if

End While Set𝑘 = 𝑘 + 1

End While □

The estimated system reliability at time 𝑡 can be obtained by

𝑅 𝑀𝐶 𝑡 = 1 -𝑘 ′ /𝑁 𝑚𝑎𝑥 (11)
where k' represents the number of trials that end in the failure state of the system, and the sample variance [START_REF] Lewis | Monte Carlo simulation of Markov unreliability models[END_REF] is:

𝑣𝑎𝑟 𝑅 𝑀𝐶 𝑡 = 𝑅 𝑀𝐶 𝑡 (1 -𝑅 𝑀𝐶 𝑡 )/(𝑁 𝑚𝑎𝑥 -1) (12)
The MC simulation method is widely used in practice to evaluate system reliability [START_REF] Zio | The Monte Carlo simulation method for system reliability and risk analysis[END_REF]. It is based on the strong law of large numbers and the central limit theorem and provides an unbiased estimator [START_REF] Zio | The Monte Carlo simulation method for system reliability and risk analysis[END_REF]. The error on the estimate can be controlled within a confidence interval built based on the sample variance given in eq. ( 12), which can guarantee the consistency of the estimate.

The accuracy of the MC simulation method increases as the number of replications increases. The MC simulation method is efficient in solving high-dimensional problems, since the sample variance does not depend on the number of dimensions. There are techniques to further improve the efficiency of MC simulation method (such as importance sampling, sequential MC, linear sampling, subset sampling, etc.) [START_REF] Zio | The Monte Carlo simulation method for system reliability and risk analysis[END_REF], which have to be designed according to the specific problems and have not been considered in our general reliability assessment framework.

FV method

The FV method is an alternative for theapproximated solution of the system reliability, based on a discretization of the state space of the continuous variables and time space [START_REF] Eymard | Comparison of numerical methods for the assessment of production availability of a hybrid system[END_REF].Here, we employ an explicit FV scheme developed by Cocozza-Thivent et al. [START_REF] Cocozza-Thivent | A finite-volume scheme for dynamic reliability models[END_REF].The numerical scheme aims at constructing an approximate value 𝜌 𝑡 𝒙, 𝒚 𝑖 𝑑𝒙 for 𝑝 𝑡 𝑑𝒙, 𝒚 𝑖 . The estimated system reliability at time 𝑡, then, can be calculated as follows:

𝑅 𝐹𝑉 𝑡 = ∫ 𝜌 𝑡 𝒛 𝑑𝒛 𝒛∉𝓕 (13)
Appendix A contains a detailed description of the FV method. Due to the complexity of the Chapman-Kolmogorov equation (eq. ( 9)), there is no explicit expression for the variance or uncertainty associated with the estimate. However, the convergence of the method is proven in [START_REF] Cocozza-Thivent | A finite-volume scheme for dynamic reliability models[END_REF] under the condition that ∆𝑡 → 0 and ℳ /∆𝑡 → 0, where ℳ is the space step and ∆𝑡 is the time step. The efficiency and the accuracy of the method have been shown through the numerical example in [START_REF] Cocozza-Thivent | A finite-volume scheme for dynamic reliability models[END_REF].

CASE STUDY

We consider a subsystem of a residual heat removal system (RHRS) in a nuclear power plant, which consists of a pneumatic valve and a centrifugal pump in series shown in Fig. 4.

For the degradation model of the pump,weconsider a MSM modified from the one originally supplied by EDF (Lin, et al., 2015a), while for the valve we take the PBM proposed inDaigle and Goebel (2011).

Fig. 4. Subsystem of RHRS, consisting of a centrifugal pump and a pneumatic valve.

Centrifugal pump

The degradation process of the pump is modeled by a four-state, continuous-time, homogeneous Markov chain as shown in Fig. 5.

Fig. 5. Degradation process of the pump.

Among the four states of the pump, state3 is the perfect functioning state and state0 is the complete failure state. Let 𝑌 𝑝 𝑡 denote the degradation state of the pump at time 𝑡 and 𝑺 𝑝 = {3, 2, 1, 0} denote the degradation states set.The pump is functioning until 𝑌 𝑝 𝑡 = 0. The parameters 𝜆 32 , 𝜆 21 and 𝜆 10 are the transition rates between the degradation states, estimated from the available degradation and/or failure data. The pump vibrates when it reaches the degradation states 2 and 1; the intensity of the vibration of the pump on states 2 and 1 is evaluated by the experts as 'smooth' and 'rough', respectively. The set of the failure states of the pump is 𝓕 𝑝 = {0}.

Pneumatic valve

The simplified scheme of the pneumatic valve is shown in Fig. 6. The degradation of the valve is the external leak at the actuator connections to the bottom pneumatic port due to corrosion, and is modeled by a PBM due to limited statistical degradation data on the valve behavior. It is much more significant than the other degradation mechanisms according to the results shown inDaigle and Goebel ( 2011).

Dependency between degradation processes

Dependency in the degradation processes of the two components has been indicated as a relevant problem by the experts of EDF: the pump vibrates due to degradation [START_REF] Zhang | Machinery condition prognosis using multivariate analysis[END_REF] which, in turn, leads the valve to vibrate, aggravating its own degradation processes [START_REF] Moussou | Vibration investigation of a French PWR power plant piping system caused by cavitating butterfly valves[END_REF].The development of the leak size of the valve is, then, reformulated as follows (Lin, et al., 2015a):

𝐷 𝑏 𝑡 = 𝜔 𝑏 (1 + 𝛽(𝑌 𝑝 𝑡 )) ( 14
)
where 𝛽(𝑌 𝑝 𝑡 ) is the function indicating the relative increment of the growth rate of the external leak caused by the vibration of the pump at the degradation state 𝑌 𝑝 𝑡 .

Random shocks

According to the experts of EDF, random shocks like water hammers and internal thermal shocks [START_REF] Salonen | Experience on in-service damage in power plant components[END_REF] can worsen the degradation condition of both components of the subsystem considered or even immediately lead them to failures.

Random shocks can deteriorate the pump from its currentstate𝑖 to a degraded state𝑗,as 𝑝 𝑖𝑗 = 9×(0.1) (𝑖-𝑗 +1) 1-(0.1) (𝑖+1) , 𝑖 ≥ 𝑗,where 𝑝 𝑖0 denotes the probability of an extreme random shock leading the pump For the valve, the 𝑖-th shock becomes extreme if the shock load 𝑊 𝑖 exceedsthe maximal material strength 𝐷 ,otherwise, it can bring aninstantaneous random increase 𝐻 𝑖 to the total externalleak size (Song, et al., 2014b). Since the shock load and the damage cannot be negative,𝑊 𝑖 and 𝐻 𝑖 are assumed to be i.i.d. random variables following folded normal distributions [START_REF] Leone | The folded normal distribution[END_REF],𝑊 𝑖 = 𝑎 and 𝐻 𝑖 = 𝑏 , where 𝑎~𝑁(𝜇 , 𝜎 2 ) and 𝑏~𝑁(𝜇 𝑤 , 𝜎 𝑤 2 ).

PDMP for the system considering dependency

An illustration of the composite degradation process of the valve considering random shocks and the degradation state of the pump is shown in Fig. 8, where the system experienced a random shock at time 𝑡 𝑖 , with the shock load 𝑊 𝑖 , 𝑖 = 1,3,4. The first two shocks cause instantaneous random increases on 𝐷 𝑡 , the last shock leads the valve to failure. The vibration of the pump accelerates the degradation process of the valve at times𝑡 2 and 𝑡 3 , when the pump stepped to a further degraded state.The development of the leak size of the valvedoes not depend on other physical variables according to the given physics equations. Therefore, no physical variables are considered in Fig. 8 and no randomness is observed between two changing points. Nevertheless, there is actually randomness, i.e. the random changing points and the random increments. Moreover, if we consider the randomness in physical variables, then there will be randomness on the curve between two changing points. The degradation processes of the whole system can berepresented by:

𝒁 𝑡 = 𝐷 𝑡 , 𝑌 𝑡 ∈ ℝ + × 𝑺 = 𝑬 (15)
Let 𝑇 𝑘 , 𝑘 ∈ ℕ denote the 𝑘 -th jump timein𝑌 𝑡 and𝒁 𝑘 = 𝐷 𝑘 , 𝑌 𝑘 = 𝒁 𝑇 𝑘 . The evolution of 𝒁 𝑡 between two consecutive jumps of 𝑌 𝑡 , between which no shock occurs to the system and the degradation state of the pumpdoes not change, can be written as follows:

𝒁 𝑡 = 𝐷 𝑡 , 𝑌 𝑡 = 𝜔 𝑏 (1 + 𝛽(𝑌 𝑝 (𝑡))), (0, 0) = 𝜈(𝑌(𝑡)), (0, 0) , 𝑓𝑜𝑟 𝑡 ∈ 𝑇 𝑘 , 𝑇 𝑘+1 (16)

where 𝜈(•)is used to denote the corresponding equation.

By integrating eq. ( 25), we can obtain that:

𝒁 𝑡 = 𝐷 𝑘 + 𝑡 -𝑇 𝑘 𝜔 𝑏 (1 + 𝛽(𝑌 𝑝 (𝑇 𝑘 ))), 𝑌 𝑘 = (𝜑 1 𝒁 𝑘 , 𝑡 -𝑇 𝑘 , 𝑌 𝑘 ), 𝑓𝑜𝑟 𝑡 ∈ 𝑇 𝑘 , 𝑇 𝑘+1 = 𝜑 𝒁 𝑘 , 𝑡 -𝑇 𝑘 , 𝑓𝑜𝑟 𝑡 ∈ 𝑇 𝑘 , 𝑇 𝑘+1 (17)
where 𝜑 1 (•) and 𝜑(•) are used to denote the corresponding equations.

Let 𝑝 𝑡 (𝑑𝑥, 𝒚 𝑖 ) denote the probability distribution of 𝒁 𝑡 . Given the series logic configuration of the system considered, the system fails when one of the two components fails;the reliability of the system at time 𝑡 is, then, defined as follows:

𝑅 𝑡 = 𝑃 𝒁 𝑠 ∉ 𝓕, ∀𝑠 ≤ 𝑡 = ∫ 𝑝 𝑡 (𝑑𝑥, 𝒚 𝑖 ) 𝒚 𝑖 ∉𝓕 𝒑 ′ 𝑥∉𝓕 𝑣 (18)
where 𝓕 = ℝ + × 𝓕 𝒑 ′ ∪ 𝓕 𝑣 × 𝑺isthe set of the failure states of the system.

The parameter values related to the system degradation processes and random shocks under accelerated aging conditions are presented in Table I

NUMERICAL RESULTS AND ANALYSIS

The MC simulation and the FV methods are employed to estimate the system reliability. All the experiments are carried out in MATLAB on a PC with an Intel Core 2 Duo CPU at 3.06 GHz and a RAM of 3.07 GB. MC simulations with 10 3 , 10 4 and 10 5 replications (named MC1, MC2 and MC3, respectively) are applied over a time horizon of 𝑇 𝑚𝑖𝑠𝑠 = 1000 𝑠 for the system reliability estimation.System holding time, arrival state for stochastic process 𝑌 𝑡 and arrival state for process 𝐷 𝑡 can be sampled by using the probability distribution eq. ( 28), the probability mass function eq. ( 30) and the probability distribution eq. ( 31), respectively. See Appendix B for detailed descriptions of these equations.

The results are shown in Fig. 9. It is seen that the MC simulation method requires a number of replications to achieve the desired level of accuracy. The average computation times of MC1, MC2and MC3 are 0.21 s, 2.17 s and 21.77 s, respectively.

Fig. 9. System reliability estimated by MC1, MC2 and MC3.

For the FV method, the state space ℝ + of 𝐷 𝑡 has been divided into an admissible mesh . See Appendix C for the application of FV method.

The system reliability estimated by the FV method, is shown in Fig. 10 II.The sample variances associated with system reliability values estimated by MC3 are less than 2.5e-6 according to eq. ( 12), which means the results are sufficiently consistent and accurate. The quantitative comparison of results obtained by MC3 and FV3 shown in Table II is only used to show that FV scheme can achieve comparable results to the MC simulation method (relative error less than 0.9%) in the illustrative case. that FV3 gives deterministic results since the values of ∆𝑥 and ∆𝑡 do not change, which guarantees the accuracy and consistency of the quantitative comparison. To provide more information, we have added Fig. 11 to compare the results obtained by MC3 with those obtained by FV3 over the time horizon. For this case study, the computational expense of the two methods is similar. The reliability values of the valve, the pump and the system with/without random shocks, obtained by MC3, are shown in Fig. 12. The numerical comparisons on the reliability of the system, the valve and the pumpwith/without random shocks at the final time of 1000 s are presented in Table III. When random shocks are ignored, the system reliability is basicallydetermined by the pump before around 870 s, since the valve is highly reliable. After that, the sharp decrease of the valve reliabilitydue to degradation leads tothe same behavior in the system reliability. When random shocks are considered, the system reliability is determined by both the pump reliability and the valve reliability from the beginning until around 850 s, since the valve is no longer as highly reliable as before. Then, the valve reliability decreases sharply due to the joint effects of random shocks and degradation, and thisdrives alsothe sharp decrease of the system reliability. We can see from the results that neglecting random shocks can result inan underestimation of the reliability of the system and of the components.

Solution approach

For ease of notation, we let 𝒈 𝒚

with

𝒈 𝒚 𝑖 𝒙, 0 | 𝜽 𝑳 = 𝒙, ∀𝒚 𝑖 ∈ 𝑺 ′ , 𝒙 ∈ ℝ d L (20)
and 𝒈 𝒚 𝑖 𝒙, 𝑡 | 𝜽 𝑳 being the result of the deterministic behavior of 𝑿 𝑡 after time t, starting from the point 𝒙 while the processes 𝒀 ′ 𝑡 hold on state 𝒚 𝑖 .

The state space ℝ 𝑑 𝐿 of continuous variables 𝑿 ′ 𝑡 is divided into an admissible mesh ℳ, which is a family of measurable subsets of ℝ 𝑑 𝐿 , i.e., ℳ is a partition of ℝ 𝑑 𝐿 such that:

(1) 𝐴 𝐴∈ℳ = ℝ 𝑑 𝐿 .

(2) ∀𝐴, 𝐵 ∈ ℳ, 𝐴 ≠ 𝐵 ⇒ 𝐴 ∩ 𝐵 = ∅.

(3) 𝑚 𝐴 = ∫ 𝑑𝒙 𝐴 > 0, ∀𝐴 ∈ ℳ, where 𝑚 𝐴 is the volume of grid 𝐴.

(4) 𝑠𝑢𝑝 𝐴∈ℳ 𝑑𝑖𝑎𝑚 𝐴 < +∞ where 𝑑𝑖𝑎𝑚 𝐴 = 𝑠𝑢𝑝 ∀𝒙,𝒚∈𝐴 𝒙 -𝒚 .

Additionally, the time space ℝ + is divided into small intervals ℝ + = [𝑛∆𝑡, (𝑛 + 1)∆𝑡[

is the volume of part of grid 𝐵 which will enter grid 𝐴 after time ∆𝑡, according to the deterministic evolution of 𝑿 𝑡 .

The approximated solution 𝜌 𝑡 𝒙,• 𝑑𝒙 weakly converges towards 𝑝 𝑡 𝑑𝒙,• when ∆𝑡 → 0 and ℳ / ∆𝑡 → 0 where ℳ = 𝑠𝑢𝑝 𝐴∈ℳ 𝑑𝑖𝑎𝑚 𝐴 .

Appendix B: Equations for MC simulation method in case study

The semi-Markov kernel of 𝒁 𝑛 , 𝑇 𝑛 𝑛≥0 is 𝒊 = (𝑥, 𝒚 𝑖 ), (𝑑𝑥, 𝒚 𝑗 ), 𝑑𝑡 = 𝑄(𝜑 𝒊, 𝑡 , (𝑑𝑥, 𝒚 𝑗 ))𝑑𝐹 𝒊 𝑡 , ∀𝑘 ∈ ℕ, 𝒚 𝑖 , 𝒚 𝑗 ∈ 𝑺, 𝑥 ∈ ℝ + , 𝑑𝑥 → 0, 𝑑𝑡 → 0 .

According to the degradation models of the system, we can obtain that:

𝑑𝐹 𝒊=(𝑥,𝒚 𝑖 ) 𝑡 = 𝜆 𝒚 𝑖 𝑒 -𝜆 𝒚 𝑖 𝑡 𝑑𝑡(28)

where 𝜆 𝒚 𝑖 is the sum of the outgoing transition rates of 𝑌(𝑡) from state 𝒚 𝑖 , and

𝑄

Fig. 1 .

 1 Fig. 1. Random shock process

  , with𝑝 𝑖0 denoting the probability that the random shockis extreme, i.e. leading to failure state 0 upon occurrencefrom state 𝑌 𝐾 𝑛 𝑡 = 𝑖 . By combining the original degradation and the random shock processes, the resulting process 𝒀 𝐾 𝑛 ′ 𝑡 is a homogeneous continuous-time Markov chain of the type depicted in Fig. 2. Each layer indicates one degradation state of 𝑌 𝐾 𝑛 𝑡 , and the numbers in each layer indicate the numbers of shocks experienced up to time 𝑡 in the process 𝐾 𝑛 , denoted by 𝑘. The state of 𝒀 𝐾 𝑛 ′ 𝑡 is, then, represented by thepair 𝑌 𝐾 𝑛 𝑡 , 𝑘 . The transitions represented by solid lines are due to the original degradation process, characterized by the original transition rates, which do not influence the value of 𝑘. The transitions represented by dotted lines are due to random shocks, which cause 𝑘 to be increased by one. 𝜇𝑝 𝑖𝑗 , 𝑖 > 𝑗 is the rate of occurrence of a shock which will cause the process stepping to the 𝑗-th layer from the𝑖-th layer. Note that 𝐾 𝑛 fails whenever𝑌 𝐾 𝑛 𝑡 reaches the degradation state 0, no matter how many shocks it has experienced. Therefore, the space of the failure states of 𝒀 𝐾 𝑛 ′ 𝑡 is denoted by 𝓕 𝐾 𝑛 ′ = { 0, 𝑏 , ∀𝑏 ∈ ℕ}. The state space of 𝒀 𝐾 𝑛 ′ 𝑡 is denoted by 𝑺 𝐾 𝑛 ′ = 𝑎, 𝑏 , ∀𝑎 ∈ 𝑺 𝐾 𝑛 , 𝑏 ∈ ℕ .

Fig. 2 .

 2 Fig. 2. Degradation process 𝐾 𝑛 and random shocks.

  at time 𝑡 𝑖 , 𝑖 = 1,2,3.The center figure in Fig. 3 represents the evolution of the physical variable (e.g. velocity and force), which can influence the degradation variable (top figure)and may also be influenced by random shocks (bottom figure).

Fig. 3 .

 3 Fig. 3. An example of degradation process𝐿 𝑚 with random shocks. Top Figure:degradation variable; Center Figure: physical variable; Bottom Figure: random shock process.

Fig. 6 .

 6 Fig.6. Simplified scheme of the pneumatic valve[START_REF] Daigle | A model-based prognostics approach applied to pneumatic valves[END_REF].

  from state 𝑖 directly to failure state 0.The formulation is taken fromYang, et al. (2011)By combining the degradation process of the pump with therandom shock process, the resultingprocesstakes the form shown in Fig. 7. The state of the process is represented by𝑌 𝑡 = 𝑌 𝑝 (𝑡), 𝑚 , 𝑚 ∈ ℕ, wherem is the number of shocks experiencedby the pump.The state space of the new process is denoted by 𝑺 = { 𝑎, 𝑏 , ∀𝑎 ∈ 𝑺 𝑝 , 𝑏 ∈ ℕ} andthe set of failure states of the pump is 𝓕 𝒑 ′ = { 0, 𝑏 , ∀𝑏 ∈ ℕ}.

Fig. 7 .

 7 Fig. 7. Degradation and random shock processes of the pump.

Fig. 8 .

 8 Fig. 8. An illustration of the degradation of the valveconsidering random shocks and the degradation state of the pump. Top Figure: degradation process of the valve; Center Figure: random shock processes; Bottom Figure: degradation process of the pump.

  . The first eight parameter values related to the degradation processes are taken fromLin, et al. (2014), the values of 𝜇 𝑤 , 𝜎 𝑤 and 𝐷 are taken from Peng, et al. (2010) and those of𝜇, 𝜇 and 𝜎 are assumed by expert judgment.Indeed, all parameter values are set upon the discussion with the experts from EDF.Indeed, all parameter values are set upon the discussion with the experts from EDF.

  Fig. 10. System reliability estimated by FV1, FV2 and FV3.

Fig

  Fig. 12. The reliability of the system, the valve and the pump with/without random shocks.

  𝜑 𝒊, 𝑡 , (𝑑𝑥, 𝒚 𝑖 ) = 𝑃 𝐷 𝑘+1 ∈ 𝑥, 𝑥 + 𝑑𝑥 | 𝑌 𝑘+1 = 𝒚 𝑗 , 𝑇 𝑘+1 -𝑇 𝑘 ∈ 𝑡, 𝑡 + 𝑑𝑡 , 𝒁 𝑘 = 𝒊 • 𝑃 𝑌 𝑘+1 = 𝒚 𝑗 | 𝑇 𝑘+1 -𝑇 𝑘 ∈ 𝑡, 𝑡 + 𝑑𝑡 , 𝒁 𝑘 = 𝒊 (29) where 𝑃 𝑌 𝑘+1 = 𝒚 𝑗 | 𝑇 𝑘+1 -𝑇 𝑘 ∈ 𝑡, 𝑡 + 𝑑𝑡 , 𝒁 𝑘 = 𝒊 = 𝑃 𝑌 𝑘+1 = 𝒚 𝑗 | 𝑌 𝑘 = 𝒚 𝑖 = 𝜆 𝒚 𝑖 ,𝒚 𝑗

  dynamic reliability to incorporate random changes of the degradation variables due to random shocks;[START_REF] Ye | A distribution-based systems reliability model under extreme shocks and natural degradation[END_REF]considered the destructive power of a shock depending not only on the shock magnitude but also on the state of the system;[START_REF] Wang | An approach to reliability assessment under degradation and shock process[END_REF]considered two types of the effects of shocks: a sudden increase in the failure rate after a shock and a direct random change in the degradation after the occurrence of a shock;[START_REF] Rafiee | Reliability modeling for dependent competing failure processes with changing degradation rate[END_REF]proposed reliability models for systems for whichthe degradation path has achanging degradation rate according to particular random shock patterns;Song, et al. (2014a)studied random shocks with specific sizes or functions,which can selectively affect the degradation processes of one or more components (not necessarily all components) in one system.For multi-state degradation processes,Yang, et al. (2011)combined random shocks with Markov degradation models where shocks can lead the systems to further degraded states;Lin, et al. (2015b)integrated random shocks into multi-state physics models of

processes (continuous or multi-state) and random shocks.For continuous degradation processes,

[START_REF] Peng | Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes[END_REF]

considered systems with one lineardegradation path where shocks can bring additional abrupt degradation damage if the shock loads donot exceed the maximum strength of the material;multi-component systems subject to multiple linear degradation paths have been further considered bySong, et al. (2014b); Jiang, et al. (2012)considered changes in themaximal strength of the material when systems are deteriorating under different situations;Becker, et al. (2002)extended the theory of degradation processeswhere the influences of shocks are dependent on the current degradation condition; Ruiz-Castro (2016)considered external shocks which could produce several effects; extreme failure, cumulative damage and when the damage reaches a threshold state, a non-repairable failure occurs, and changes in the internal performance of the device.Note that no work has considered systems with both continuous and multi-state degradation processes and subject to random shocks, and few studies have explicitly considered both the dependencies between degradation

. Degradation models 2.1.1. MSMs We

  follow the assumptions on MSMs made in Lin, et al. (2014):  A degradation process, 𝑌 𝐾 𝑛 𝑡 , 𝐾 𝑛 ∈ 𝑲of group (1), takes values from a finite state set denoted by 𝑺 𝐾 𝑛 = {0, 1, … , 𝑑}, where 𝑑 is the perfect functioning state and 0 is the complete failure state. The component is functioning or partially functioning in the intermediate degradation states. The transition rates 𝜆 𝑖 𝑗 | 𝜽 𝐾 𝑛 , ∀ 𝑖, 𝑗 ∈ 𝑺 𝐾 𝑛 , 𝑖 > 𝑗 characterize the degradation transition probabilities from state 𝑖 to state 𝑗 , where 𝜽 𝐾 𝑛 represents the environmental factors relevant to 𝐾 𝑛 and the related parameters of 𝜆 𝐾 𝑛 . We follow the assumption of Markov property made inGiorgio, et al. (2011),

	Each component may be affected by multiple
	degradation mechanisms or processes, possibly dependent. The degradation processes can be
	separated into two groups: (1)𝑲consists ofprocesses fit to be modeled by MSMs; (2) 𝑳consists
	ofprocesses fit to be modeled by PBMs.
	2.1

  process 𝑿 𝐿 𝑚 𝑡 , 𝐿 𝑚 ∈ 𝑳 of group (2), has 𝑑 𝐿 𝑚 time-dependent continuous variables, whose evolution is characterized by a system of first-order differential equations 𝑿 𝐿 𝑚 𝑡 = 𝒇 𝐿 𝑚 𝑿 𝐿 𝑚 𝑡 , 𝑡 𝜽 𝐿 𝑚 , i.e. physics equations, where 𝜽 𝐿 𝑚 represents the environmental factors influential to 𝐿 𝑚 (e.g. temperature and pressure) and the parameters used in 𝒇 𝐿 𝑚 .

  𝑿 𝐿 𝑀 𝑡 = 𝒇 𝐿 1 𝒀 𝑡 𝑿 𝑡 , 𝑡 𝜽 𝐿 1 , … , 𝒇 𝐿 𝑀 𝒀 𝑡 𝑿 𝑡 , 𝑡 𝜽 𝐿 𝑀

	= 𝒇 𝑳	𝒀 𝑡 𝑿 𝑡 , 𝑡 𝜽 𝑳 =	𝑀 𝑚 =1	𝜽 𝐿 𝑚

  𝑃 𝒁 𝑘+1 = 𝒋, 𝑇 𝑘+1 ∈ 𝑇 𝑘 , 𝑇 𝑘 + 𝑡 | 𝒁 𝑖 , 𝑇 𝑖 𝑖≤𝑘 = 𝑃 𝒁 𝑘+1 = 𝒋, 𝑇 𝑘+1 ∈ 𝑇 𝑘 , 𝑇 𝑘 + 𝑡 | 𝒁 𝑘 , 𝒁 𝑛 , 𝑇 𝑛 𝑛≥0 is characterized by the semi-Markov kernel 𝑁 𝒊 = (𝒙 𝑖 , 𝒚 𝑖 ), (𝑑𝒙, 𝒚 𝑗 ), 𝑑𝑡 = 𝑃 𝑿 𝑘+1 𝑇 𝑘+1 -𝑇 𝑘 ∈ 𝑡, 𝑡 + 𝑑𝑡 | 𝒁 𝑘 = 𝒊 , ∀𝑘 ∈ ℕ, 𝒚 𝑖 , 𝒚 𝑗 ∈ 𝑺 ′ , 𝒙 𝑖 , 𝑑𝒙 ∈ ℝ 𝑑 𝐿 , 𝑑𝒙 → 𝒁 𝑘 = 𝒊 and 𝑑𝐹 𝒊 𝑡 is the probability distribution of 𝑇 𝑘+1 -𝑇 𝑘 given 𝒁 𝑘 = 𝒊.𝑄 𝜑 𝒊, 𝑡 , (𝑑𝒙, 𝒚 𝑗 ) can be reformulated as follows:𝑄 𝜑 𝒊 = (𝒙 𝑖 , 𝒚 𝑖 ), 𝑡 , (𝑑𝒙, 𝒚 𝑗 ) 𝜆 𝒚 𝑖 ,𝒚 𝑗 (𝒙 | 𝜽 𝑲 )( 𝜓 𝒚 𝑗 , 𝑦 𝜇 𝒚 𝑖 , 𝒚 𝑗 , 𝒙 𝑑𝒚 -𝜓 𝒚 𝑖 , 𝒙 where 𝜆 𝒚 𝑖 ,𝒚 𝑗 (𝒙 | 𝜽 𝑲 ) is the transition rate of 𝒀 ′ 𝑡 from state 𝒚 𝑖 to 𝒚 𝑗 , 𝜓(•,•) is any continuously differentiable function from 𝑺 ′ × ℝ 𝑑 𝐿 to ℝ with a compact support and 𝜇 𝒚 𝑖 , 𝒚 𝑗 , 𝒙 𝑑𝒚 is the probability of 𝑿 ′ 𝑡 ∈ 𝒚, 𝒚 + 𝑑𝒚 after jumping from 𝒙 when 𝒀 ′ 𝑡 steps to state 𝒚 𝑗 from state 𝒚 𝑖 .

			= 𝑃 𝑿 𝑘+1 ′	∈ 𝒙, 𝒙 + 𝑑𝒙 , 𝒀 𝑘+1 ′	= 𝒚 𝑗 | 𝑇 𝑘+1 -𝑇 𝑘 ∈ 𝑡, 𝑡 + 𝑑𝑡 , 𝒁 𝑘 = 𝒊
			= 𝑃 𝑿 𝑘+1 ′	∈ 𝒙, 𝒙 + 𝑑𝒙 |𝒀 𝑘+1 ′	= 𝒚 𝑗 , 𝑇 𝑘+1 -𝑇 𝑘 ∈ 𝑡, 𝑡 + 𝑑𝑡 , 𝒁 𝑘 = 𝒊
								• 𝑃 𝒀 𝑘+1 ′	= 𝒚 𝑗 | 𝑇 𝑘+1 -𝑇 𝑘 ∈ 𝑡, 𝑡 + 𝑑𝑡 , 𝒁 𝑘 = 𝒊 (8)
	Let 𝑝 𝑡 (𝑑𝒛 = (𝑑𝒙, 𝒚 𝑖 )) denote the probability distribution of 𝒁 𝑡 , which obeys the Chapman-
	Kolmogorov equation (Davis, 1993) as follows:
	𝑡
	0	𝒚 𝑖 ∈𝑺 ′	ℝ 𝑑 𝐿	𝒚 𝑗 ∈𝑺 ′			ℝ 𝑑 𝐿	)𝑝 𝑠 (𝑑𝒙, 𝒚 𝑖 )𝑑𝑠	+
				0 𝑡	𝒚 𝑖 ∈𝑺 ′	ℝ 𝑑 𝐿	𝒇 𝑳	𝒚 𝑖 (𝒙|𝜽 𝑳 )𝑑𝑖𝑣 𝜓 𝒚 𝑖 , 𝒙 𝑝 𝑠 𝑑𝒙, 𝒚 𝑖 𝑑𝑠	-
						𝒚 𝑖 ∈𝑺 ′	∫ 𝜓 𝒚 𝑖 , 𝒙 ℝ 𝑑 𝐿	𝑝 𝑡 𝑑𝒙, 𝒚 𝑖 +	𝒚 𝑖 ′ ∈𝑺 ′	∫ 𝜓 𝒚 𝑖 , 𝒙 ℝ 𝑑 𝐿	𝑝 0 𝑑𝒙, 𝒚 𝑖 = 0(9)
								, 𝒀 ′ 𝑡
								= 𝒇 𝑳	𝒀 ∀𝑘 ∈ ℕ , 𝒋 ∈ 𝑬, 𝒋 ≠ 𝒁 𝑘	(6)
								′	∈
	𝒙, 𝒙 + 𝑑𝒙 , 𝒀 𝑘+1 ′ = 𝒚 𝑗 , 𝟎, 𝑑𝑡 → 0, which can be reformulated as follows:
							𝑁 𝒊 = (𝒙 𝑖 , 𝒚 𝑖 ), (𝑑𝒙, 𝒚 𝑗 ), 𝑑𝑡
			= 𝑃 𝑿 𝑘+1 ′	∈ 𝒙, 𝒙 + 𝑑𝒙 , 𝒀 𝑘+1 ′	= 𝒚 𝑗 | 𝑇 𝑘+1 -𝑇 𝑘 ∈ 𝑡, 𝑡 + 𝑑𝑡 , 𝒁 𝑘 = 𝒊
						• 𝑃 𝑇 𝑘+1 -𝑇 𝑘 ∈ 𝑡, 𝑡 + 𝑑𝑡 | 𝒁 𝑘 = 𝒊

′ 𝑡 (𝑿 𝑡 |𝜽 𝑳 ), (𝟎, 0) , 𝑓𝑜𝑟 𝑡 ∈ 𝑇 𝑘 , 𝑇 𝑘+1

(5)

According to the definition inCocozza-Thivent (2011), 𝒁 𝑡 is a PDMP since (1)it can be written as 𝒁 𝑡 = 𝜑 𝒁 𝑘 , 𝑡 -𝑇 𝑘 , 𝑓𝑜𝑟 𝑡 ∈ 𝑇 𝑘 , 𝑇 𝑘+1 and 𝜑 satisfies 𝜑 𝒚, 𝑡 + 𝑠 = 𝜑 𝜑 𝒚, 𝑡 , 𝑠 , ∀𝑡, 𝑠 ≥ 0, 𝒚 ∈ 𝑬, and 𝑡 → 𝜑 𝒚, 𝑡 , ∀𝑡 ≥ 0, 𝒚 ∈ 𝑬 is right continuous with left limits and (2) 𝒁 𝑛 , 𝑇 𝑛 𝑛≥0 is a Markov renewal process defined on the space𝑬 × ℝ + .The probability that 𝒁 𝑡 will step to state 𝒋from state𝒁 𝑘 in the time interval 𝑇 𝑘 , 𝑇 𝑘 + 𝑡 , given 𝒁 𝑖 , 𝑇 𝑖 𝑖≤𝑘 is as follows:

= 𝑄 𝜑 𝒊, 𝑡 , (𝑑𝒙, 𝒚 𝑗 ) 𝑑𝐹 𝒊 𝑡

(7)

where 𝑄 𝜑 𝒊, 𝑡 , (𝑑𝒙, 𝒚 𝑗 ) is the probability distribution of state 𝒁 𝑘+1 given 𝑇 𝑘+1 -𝑇 𝑘 = 𝑡 and

Table IIQuantitative

 IIQuantitative

	Method	MC3		FV3	Relative
	Time						error
	100s		0.9611	0.9607	0.0438%
	200s		0.9021	0.9011	0.1162%
	300s		0.8230	0.8205	0.3027%
	400s		0.7285	0.7263	0.2974%
	500s		0.6284	0.6271	0.2109%
	600s		0.5312	0.5300	0.2394%
	700s	1	0.4395	0.4397	0.0365%
	0.9 800s	0.3576	0.3591	FV3 FV2 0.4157%
	0.8 900s	0.2467	0.2459	FV1 0.3204%
	0.7 1000s	0.0335	0.0332	0.8955%
	Reliability	0.4 0.5 0.6
		0.3
		0.2
		0.1
			0 0	200	400	600	800	1000
					Time (s)
	Fig. 11. Comparison of the results obtained by MC3 and FV3.
				comparison of the results obtained by MC3 and FV3

Table IIIComparison

 IIIComparison

		1
		0.9
		0.8
		0.7
	Reliability	0.4 0.5 0.6
		0.3
		0.2
		0.1
		0 0	200	400	600	800	1000
				Time (s)
			of reliabilitywith/without random shocks at 1000 s
	Reliability without		Reliability with	Relative change
	random shocks		random shocks
	System	0.18			0.033		81.67%
	Valve	0.50			0.099		80.20%
	Pump	0.43			0.32		25.58%
	The uncertainties associated with the parameter estimates can influence the estimation of system
	reliability. The actual effect depends on the types and degrees of uncertainties, which are problem

specific. Following one assumption of our work (i.e. limited historical data), epistemic uncertainty can arise due to the incomplete or imprecise knowledge about the degradation processes and the governing parameters of the pump and the valve, which has been considered in

Lin, et al. (2015a)by



  The transition rates 𝜆 𝒚 𝑖 ,𝒚 𝑗 (• | 𝜽 𝑲 ), ∀𝒚 𝑖 , 𝒚 𝑗 ∈ 𝑺 ′ are continuous and bounded functions from ℝ 𝑑 𝐿 to ℝ + .  The physics equations𝒇 𝑳 𝒚 𝑖 • 𝜽 𝑳 , ∀𝒚 𝑗 ∈ 𝑺 ′ are continuous functions from ℝ 𝑑 𝐿 to ℝ 𝑑 𝐿 and locally Lipschitz continuous.  The physics equations𝒇 𝑳 𝒚 𝑖 • 𝜽 𝑳 , ∀𝒚 𝑖 ∈ 𝑺 ′ are sub-linear, i.e. there are some 𝑉 1 > 0 and 𝑉 2 > 0 such that ∀𝒙 ∈ ℝ 𝑑 𝐿 , 𝑡 ∈ ℝ + 𝒇 𝑳 𝒚 𝑖 𝒙 𝜽 𝑳 ≤ 𝑉 1 𝒙 + 𝑉 2  The functions 𝑑𝑖𝑣(𝒇 𝑳 𝒚 𝑖 • 𝜽 𝑳 ), ∀𝒚 𝑖 ∈ 𝑺 ′ are almost everywhere bounded in absolute value by some real value 𝐷 > 0 (independent of 𝒚 𝑖 ).  If 𝜙(•) is a continuous and bounded function from ℝ 𝑑 𝐿 to ℝ , then, 𝒙 → ∫ 𝜙(𝑦 )𝜇 𝒚 𝑖 , 𝒚 𝑗 , 𝒙 𝑑𝒚 is continuous from ℝ 𝑑 𝐿 to ℝ.

  𝑖

  •, • | 𝜽 𝑳 : ℝ 𝑑 𝐿 × ℝ → ℝ 𝑑 𝐿 denote the solution of 𝜕 𝜕𝑡 𝒈 𝒚 𝑖 𝒙, 𝑡 | 𝜽 𝑳 = 𝒇 𝑳 𝒚 𝑖 (𝒈 𝒚 𝑖 𝒙, 𝑡 | 𝜽 𝑳 | 𝜽 𝑳 , ∀𝒚 𝑖 ∈ 𝑺 ′ , 𝒙 ∈ ℝ 𝑑 𝐿 , 𝑡 ∈ ℝ

  The numerical scheme aims at constructing an approximate value 𝜌 𝑡 𝒙,• 𝑑𝒙 for 𝑝 𝑡 𝑑𝒙,• , such that 𝜌 𝑡 𝒙,• is constant on each [𝑛∆𝑡, (𝑛 + 1)∆𝑡[× 𝐴 × {𝒚 𝑖 }, ∀𝐴 ∈ ℳ, 𝒚 𝑖 ∈ 𝑺 ′ : 𝑃 𝑛+1 𝐴, 𝒚 𝑖 can be calculated considering the deterministic evaluation of 𝑿 𝑡 and the stochastic evolution of 𝒀 ′ 𝑡 based on 𝑃 𝑛 ℳ, 𝒚 𝑖 by the Chapman-Kolmogorov forward equation, as 𝒚 𝑖 = ∫ 𝜆 𝒚 𝑗 ,𝒚 𝑖 (𝒙 | 𝜽 𝑲 ) ∫ 𝜇 𝒚 𝑗 , 𝒚 𝑖 , 𝒙 𝑑𝒚 𝒙 is the average transition rate from state 𝒚 𝑗 and grid 𝐵 to state 𝒚 𝑖 and grid 𝐴, 𝑏 𝐴 𝒚 𝑖 = ∫ 𝜆 𝒚 𝑖 ,𝒚 𝑗 (𝒙 | 𝜽 𝑲 )𝑑𝒙 𝑛 𝐵, 𝒚 𝑖 /𝑚 𝐴 (26) is the approximate value of probability density function on [(𝑛 + 1)∆𝑡, (𝑛 + 2)∆𝑡[× 𝐴 × 𝒚 𝑖 according to the deterministic evolution of 𝑿 𝑡 , 𝑚 𝐵𝐴 𝒚 𝑖 = ∫ 𝑑𝒚 {𝒚∈𝐵 |𝒈 𝒚 𝑖 𝒚,∆𝑡 | 𝜽 𝑳 ∈𝐴}

	𝑛=0,1,2,… 𝜌 𝑡 𝒙, 𝒚 𝑖 = 𝑃 𝑛 𝐴, 𝒚 𝑖 , ∀𝒚 𝑖 ∈ 𝑺 ′ , 𝒙 ∈ 𝐴, 𝑡 ∈ [𝑛∆𝑡, (𝑛 + 1)∆𝑡[ setting the time step ∆𝑡 > 0 (the length of each interval). 𝑃 0 𝐴, 𝒚 𝑖 , ∀𝒚 𝑖 ∈ 𝑺 ′ , 𝐴 ∈ ℳ is defined as follows: 𝑃 0 𝐴, 𝒚 𝑖 = ∫ 𝑝 0 𝑑𝒙, 𝒚 𝑖 𝐴 /𝑚 𝐴 𝑃 𝑛+1 𝐴, 𝒚 𝑖 = 1 1+∆𝑡𝑏 𝐴 𝒚 𝑖 𝑃 𝑛+1 𝐴, 𝒚 𝑖 + ∆𝑡 𝑎 𝐵 ,𝐴 𝒚 𝑗 ,𝒚 𝑖 1+∆𝑡𝑏 𝐴 𝒚 𝑗 𝑃 𝑛+1 𝐵, 𝒚 𝑗 𝒚 𝑗 ∈𝑺 ′ 𝐵∈ℳ where 𝑎 𝐵,𝐴 𝒚 𝑗 ,𝐵 𝐴 𝑚 𝐴 𝒚 𝑗 ∈𝑺 ′ 𝐴 /𝑚 𝐴 is the average transition rate out of state 𝒚 𝑖 for grid 𝐴, Then, follows: 𝑃 𝑛+1 𝐴, 𝒚 𝑖 = 𝑚 𝐵𝐴 𝒚 𝑖 𝐵∈ℳ	by (21) (22) (23) (24) (25)

𝑃

  𝜆 𝒚 𝑖 ,𝒚 𝑗 is the transition rate of 𝑌(𝑡) from state 𝒚 𝑖 to state 𝒚 𝑗 , and 𝜇 𝒚 𝑖 , 𝒚 𝑗 , 𝑥 𝑑𝑦 = 𝑖𝑓 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝒚 𝑖 𝑡𝑜 𝒚 𝑗 𝑖𝑠 𝑑𝑢𝑒 𝑡𝑜 𝑟𝑎𝑛𝑑𝑜𝑚 𝑠𝑜𝑐𝑘 𝑎𝑛𝑑 𝑦 < 𝐷 𝑏 * 𝒚 𝑖 𝑡𝑜 𝒚 𝑗 𝑖𝑠 𝑑𝑢𝑒 𝑡𝑜 𝑟𝑎𝑛𝑑𝑜𝑚 𝑠𝑜𝑐𝑘 𝑎𝑛𝑑 𝑦 ≥ 𝐷 𝑏 * 𝛿 𝑥 𝑑𝑦 , 𝑖𝑓 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝒚 𝑖 𝑡𝑜 𝒚 𝑗 𝑖𝑠 𝑑𝑢𝑒 𝑡𝑜 𝑑𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛 𝑃 0 𝑚, 𝒚 𝑖 is defined as follows: 𝑑𝑥, 𝒚 𝑖 = 𝛿 0 𝑑𝑥 • 𝟏 {𝒚 𝑖 =(3,0)} . Then, 𝑃 𝑛+1 𝑚, 𝒚 𝑖 , 𝑛 ∈ ℕ can be calculated considering the deterministic evolution of 𝐷 𝑡 and the stochastic evolution of 𝑌 𝑡 based on 𝑃 𝑛 ⋅, ⋅ by the Chapman-Kolmogorov forward equation, as follows: 𝑎 𝑚 ′ ,𝑚 𝒚 𝑗 ,𝒚 𝑖 = 𝜆 𝒚 𝑗 ,𝒚 𝑖 ∫ ∫ 𝜇 𝒚 𝑗 , 𝒚 𝑖 , 𝑥 𝑑𝑦 𝑑𝑥 is the average transition rate from state 𝒚 𝑗 and grid [𝑚 ′ ∆𝑥, (𝑚 ′ + 1)∆𝑥[ to state 𝒚 𝑖 and grid is the approximate value of probability density function on [𝑚∆𝑥, (𝑚 + 1)∆𝑥[× 𝒚 𝑖 according to the deterministic evolution of 𝐷 𝑡 between jumps of 𝑌 𝑡 and [𝑚 ′ ∆𝑥,(𝑚 ′ +1)∆𝑥[ |(𝜑 1 (𝑥,𝒚 𝑖 ),∆𝑡 ∈[𝑚 ∆𝑥,(𝑚+1)∆𝑥[} (39) is the volume of the part of grid [𝑚 ′ ∆𝑥, (𝑚 ′ + 1)∆𝑥[ which will enter grid [𝑚∆𝑥, (𝑚 + 1)∆𝑥[ after time ∆𝑡 according to the deterministic evaluation of 𝐷 𝑡 .

	𝜆 𝒚 𝑖 ))𝑑𝑦 𝑖𝑓 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 (34) (30) 𝐷 -𝜇 𝑤 𝜎 𝑤 ) • 1 𝜎 𝜙( 𝑦 -𝑥 -𝜇 𝜎 ))𝑑𝑦, (1 -Φ( 𝐷 -𝜇 𝑤 𝜎 𝑤 )) • 𝛿 𝑥+𝐷 𝑏 * 𝑑𝑦 + Φ( 𝐷 -𝜇 𝑤 𝜎 𝑤 ) • 1 𝜎 𝜙( 𝑦 -𝑥 -𝜇 𝜎 𝑃 0 𝑚, 𝒚 𝑖 = ∫ 𝑝 0 𝑑𝑥, 𝒚 𝑖 (𝑚 +1)∆𝑥 𝑚 ∆𝑥 /∆𝑥 (35) where 𝑝 0 𝑃 𝑛+1 𝑚, 𝒚 𝑖 = 1 1+∆𝑡𝜆 𝒚 𝑖 𝑃 𝑛+1 𝑚, 𝒚 𝑖 + ∆𝑡 𝑎 𝑚 ′ ,𝑚 𝒚 𝑗 ,𝒚 𝑖 1+∆𝑡𝜆 𝒚 𝑗 𝑃 𝑛+1 𝑚 ′ , 𝒚 𝑗 𝒚 𝑗 ∈𝑺 𝑚 ′ ∈ℕ (36) where (𝑚 +1)∆𝑥 𝑚 ∆𝑥 (𝑚 ′ +1)∆𝑥 𝑚 ′ ∆𝑥 ∆𝑥 (37) [𝑚∆𝑥, (𝑚 + 1)∆𝑥[, 𝑃 𝑛+1 𝑚, 𝒚 𝑖 = 𝑣 𝑚 ′ ,𝑚 𝒚 𝑖 𝑚 ′ ∈ℕ 𝑃 𝑛 𝑚 ′ , 𝒚 𝑖 /∆𝑥 (38) where Φ( 𝑣 𝑚 ′ ,𝑚 𝒚 𝑖 = ∫ 𝑑𝑥

{𝑥∈

Acknowledgement

The authors would like to thank Mrs. Dominique VASSEUR,Mr. Antoine DESPUJOLS and Mr.

Emmanuel ARDILLON from the Department Industrial Risks Management (MRI), Electricité de France R&D for their insightful comments. The authors would like to acknowledge the financial support fromthe Electricité de France (Contract No.8610-5910112096) and the GRF project of city university of Hong Kong (GRF project No. 9042183).

describing the degradation model parameters as intervals (or fuzzy numbers). In the revised manuscript, we follow the settings in Lin, et al. (2015a) where a relative deviation of ±10% to the original parameters values has been considered for 𝜆 32 , 𝜆 21 , 𝜆 10 , 𝜔 𝑏 , 𝛽(3), 𝛽(2), 𝛽(1) and𝛽(0) upon the discussionswith the domain experts from EDF. The lower and upper bounds of system reliability under uncertainty, and the original values without uncertainty obtained by MC3 are shown in Fig. 13. The lower bound of system reliability with uncertainty decreases more sharply after around 790 s, earlier than that without uncertainty. It is seen that the system fails after around 964 s, because at that time the valve is completely failed. The upper bound of system reliability with uncertainty does not experience a rapid decrease because the valve is mostly functioning over the time horizon.

CONCLUSIONS

In this paper, we presentedreliability models for systems experiencing both degradation processes and random shocks. The degradation processes involve both continuous and multi-state processes, which are modeled by MSMs and PBMs, respectively.The dependencies between degradation processes and random shocks and among degradation processes are addressed by PDMP modeling.

The procedures of the MC simulation and FV methods to solve the model are developed.A subsystem of a RHRS in a nuclear power plant, which consists of a pneumatic valve and a centrifugal pump, is considered as the illustrative exampleto demonstrate the effectiveness and modeling capabilities of the proposed framework.As original contribution and differently from our previous work (Lin, et al., 2015a), this work is first in considering system reliability under both continuous and multi-state degradation processes, random shocks and their dependencies.

As future work, we will include maintenance in the model and derive optimal maintenance policies under the conditions considered.

Assumptions

The FV method for determining the approximated solution of the system reliability can be developed under the following assumptions [START_REF] Cocozza-Thivent | A finite-volume scheme for dynamic reliability models[END_REF] (31) where 𝐻(𝑇 𝑘 + 𝑡) is the instantaneous random increase caused by shock at time 𝑇 𝑘 + 𝑡, 𝛿 is the Dirac delta function and

where Φ(•) and 𝜙(•) are the cumulative distribution function and the probability density function of a folded normal distribution related to the standard normal distribution, respectively. Here, since an extreme shock can directly lead the valve to failure, we assume each extreme shock increase the total external leak size by 𝐷 𝑏 * to formulate the problem within the settings of PDMP. Note that this assumption will not change the reliability of the valve.

Appendix C: Application of FV method in case study

The probability distribution of 𝒁 𝑡 ,𝑝 𝑡 (𝑑𝑥, 𝒚 𝑖 ), obeys the Chapman-Kolmogorov equation [START_REF] Davis | Markov Models & Optimization[END_REF]


Ping Wang
email: ping.wang@utu.fi

Understanding the Influence of Electronic Word-of-Mouth on Outbound Tourists' Visit Intention

Keywords: electronic word-of-mouth (eWOM), travel decision, online travel information, visit decision, elaboration likelihood model, theory of planned behavior 1

The valence of online user-generated reviews is an increasing important antecedents affecting tourist's decision with the pervasion of Web 2.0 and information and communication technology. The purpose of this study is to explore the influence of electronic word-of-mouth (eWOM) on outbound tourists' intention to visit a destination through a dual-process perspective. A research model was proposed based on the dual-route theory of elaboration likelihood model (ELM) and theory of planned behavior (TPB). The research model was empirically tested with the data collected among the Chinese outbound tourists. The research results indicate that, tourist's attitude towards a destination was positively influenced by argument quality of eWOM, and intention to recommend the destination before travel was positively influenced by attitude towards destination and source credibility of destination related eWOM. Outbound tourists' intention to visit a destination was positively influenced by argument quality, attitude towards destination, and WOM intention. Several practical and theoretical implications are also discussed in the paper.

Introduction

With the advancement of information and communication technology (ICT) and advent of Web 2.0 in recent years, tourists are enabled to communicate virtually and share travel experience, reviews online [START_REF] Kim | Factors Affecting Online Tourism Group Buying and the Moderating Role of Loyalty[END_REF]. Increasing amounts of user-generatedcontent (UGC) were spawned in the form of online travel experience or online reviews that pertain to personal experience with particular service or products which is also described as electronic word-of-mouth (eWOM) [START_REF] Bronner | Vacationers and eWOM: Who Posts, and Why, Where, and What[END_REF]. EWOM are available to a multitude of people via Internet and Web 2.0 platforms, which is likely to generate persuasive effects on target audiences, such as potential customers [START_REF] Shih | Informational and Relational Influences on Electronic Word of Mouth: An Empirical Study of an Online Consumer Discussion Forum[END_REF]. As an information-intensive industry, tourism was deeply influenced by eWOM [START_REF] Filieri | E-WOM and Accommodation: An Analysis of the Factors That Influence Travelers' Adoption of Information from Online Reviews[END_REF][START_REF] Kozak | Holiday taking decisions -The role of spouses[END_REF][START_REF] Jalilvand | The impact of electronic word of mouth on a tourism destination choice Testing the theory of planned behavior (TPB)[END_REF][START_REF] Li | Post adoption behaviour of e-service users: an empirical study on Chinese online travel service users[END_REF] . Electronic word-of-mouth have facilitated travel information searching behavior, and influenced tourists' travel planning behavior [START_REF] Cox | The role of usergenerated content in tourists' travel planning behavior[END_REF][START_REF] Li | Understanding post-adoption behaviors of e-service users in the context of online travel services[END_REF]. Tourists nowadays are increas-ingly using eWOM to inform themselves about travel-related services and products, for travel planning and travel related purchasing [START_REF] Tham | Social Media in Destination Choice: Distinctive Electronic Word-of-Mouth Dimensions[END_REF][START_REF] Standing | The Impact of the Internet in Travel and Tourism: A Research Review 2001-2010[END_REF][START_REF] Amaro | Online Travel Purchasing: A Literature Review[END_REF].

As eWOM has strongly affected tourism industry especially in tourist's decision making process, a considerable amount of literature has been focused on eWOM in tourism [START_REF] Cantallops | New consumer behavior: A review of research on eWOM and hotels[END_REF][START_REF] Litvin | Electronic word-of-mouth in hospitality and tourism management[END_REF][START_REF] Gretzel | Do Negative Experiences Always Lead to Dissatisfaction? -Testing Attribution Theory in the Context of Online Travel Reviews[END_REF][START_REF] Jeong | Restaurant experiences triggering positive electronic word-of-mouth (eWOM) motivations[END_REF]. These studies mainly focused on two streams: one stream focused on exploring the factors influencing eWOM generating motivation [START_REF] Bronner | Vacationers and eWOM: Who Posts, and Why, Where, and What[END_REF][START_REF] Li | Understanding post-adoption behaviors of e-service users in the context of online travel services[END_REF][START_REF] Munar | Motivations for sharing tourism experiences through social media[END_REF], while the other stream concentrated on the impacts of eWOM on target behavior [START_REF] Cheung | The impact of electronic word-of-mouth -The adoption of online opinions in online customer communities[END_REF][START_REF] Verhagen | Negative online word-of-mouth: Behavioral indicator or emotional release?[END_REF]. Notwithstanding, our understanding about how eWOM influence tourists' visit intention is still scant. What is the most effective information influencing tourists' attitude towards destination, and furthermore their visit intention, and how? Thus, researches aiming at solving this puzzle are needed.

A structural model based on well-tested theories was proposed in this research to explore the influence process of eWOM on outbound tourists' intention to visit a destination. Empirical data was collected among Chinese outbound tourists via structural questionnaire survey. This study contributes to the understanding of how destination related electronic word-of-mouth impact outbound tourists' leisure travel destination decision-making with empirical evidence. Furthermore, the influence route before initial attitude formation toward a destination is also explored.

The remainder of this article is structured as follows: In section 2, theory of elaboration likelihood is introduced, and incorporated to the theory of planned behavior holding that behaviours are influenced by intentions, intentions by attitudes [START_REF] Ajzen | The theory of planned behavior[END_REF][START_REF] Ajzen | Nature and operation of attitudes[END_REF]. Nine hypotheses are proposed. Research method is delineated in section 3, including data collection, descriptive analysis of the sample characters, and measurement model. In section four, structural equation model is used to analyse data with AMOS22.0. In section five, we give implications for both academic and practice. At the end of the paper in section six, limitations of current research and future research suggestions were discussed.

2

Research model and hypotheses

Elaboration likelihood model

Elaboration likelihood model (ELM) originates from social and consumer psychology, which suggests that attitude changes in two distinct routes: central route and peripheral cue [START_REF] Petty | Central and peripheral routes to advertising effectiveness: The moderating role of involvement[END_REF]. The basic idea of ELM suggests that the way individuals are persuaded varies according to the extent to which they are willing to engage in elaboration of the persuasive issue. In the central route, individuals think more critically about issuerelated arguments in an informational message and scrutinize the both pros and cons as related to those arguments prior to forming their target behavior [START_REF] Bhattacherjee | Influence processes for information technology acceptance: An elaboration likelihood model[END_REF]. In contrast, in peripheral route to attitude change, a relatively less cognitive effort is needed. A person may simply rely on cues related to target behavior, like prior users, prior related personal experience, and credibility. The central route is message-related argument oriented, while the peripheral route is process cues-oriented. 'Elaboration' is defined as 'the extent to which the individuals engage in information contained in the communication, and mentally modify or process the issue' [START_REF] Priester | The influence of spokesperson trustworthiness on message elaboration, attitude strength, and advertising effectiveness[END_REF].

The term 'likelihood' illustrates whether elaboration is likely or unlikely [START_REF] Priester | The influence of spokesperson trustworthiness on message elaboration, attitude strength, and advertising effectiveness[END_REF], and is used to describe individuals would add something of their own to a given information in a concrete communication [START_REF] Petty | Central and peripheral routes to advertising effectiveness: The moderating role of involvement[END_REF][START_REF] Bhattacherjee | Influence processes for information technology acceptance: An elaboration likelihood model[END_REF]. In the context of current study, people in high likelihood of having an outbound travel are more likely to be persuaded by potential destination related electronic word-of-mouth through a central route, what's more, they think more critically about the destination related-message of eWOM. On the contrary, people in a low likelihood would refer to peripheral cues, such as the credibility of the information source. It is suggested that individuals' degree of elaboration forms a spectrum of message-related thinking, which could vary from little to high extent. What's more, the attitude change may happen at any extent of elaboration [START_REF] Bhattacherjee | Influence processes for information technology acceptance: An elaboration likelihood model[END_REF], that is, both central route and peripheral route can lead to attitude change, as shown in Figure 1. In the context of tourism of this study, source credibility refers to the credibility of website or online community in which eWOM of travel destination is disseminated. Argument quality refers to the quality of content/message contained in the travel destination-related eWOM. Source credibility and argument quality of social media material are empirically tested to be related with attitude formation in the context such as outbound studying destination choice [START_REF] Shu | Influence of Social Media on Chinese Students' Choice of An Overseas Study Destination: An Information Adoption Model Perspective[END_REF] and adoption of accommodation related online review [START_REF] Filieri | E-WOM and Accommodation: An Analysis of the Factors That Influence Travelers' Adoption of Information from Online Reviews[END_REF]. Thus, we propose that argument quality and source credibility of destination-related eWOM have positive influence on tourists' attitude towards the destination. Hypotheses 1 and 2 are:

H1: Argument quality of destination-related eWOM will positively influence tourists' attitude towards leisure travel destination.

H2: Source credibility of destination-related eWOM will positively influence tourists' attitude towards leisure travel destination.

Incorporating behavior intention to ELM

Intentions to perform different kinds of behaviors can be predicted from attitude towards the behavior in one of the most researched and reputational psychological theory-theory of planned behavior [START_REF] Ajzen | The theory of planned behavior[END_REF]. Several prior studies applied theory of planned behavior to explore the relationship between tourists' attitude and behavior intention [START_REF] Lam | Predicting behavioral intention of choosing a travel destination[END_REF][START_REF] Hsu | An Extension of the Theory of Planned Behavior Model for Tourists[END_REF][START_REF] Song | Behavioral intention of visitors to an Oriental medicine festival: An extended model of goal directed behavior[END_REF]. [START_REF] Ajzen | The theory of planned behavior[END_REF] also assumes that a person's likelihood behavior can be dictated to his/her available resources. Therefore, we incorporate intention into the elaboration likelihood model. Concretely, the tourists' behavior intention in our study is discussed with the terms of intention to visit a destination and WOM intention. Wordof-Mouth intention refers to tourist intention to recommend a destination to others according to their knowledge gained from destination-related eWOM before their own travel. Argument quality describes the persuasive strength embedded in the eWOM related to a leisure travel destination. The dependent variables of intention imitated from the theory of planned behavior (TPB) are intention to visit an outbound leisure travel destination, and the intention to recommend the destination (WOM intention). Prior research has focused on predicting WOM adoption from information receiver's perspective [START_REF] Cheung | Credibility of Electronic Word-of-Mouth: Informational and Normative Determinants of On-line Consumer Recommendations[END_REF][START_REF] Jin | Following Celebrities' Tweets About Brands: The Impact of Twitter-Based Electronic Word-of-Mouth on Consumers' Source Credibility Perception, Buying Intention, and Social Identification With Celebrities[END_REF][START_REF] Fang | Beyond the Credibility of Electronic Word of Mouth: Exploring eWOM Adoption on Social Networking Sites from Affective and Curiosity Perspectives[END_REF], few researches focused on exploring WOM intention from information sender's perspective [START_REF] Shih | Informational and Relational Influences on Electronic Word of Mouth: An Empirical Study of an Online Consumer Discussion Forum[END_REF]. Thus, our research will address the intention to distribute WOM through information sender's perspective based on ELM. Hypotheses 3 to 6 are proposed based on the combination of elaboration likelihood model and theory of planned behavior.

H3: The argument quality of eWOM regarding travel destination will positively influence potential tourist's visit intention.

H4: The argument quality of eWOM regarding travel destination will positively influence potential tourist's WOM intention before actual travel behavior.

H5: The source credibility of eWOM regarding travel destination will positively influence potential tourist's WOM intention before actual travel behavior.

H6: The source credibility of eWOM regarding travel destination will positively influence potential tourist's visit intention.

After information searching behavior, an initial destination image will come into formation in the mind of potential tourists [START_REF] Fodness | Tourist information search[END_REF]. We also propose that positive attitude will lead to word-of-mouth before practical travel experience, and strengthen visit intention.

H7: Tourist's attitude towards destination will positively influence visit intention. H8: Tourist's attitude towards destination will positively influence WOM intention. H9: Tourist's WOM intention will positively influence visit intention. Prior to our formal survey in China, pilot studies for both English and Chinese versions of questionnaire have been done during May 5th to 15th 2014. Some Englishspeaking experts and professionals in tourism were interviewed, including academic researchers in University of Turku and the Finnish Tourist Board, to test the logistics, validity, and construct of the questionnaire. The questionnaire was then translated into Chinese after that, and proofread by some bilinguals capable of Chinese and English to ensure the consistence of our questionnaire. The pilot survey of Chinese questionnaire was done among 15 Chinese people to make sure the language and logic of questionnaire in Chinese. The final version was achieved after all the interviews, pilot survey and discussion with experts. Our data were collected through online survey due to its advantage of faster, cheaper, and easier use for both participants and researchers compared to off-line survey. As our target group is those who are interested in Finland and most potential tourists to Finland in the near future, questionnaire was distributed through the official account of VisitFinland on Wechat and Weibo-two of the most popular social media in China. In this way, potential respondents will mostly be the followers of Visit-Finland. As being the followers of official account of Finnish Tourist Board Weibo and Wechat, it's true that they already paid attention to Finland as a travel destination. 959 responses were collected in two weeks after our questionnaire distribution. For our study in this paper, only respondents who have never travelled to Finland, and were influenced by online travel experience or reviews during their destination decision process, were included. Our final samples for analysis consist of 195 respondents.

Sample characteristics

The demographic profile of our sample is presented in Table 1. More than 80% are between the age of 20 and 40 years old, and nearly a half of them are singles. Most (89.7%) of them received relatively high education from university with a bachelor degree or above. 79% of them have a monthly income of more than 5,000 Yuan, and more than 40 % of them earn more than 10,000 Yuan per mouth, which confirmed their likelihood of taking an outbound travel in recent three years. In addition, nearly 87% of the respondents have outbound travel experience in recent three years, and 60% of them have travelled abroad for at least three times in recent three years.

Measurement

Five factors were included in our model: argument quality, source credibility, attitude towards destination, WOM intention, and visit intention. Each construct was measured with multiple items adapted from previous literatures to validate content. Necessary modifications have been done according to our current research context.

Data analysis and results

The data were analysed using structural equation model with SPSS Amos 22.0. First, the reliability and validity of the scales used in our measurement model were tested. Model fit was also examined.

4.1

Reliability and validity

The validation of our measurement model was investigated in both convergent validity and discriminant validity. We investigated convergent validity by computing all factor loadings, composite reliabilities, Cronbach's Alpha and the average variance extracted (AVE). As shown in Table 3, all the factor loadings exceeded the recommended value of 0.70, composite reliabilities exceeded 0.8, and all AVEs exceeded 0.5, which shows a good convergent validity was achieved [START_REF] Fornell | Structural equation models with unobservable variables and measurement error: Algebra and statistics[END_REF]. All Cronbach's Alpha values are higher than 0.7, which implies good reliability [START_REF] Nunnally | Psychometric theory[END_REF]. In addition, we compared the square root of the AVE and factor correlation coefficients to examine the discriminant validity of our constructs. As shown in Table 4 below, all factors' latent variable correlations with other factors are smaller than the square root of its AVEs, which shows a good discriminant validity of our scales [START_REF] Fornell | Structural equation models with unobservable variables and measurement error: Algebra and statistics[END_REF][START_REF] Haas | Changes in the Use of Postmenopausal Hormone Therapy after the Publication of Clinical Trial Results[END_REF].

Hypotheses Testing

Before exploring the path coefficient, the goodness of model fit was tested in AMOS.

The results of model fit were shown in Table 5. According to the rules of thumb, the values of GFI, NFI,CFI all proved a satisfactory structural model fit to the data [START_REF] Gefen | Structural equation modeling and regression: Guidelines for research practice[END_REF]. Figure 3 graphically presents our path coefficient results and variance explained. Six out of nine hypotheses were supported in our results (see Table 6). The results indicate that: tourist's attitude towards destination was positively influenced by argument quality (β=0.173, p<0.01); word-of-mouth intention was positively influenced by attitude (β=0.720, p<0.001) and source credibility (β=0.104, p<0.01); visit intention was positively influenced by argument quality (β=0.192, p<0.01), attitude towards destination (β=0.149, p<0.05), and WOM intention(β=0.620, p<0.001). It is estimated that predictors in our model of visit intention can explain 58.5 percent of its variance, 52.7 percent of WOM intention, and 3.5 percent of attitude.

Main results

The results of this study demonstrate a combination of dual process attitude change theory-elaboration likelihood model-with the theory of planned behavior. The empirical results indicate that tourist's attitude towards travel destination is positively influenced by argument quality rather than source credibility of eWOM. However, argument quality of eWOM will only influence tourists' own attitude and visit intention, but not their recommendation behavior. Additionally, it's not argument quality but source credibility of eWOM that would lead to tourist's recommendation intention even before their own travel experience. Contrarily, tourist's visit intention is influenced by eWOM through a central route of argument quality, but the influence of source credibility is not significant as implicated by our empirical results. Consistent with prior research results, visit intention and recommendation intention were positively influenced by attitude [START_REF] Wang | Understanding accommodation managers' crisis planning intention: An application of the theory of planned behaviour[END_REF].

Practical implications

This research contributed to tourism industry for giving implications on better understanding tourists' decision making behavior. As an information intensive industry, nowadays increasing amount of new information and communication technology (ICT) has been penetrating into nearly every tourism sector [START_REF] Zelenka | Information and Communication Technologies in Tourism -Influence, Dynamics[END_REF]. As to tourism stakeholders, especially for destination marketers, this study makes great value in their understanding of what types of information positively motivate potential tourist attitude towards destination, and finally visit intention. Our empirical findings also indicated that during tourist's destination decision making process, argument quality of online information sources is highly valued for the formation of positive initial image and attitude towards travel destination. It means that, in tourist's destination decision making process, tourist will think critically about destination-related arguments and scrutinize the relative merits and relevance of those arguments prior to forming a positive attitude to travel destination, and further visit intention. In this case, eWOM will influence tourist's destination decision through a central route.

However, tourist's recommendation behavior was influenced by source credibility and attitude towards destination rather than argument quality. It implies that individuals' recommendation behavior is determined more by the credibility of the source they obtained, but requires less scrutinize of the information and content contained in the eWOM itself. Thus, eWOM will influence tourist's recommendation behavior through a peripheral route, which is cues-oriented.

Theoretical implications

This research also has theoretical implications in IS user behavior research. As illustrated, our research model synthesized the dual-process theory and the theory of planned behavior in social psychology literature by incorporating behavior intention into ELM. The model was empirically tested in the context of electronic word-ofmouth in tourism. These two models complete each other. Theory of planned behavior illustrates the relationship between attitude and intention, but does not explain the how the influence process before attitude formation. Elaboration likelihood model supplement TPB in the influence process before the very initial attitude change. The combination of these two models shows good model fitness with our data. Thus, our research contributes a predictive model of influence process of IS on user's intention in the context of tourism.

Limitation and future research

Some limitations exist in this research. Exploring outbound tourist behavior is challenging, especially for an empirical research not only due to the difficulties in data collection, but also in the uncertainty influence of multi-culture values. Thus, data collection could conduct through wider channels in future study. In addition, the impact of culture values should be taken into consideration in future research. We explored potential tourist's visit intention through a general dual influence process perspective, which limits the explanation power of attitude in our model. Therefore, research in the future could decompose attributes of argument quality of eWOM to identify the decomposed attribute of argument quality.

Figure 1 .

 1 Figure 1. Elaboration likelihood model

Figure 2 Figure 2 .

 22 Figure 2. Research model and hypotheses

Figure 3 .

 3 Figure 3. Results of analysis

Table 1 .

 1 Sample characteristics (N=195)

	Sample characteris-tic	Category	Frequency	Percent %
	Gender	Male Female	4 141	27.7 72.3
		Less than 20	6	3.1
		20-30	94	48.2
	Age	31-40	76	39.0
		41-50	15	7.7
		51-60	4	2.1
		Under bachelor degree	22	11.3
	Education	Bachelor degree Master degree	130 40	66.7 20.5
		Doctoral degree	3	1.5
		Single	95	48.7
		Couple without children	44	22.6
	Family size	Couple without children at home	5	2.6
		Couple with children at home 48	24.6
		Other	3	1.5
		Less than 5,000	41	21.0
		5,001-10,000	69	35.4
	Income per mouth	10,001-20,000	51	26.2
		20,001-30,000	20	10.3
		More than 30,000	14	7.2
	Outbound Travel Frequency (in recent three years)	1 2 3 4 5 or more	95 44 5 48 3	13.8 17.9 26.2 8.2 33.8

Table 2 .

 2 Convergent validity: Factor loading, composite reliability, Cronbach's Alpha and AVE

	Item	Mean (N=195)	Factor Loading	Composite Reliability	Cronbach's Alpha	AVE
	AQ1	4.09	0.8867
	AQ2	3.73	0.8151	0.8790	0.7952	0.7081
	AQ3	3.90	0.8208
	SC1	3.89	0.7844
	SC2	3.84	0.8909	0.8855	0.8591	0.7211
	SC3	3.99	0.8686
	ATT1	4.51	0.8828
	ATT2	4.52	0.9361	0.9143	0.8591	0.7809
	ATT3	4.58	0.8289
	WOM1	4.29	0.9356
	WOM2	4.46	0.8730	0.9381	0.9012	0.8349
	WOM3	4.27	0.9313
	INT1	4.23	0.9142
	INT2	4.35	0.9539	0.9538	0.9273	0.8731
	INT3	4.45	0.9346

Table 3 .

 3 Discriminant validity: latent variable correlations and the square roots of AVEs (Square root of AVEs in the main diagonal)

		AQ	SC	ATT	WOM INT
	AQ	0.8415
	SC	0.5987 0.8492
	ATT	0.1750 0.1480 0.8837
	WOM 0.1281 0.1768 0.6563 0.9137
	INT	0.2400 0.1525 0.5903 0.6747 0.9344

Table 4 .

 4 Goodness-of-fit measures for original model

	Chi-square	Degrees of free-dom	GFI	NFI	CFI
	199.890 (.000)	81	0.891	0.853	0.937

Notes: p-value in parentheses; GFI=goodness of fit; NFI=normal fit index; CFI=comparative fit index.

Table 5 .

 5 Summary of hypotheses testing

	Hypothesis

Acknowledgement

I would like to state my gratitude to Katarina Wakonen and Kristiina Hietasaari in Finnish Tourist Board and VisitFinland representatives in China for the data collection, the participants for pilot study, as well as Hongxiu Li, Reima Suomi for all the assistance in conducting this study. This research is supported by China Scholarship Council, and part of the achievements of the China MOE Project of Humanities and Social Sciences (No.13YJC630228), and the National Natural Science Foundation of China (No. 71362027).


Yuan Hao
email: yuan.hao@frtao.com

Laihong Lu

Yuping Zhou

Design and Implementation of Enterprise Office Management System Based on PHP

Keywords: PHP, enterprise, office management, system design

Using a network to manage enterprise office affairs is an important means of improving efficiency of the office management and achieving standardization for the enterprise business. The major technology about using PHP and MySQL to develop an enterprise office management system was illustrated in this paper. The contents including the realization of functional modules were discussed, such as: The foreground web page module used by employees, business management module, design of the database tables and web management technology of administrator. The system has features of fullfeatured, high-efficiency, advanced technology. The systems provide an important reference platform to help enterprise reduce management costs, improve internal management, and enhance competition in the market for comprehensive competitiveness.

Introduction

This system was the enterprise office management system, with full function and good maneuverability. The system was divided into the foreground use part and background management part. Its main function was to manage enterprise's daily affairs, office data management and maintenance. The foreground part was used by employees, therefore its interface design should mainly be user-friendly operation, beautiful interface, efficient and practical. Background management part was used by the system administrator. The system administrator will complete data management and updates in the system in the background. The system mainly used PHP and MySQL as a development tool, and Apache as a server. The network technology was applied in the enterprise management. It was easy for the employee and enterprise managers to operate or use. It provided the convenient, fast and practical software for the enterprise's daily management. PHP (Hypertext Preprocessor) is a server scripting language, which is designed specifically for the Web. PHP codes can be embedded in an HTML page, which were executed when the page was accessed in each time [START_REF] Ning | General Invoicing Management Platform Based on PHP[END_REF]. PHP has advantages in many aspects, such as: PHP is very fast, with high performance; PHP are open source software, with a very good development space and scalability, and it can also be effective to make horizontal extension for a large number of servers; PHP can be applied on all major operating systems, and its code can be run without any modification in different systems; PHP supports multiple databases, and it can be connected to any database providing ODBC driver; PHP is free, in which a lot of open source codes are available. If modifying or adding new features to the language, it can be free of charge, therefore the cost of using PHP is low [2]. The unique syntax of PHP is the mixture of C, Java, Perl and PHP own syntax [START_REF] Wu | Design and Implementation of the E-commerce Website Security System with Delphi and PHP[END_REF].

MySQL is a relational database management system. The relational database is the most common type of database, because of its faster access, and more flexible for data expression. MySQL supports structured query language SQL, so data query is simple and quick. For medium-sized enterprises, MySQL function can be fully met. The advantages of MySQL are its small in size, fast, cross-platform, and open-source. It is especially the feature of the open-source that a lot of free resources can be obtained, which causes many small and medium sized websites to choose MySQL as a database support of website background, in order to reduce the overall cost of the website. MySQL is a true multi-user, multi-threaded SQL database server. MySQL is small and exquisite database server software, which is ideal for small application system [START_REF] Gao Yuxin | Study on Credit Enterprise Information Systems[END_REF].

Apache server is an open source Web server of Apache Software Foundation. Apache has a good cross-platform and can run on almost any computer platform widely used.

The system was developed with today's most popular PHP and MySQL softwares. Two functions of the foreground use and background management were considered in this system. The database of this system was built scientifically, and each module function was carefully designed. Furthermore, it was a full-featured office management system, with the nice interface and simple operation, in order to satisfy the demands of all aspects of daily office management.

In the era of information, office collaboration in different place and office business in the business trip were often required for the modern enterprise. The network framework of this system was based on the application mode of a wide area network. Therefore, this system can achieve cross-regional business processing [START_REF] Hao | The Research and Implementation of[END_REF]. This was also another utility of the system.

Study Background

According to the survey, the current many enterprises exist many problems in the office management, such as low office efficiency, big proportion of artificial management, manpower and resource waste, some works still finished in manual, but can be done automatically, etc. Although some companies have bought the office software, the office automation becomes a "stopping, frozen", and office level is still in a backward state due to the backward software version, complicated interface not easy to operate, and poor maneuverability, etc. factors. It was the common desire of the people, and was also the main target of this system design to develop an office software with the humanized interface, enterprise office management level improved, the office efficiency of internal enterprise improved. The choice of development tools was also considered carefully. At present, there are a lot of development systems based on Web technology, but the three main kinds of dynamic technology are PHP, JSP and ASP.NET, etc. [START_REF] Meng | Comparative Study on Mainstream Dynamic Web Page Technology PHP, JSP, and ASP[END_REF], each technology has its own characteristics.

PHP is a completely free, and the source code can be downloaded freely. It is a development tool favored by a lot of programmers. PHP is a simple, efficient and dynamic scripting language, with the advantages of cross-platform, powerful database support [START_REF] Sulai | Using PHP and MySQL to Develop Dynamic Website[END_REF]. As the PHP is independent on the platform, it can run in a relatively high safety system platform [START_REF] Jinfang | The Advantages of PHP in the Website Background Construction[END_REF]. Therefore, it has more advantages for system background construction. PHP (Professional Hypertext Preprocessor) technology and MySQL database have many advantages. Therefore, they are the best combination to develop the dynamic website. There are many software developed using them as a main tool.

PHP outstanding characteristics are fast in performance, a powerful CGI script language, more efficient to use memory, which can take up less memory consumption. PHP has good portability, and Web back-end CGI programs written in PHP can be easily transplanted to different operating systems.

System Overall Design

The enterprise office management system is an office management system with a collection of network and computer technology and full functions. It is mainly composed of two parts of the foreground use and background management. The overall structure of the system was shown in Figure 1. The use function module block of the foreground included the notice information, file transfer, attendance, employee information, salary information, online communication and user registration and other parts. Background management function module included the section management, notice management, document management, salary management, online communication management, employee information management, system management, attendance management, user management, system management, and other parts.

Foreground function design of the system

The notice information modules in the foreground function of the enterprise office management system can complete the notice query, notice release and news alerts, and other functions. The file transfer module can complete the file upload, file access and file deletion, etc. Functions. The employee information module can complete staff recruitment, information inquiry, staff training, and other functions. The business attendance module can complete the functions such as employee attendance, leave management and attendance report. The salary information module can complete the salary query, report and printing, etc. the online communication module can complete the user login and online communication, etc. The user registration module can complete the registration information, account setting and user logged off, etc. The foreground module of the system is the interface used by common users, and the access to the system was restricted. The foreground use function module of the enterprise office management system was shown in Figure 2.

Background function design of the system

The background function in the enterprise office management system included all data information management involved in foreground functions, such as documents, employees, salary, and etc. information management. In addition, the section information management and system management were included. The management to the section can include the query, add, delete and modify, etc. to section information. The management work of the system background should be done by the system administrator. The system administrator was conferred the management function of the system, therefore, his access right was bigger than that of normal users. The background management function module in the enterprise office management system was shown in Figure 3. The development and implementation of the enterprise office management system involves the analysis and design to the database and database tables, including the design of the data entities, attributes, entity relation, etc. Two kinds of operation permissions users were designed in this system: common users and administrators. According to the permission categories, the operating range for different users was limited [START_REF] Zhiru | Several Effective SQL Server Security Configuration[END_REF]. System mainly involves the table structure design, the establishment of the link between tables, the establishment of the records in the table, etc. in the relational model. There were 31 table files involved in the database of the system. The structure of each table file table was carefully designed. On the premise of minimum redundancy guaranteed, links between tables were established scientifically to improve the efficiency of system running time, and take up less storage space. The table structure of employee basic information table (employee), department information table(dept), the announcement information table(notice), staff attendance sheet(sign), users of the system table(sysuser) and file information table (file) were given here, as shown in table 1 to table 6. The other table files involved in the system will not be illustrated here. The relation among the data tables in the system database was more complex, and more table files were involved, such that the employee information management involves the operation and run of many table. Its link establishment must be accurate to reduce the redundancy of database. Only when created, stored procedure was compiled. Afterwards, recompiling was not needed whenever executing the stored procedure. Therefore, the efficiency of database access can be improved when using the stored procedure [START_REF] Liao | Design and Implementation of Virtual Machine-based Storage Process[END_REF].

In the PHP programm, there was a common.inc.php file, in which some constants, configuration files, path of the session, host information, database information, global function, etc. were stored to ensure important information needed for the program at runtime [START_REF] Wu Jinjin | PHP and MySQL Authority Guidelines[END_REF]. In the development system, constants were defined and "$magic_quotes = get_magic_quotes_gpc ()" was used in order to increase the readability of the code and ease use. The automatic escape function was shut down, and self-defining functions escape was used. The database encoding and references to the parameters configuration page were completed by the program, therefore, the modularization of the program was realized, which is easy for maintenance and modification in the future.

The development of this system also involves image processing, encoding and decoding, compressed file processing, XML parsing, identity authentication of HTTP, POP3, SNMP, database processing, network interface application, security coding mechanism, and other functions. Using PHP + MySQL technology can solve these above problems well. API function supplied in MySQL in PHP can be used to operate the database. The database management, maintenance, and data retrieval and other various operations can be completed through the MySQL function library.

Much more module designs were involved in the system development, of which each module had personalized design in the design process. Such as: the main function of the background page design in the employee information management was to achieve the management and maintenance to the enterprise staff information, therefore, ordinary users can query, but can't modify. Only admin can modify operations. Next example: file transfer management page design was to save files uploaded and downloaded to the server. The path of transferring files in the server was saved to the database for the receiver to download again. All employees had permission to upload and download files. Online communication design was a complex link, because it was a web page on which the enterprise employee can transfer information online, make real-time communication, with more services demanded in the Web service, stronger required to the interactivity and instantaneity [START_REF] Fanrong | Design of Enterprise Office Automation System Based on ASP[END_REF]. The attendance management page design was an important means for the enterprise to manage staff. It included signing in, signing out, taking a vacation, attendance statistics, etc. functions, which were used to compare and appraise staff. They were main indicators for the enterprise to evaluate staff performance. The design of the user password Settings page involves two levels of ordinary users and administrators super users. The user password settings page was for enterprise employees to reset the password, in order to ensure the safety of employees account. All employees in the enterprise can reset personal password, but the admin user had permissions to modify any employee's passwords. Employee salary management is an important part of the function, therefore, not only the real-time update should be considered, but also the security and confidentiality of data should be considered.

In short, a variety of different design technology, from hardware to software, was involved in the development and design process of the whole system, therefore, not only the development of the system should be completed well, but also the later system maintenance work should be considered.

Discussion and Implication

Today's advanced PHP + MySQL development tools were adopted in a PHP-based enterprise office management system. The system provided more comprehensive management functions, which enables the administrator and ordinary users to operate and manage conveniently. It is a relatively ideal office management platform of the enterprise. The system improves the work efficiency of the office management, reduces the waste of resources, and gets rid of the nuisance manual operation. The deficiency is that the system running speed will be slow down while the video function of online communication was used, and user's personalized printing function remains to be perfect. These will be further improved in the follow-up development process of the system.

Figure 1 .

 1 Figure 1. Overall structure of enterprise office management system

Figure 2 .

 2 Figure 2. The Function module of foreground use of enterprise office management system

Figure 3 .

 3 Figure 3. Background management function module of enterprise office management system

Table 1 .

 1 Staff basic information table (employee)

	Field name Data type Length	Whether primary key	Description
	emplid	varchar	6	Yes	Working ID
	name	varchar	16	No	Name
	sex	varchar	6	No	Gender
	age	int	4	No	Age
	birthday	datetime	8	No	Date of birth
	Birthplace	varchar	20	No	Native place
	nation	varchar	16	No	nationality
	maristatus	varchar	4	No	Marital status
	eduback	varchar	20	No	Education background

Table 2 .

 2 Sector information table(dept)

	Field name	Data types	Length	primary key or not	Description
	deptid	varchar	4	yes	Sector ID
	deptname varchar	30	No	Sector name
	memo	Text	50	No	Sector description

Table 3 .

 3 Notice information table (notice)

	Field name	Data types	Length	primary key or not	Description
	noticeid	varchar	6	yes	Notice ID
	noticetitle	varchar	40	No	Notice title
	noticetime	datetime	8	No	Notice time
	noticeperson	varchar	20	No	Notice peopole
	noticecontent	Text	50	No	Notice contents

Table 4 .

 4 Attendance table (sign)

	Field name Data types	Length	primary key or not	Description
	signid	varchar	6	yes	ID
	datetime	datetime	8	No	Date and time
	employee Name	varchar	20	No	Employee Name
	late	varchar	4	No	Late or not

Table 5 .

 5 System user table(sysuser)

	Field name	Data types Length	primary key or not	Description
	userid	varchar	6	yes	ID
	username	varchar	20	No	User name
	userpwd	varchar	20	No	User password
	logintime	datetime	8	No	Login Time
					System
	system	varchar	4	No	Administrator
					or not
	sign	varchar	4	No	Online Logo

Table 6 .

 6 File information table (file)

	Field name	Data type	Length	Whether primary key	Discription
	fileID	int	4	yes	File ID
	fileName	varchar	30	no	File name
	fileSender	varchar	20	no	Delivery man
	filereceiver	varchar	20	no	Recipient
	fileTitle	varchar	50	no	File header
	fileTime	datetime	8	no	Delivery time
	fileContent	Text	30	no	File discription
	path	varchar	100	no	File path
	recsta	varchar	10	no	Receiving state