Hanane Barrah
email: hananbarah@gmail.com

Abdeljabbar Cherkaoui
email: cherkaoui.lti@gmail.com

Fast Robust Fuzzy Clustering Algorithm for Grayscale Image Segmentation

Keywords: Fuzzy clustering, FCM algorithm, c-means, image segmentation, spatial information

Image segmentation is a primordial step in the chain of image processing. A wide range of image segmentation methods are based on the FCM algorithm. However, the lack of any spatial information in this latter algorithm makes it very sensitive in the presence of noise. To overcome this problem and faster the segmentation process, we propose two versions of a fast and robust extension of the FCM algorithm.

To prove the strength of the proposed algorithms we compare them, in a qualitative and quantitative standpoints, and four other fuzzy clustering algorithms. To this end, we use synthetic and real images as testing data.

I. INTRODUCTION

Segmentation is one of the basic tasks in image processing, it is the process of extracting the most relevant information such as points, shapes or regions. In this context, several segmentation methods have been developed [START_REF] Kumar | A Study on Image Segmentation and its Methods[END_REF], [START_REF] Nikhl | A Review on Image Segmentation Techniques[END_REF], they can be divided into three main categories: Contour based, region based and hybrid methods. Each method has its own advantages and drawbacks according to the application domain.

Because of the fuzzy nature of some kind of images, the most useful image segmentation methods are based on the fuzzy clustering approach. FCM, or fuzzy c-means, is the well-known and the best-used fuzzy clustering algorithm [START_REF] Rokach | Clustering methods[END_REF], [START_REF] Dubey | Comparative Analysis of K-Means and Fuzzy C-Means Algorithms[END_REF]. The major drawback of this algorithm lies on lack of any spatial information or constraints, which makes it sensitive to noise. To overcome this problem, many researchers have tried to include spatial constraints in many ways. Indeed, Dzung L. Pham [START_REF] Pham | Spatial Models for Fuzzy Clustering[END_REF] proposed an extension of the fuzzy c-means algorithm based on a generalized objective function that includes a spatial penalty term. Although its robustness to noise, this algorithm faces two major problems, the first one is the difficulty to select a parameter that controls the trade-off between minimizing the standard c-means objective function and obtaining smooth membership functions. The second problem is its time requirement. In order to handle noisy images and reduce the effect of intensity inhomogeneity, Mohamed N. Ahmed et al. [START_REF] Ahmed | A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data[END_REF] proposed a modified fuzzy cmeans algorithm that uses the neighborhood information to influence the belongingness of each pixel. The authors demonstrated the effectiveness of their algorithm against noise on synthetic and real images. Obviously, including neighborhood information enforces the algorithm to be much more consuming in time. To overcome this latter problem, L. Szilágyi et al. [START_REF] Szilagyi | MR brain image segmentation using an enhanced fuzzy c-means algorithm[END_REF] proposed a modification of the previous algorithm [START_REF] Ahmed | A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data[END_REF] by introducing a new factor (0.5≤ γ ≤1.2) which considerably reduces the required calculations. In addition to showing the robustness of this algorithm to noise, the authors demonstrated its quickness against its ancestors.

Our attention is this work is to provide a fuzzy clustering algorithm that is fast and robust to noisy images. To this end, we try to get benefits from two derivatives of the c-means algorithm. We get the fastness from the algorithm proposed by Jiu-Lun Fan et al. [START_REF] Fan | Suppressed fuzzy cmeans clustering algorithm[END_REF], where the authors introduced a parameter that controls the trade-off between the fastness of the hard clustering and the good quality of fuzzy clustering. Whereas the robustness to noise is gotten from the algorithm proposed by Songcan Chen and Daoqiang Zhang [START_REF] Chen | Robust Image Segmentation Using FCM With Spatial Constraints Based on New Kernel-Induced Distance Measure[END_REF]. In fact, this latter algorithm is a direct extension of [START_REF] Ahmed | A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data[END_REF] and their authors proved that it performs faster and better than its ancestors.

The remainder of this paper is organized as follows: In section II, we present the FCM algorithm with spatial information [START_REF] Chen | Robust Image Segmentation Using FCM With Spatial Constraints Based on New Kernel-Induced Distance Measure[END_REF]. The proposed algorithm is described in section III. Some experimental results and comparisons are presented in section IV. Section V is dedicated for some concluding remarks.

II. FCM WITH SPATIAL INFORMATION

FCM or c-means is an algorithm that consists of grouping data into the most homogeneous groups as much as possible [START_REF] Rokach | Clustering methods[END_REF], [START_REF] Lam | Chapter 20 -Clustering[END_REF] by minimizing iteratively the following objective function:

  CN 2 m ij i=1 j=1 J D, U, C u . =   ji xc ( 1
)
Where D is the input data, C is the set of clusters centers,

. is the Euclidean distance, m is the fuzziness exponent and ij Uu    is the fuzzy partition matrix that satisfies the following condition:

  cN ij ij ij i 1 j 1 u 0,1 u 1, j and 0 u N, i .             
The objective function does not include any spatial information, which makes the original FCM algorithm very sensitive in the presence of noise. To overcome this problem Songcan Chen and Daoqiang Zhang [START_REF] Chen | Robust Image Segmentation Using FCM With Spatial Constraints Based on New Kernel-Induced Distance Measure[END_REF] proposed a direct modification of Eq. 1. The modified objective function is defined as follows:

  2 C N C N 2 mm j i j i ij ij i=1 j=1 i=1 j=1 J D, U, C u . x c u . x c =        (2)
Where  is a parameter that controls the effect of the penalty term. As the standard FCM, the clustering is carried out by minimization of the objective function presented in Eq. 2 under the same condition of FCM. The membership values and the clusters centers are updated as follows:

        1 22 m1 j i j i ij 1 22 m1 j k j k 1 x c x c u x c x c              C k   (3)     N m ij j j j1 i m ij j1 u x x c 1u        N (4) j
x can be chosen as the mean or the median of the neighbors within a specified window around j x . When  is set to zero, the algorithm is equivalent to the original FCM, while it approaches infinite, the algorithm acquires the same effect as the original FCM on the mean or median filtered image, respectively. Thus, this new objective function (Eq. 2) leads to two algorithms that will be noted in this manuscript by FCM_S1, uses the mean values, and FCM_S2, uses the median values.

Algorithm1

 Step 0. Fix the clustering parameters (the converging error  , the fuzziness exponent m and the number of clusters C) and initialize the clusters centers.  Step 1. For FCM_S1 (FCM_S2) compute the mean (median resp.) filtered image.  Step 2. Update the partition matrix using (Eq. 3).  Step 3. Update the clusters centers using (Eq. 4).

Repeat steps 2-3 until the following criterion is satisfied:

new old CC   

III. FAST AND ROBUST FCM ALGORITHM

The modifications in the updating equations (Eq. 3 and Eq. 4) alter the algorithm speed in a negative way. To deal with this problem, we have adopted the idea of Jiu-Lun Fan et al. [START_REF] Fan | Suppressed fuzzy cmeans clustering algorithm[END_REF]. Actually, we modified the previous algorithms, FCM_S1 and FCM_S1, by introducing a parameter  that controls the trade-off between the fastness of the hard clustering and the robustness of FCM_S1/S2 to noise. the idea behind Jiu-Lun Fan"s algorithm is to prize the biggest membership and suppress the others. Let j x be a pixel and bj u be its degree of belongingness to the b th cluster. If bj u is the biggest value of all the clusters, then the membership degrees of j x will be modified as follows:

bj ij bj ib u 1 u 1 u          (5) ij ij u u , i b    ( 6
)
Where

  0, 1  .
When  gets closer to 0, the algorithm becomes more hard and when it approaches 1 the algorithm tends to the fuzzy version. This modification has to be done immediately after updating the fuzzy partition matrix. Thus, we come up with two algorithms that are slightly different from the previous ones, FRFCM1 (FRFCM2) that uses the mean (median resp.) filtered image.

Algorithm2

 Step 0. Fix the clustering parameters (the converging error  , the fuzziness exponent m and the number of clusters C) and initialize the fuzzy partition matrix and the new parameters and  .

 Step 1. For FRFCM1 (FRFCM2) compute the mean (median resp.) filtered image.  Step 2. Update the clusters centers using (Eq. 4).  Step 3. Update the partition matrix using (Eq. 3).  Step 4. Modify the partition matrix using Eq. 5 and Eq.

6.

Repeat steps 2-4 until the following criterion is satisfied:

new old UU    IV. EXPERIMENTAL RESULTS
To demonstrate the strength of our resulting algorithms, in both running times and accuracy standpoints, we compare them and four other fuzzy clustering algorithms: The standard FCM, the algorithm proposed in [START_REF] Fan | Suppressed fuzzy cmeans clustering algorithm[END_REF] (S_FCM), FCM_S1 and FCM_S2. To do so, we test the six algorithms upon synthetic and real data.

A. Synthetic data

The synthetic data is an image of 250X250 pixels divided into three clusters with three intensity values taken as 0, 200 and 255. We test the algorithms when this synthetic image is corrupted by Gaussian and "Salt and pepper" noises respectively. The results are shown in Fig. 1 andTable I. The clustering parameters are initialized as follows: From Fig. 1 and Table I, we note that the segmentation results of FRFCM1 (FRFCM2) and FCM_S1 (FCM_S2 resp.) are similar and superior to those of the FCM and S_FCM. It is remarkable that FRFCM2 and FCM_S2 are more robust to "salt and pepper" noise than FRFCM1 and FCM_S 1 , this is due to the usage of the median filtered image.

In a running time point of view, and from the values depicted in Table I, we find out that our algorithms, FRFCM1 and FRFCM2, are the fastest.

B. Real data

In this sub-section we test the previous algorithms upon a real image [START_REF]Image Processing Toolbox[END_REF] corrupted at the same time by Gaussian and "salt and pepper" with the same clustering parameters as fixed before. The segmentation results and the running times are presented in Fig. 2 and Fig. 3 respectively. From Fig. 2, we notice that the algorithms FCM and S_FCM are very sensitive to noise. However, the four other algorithms FCM_S1, FCM_S2, FRFCM1 and FRFCM2 have succeeded to handle noise and their segmentation results are very close.

The results depicted in Fig. 3 show that our algorithms FRFCM1 and FRFCM2 are the fastest. Which prove their effectiveness over the other algorithms.

V. CONCLUSION

To provide a fast and robust fuzzy clustering algorithm for image segmentation, we merged the advantages of two fuzzy clustering algorithms, FCM_S1/2 and S_FCM. By testing the resulting algorithms upon synthetic and real data, we concluded that they outperform their ancestors.

It is worth mentioning that the selection of and  plays an important role in the segmentation accuracy. In fact, a reasonable choice of   ,  leads to an accurate segmentation in a reasonable time. Thus, the selection of the couple   ,  is left as perspective

Fig. 1 .

 1 Fig. 1.Segmentation results on the synthetic image. (a) The original image corrupted by salt and pepper noise. (b) FCM result. (c) S_FCM result. (d) FCM_S1 result. (e) FCM_S2 result. (f) FRFCM1 result. (g) FRFCM2 result.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Segmentation results on real image. (a) The original image corrupted by Gaussian and "salt and pepper" noise. (b) FCM result. (c) S_FCM result. (d) FCM_S1 result. (e) FCM_S2 result. (f) FRFCM1 result. (g) FRFCM2 result.

TABLE I .

 I SEGMENTATION ERRORS AND RUNNING TIMES OF SIX ALGORITHM

Salt and pepper noise Gaussian noise Segmentation Error Running Time Segmentation Error Running Time

	FCM	5.844	1.221	7.503	3.603
	S_FCM	5.844	0.907	7.393	2.281
	FCM_S1	5.096	0.63	4.919	0.653
	FCM_S2	4.822	0.478	4.72	0.716
	FRFCM1	5.095	0.650	4.917	0.688
	FRFCM2	4.822	0.472	4.72	0.609

Xème Conférence Internationale : Conception et Production Intégrées, CPI 2015, 2-4 Décembre 2015, Tanger -Maroc. Xth International Conference on Integrated Design and Production, CPI 2015, December 2-4, 2015, Tangier -Morocco.


Khaoula Khlie
email: k.khaoula40@gmail.com

Abdellah Abouabdellah
email: a.abouabdellah2013@gmail.com

Modelling and simulation of the patient pathway with Arena: case of the mother-child hospital at Marrakech

Keywords: hospital sector, modelling and simulation, performance improvement, healthcare quality, I

Healthcare quality improvement, operational performance increasing, patient satisfaction: such are the challenges of the hospital sector in Morocco and elsewhere. To tackle those challenges, it is necessary to start by studying the patient pathway from the entrance to the exit of the hospital in order to detect problems that can affect the proper functioning of the hospital processes. In this context, this paper intends to reduce the patient waiting times and provides solutions to improve the performance of the medical staff and healthcare quality. For that, a modelling and simulation of the patient pathway within the mother-child hospital at Marrakech is proposed in order to better understand the demand, to highlight the need in terms of human resources, and also to detect different sources of waste present in the value chain. Then, we will discuss the simulation results, evaluate the operational performance of the hospital and propose solutions to improve it.

INTRODUCTION

Nowadays, the healthcare sector represents one of the worldwide priorities. Several researches are conducted in this sector to improve its situation. Managing the patient flows is one of the principal missions of hospitals. The randomly arrival of patients causes a lack of demand control and sometimes an unavailability of human or material resources that causes the patient dissatisfaction. The main objective is to guarantee a fast management of patients especially in the case of the women and child, a demand control is compulsory. In this context, this paper tackles the problem of waiting time minimization in a hospital in order to improve its performance and then satisfy the patient. The study is done in the motherchild hospital at Marrakech. This paper includes four parts:

The first part proposes a small description of the health system situation in Morocco, its flaws and the efforts committed by the state to improve it. The second part provides a literature review on patient pathway modelling and the use of different tools of simulation to evaluate hospitals. The third part presents our study and simulation of the patient (mother) pathway in the mother-child hospital based on the queuing theory. This part will help not only to highlight the need in terms of human resources, but also to detect bottlenecks and different sources of waste present in the value chain.

Finally, the last part presents a discussion of the results obtained, some recommendations and prospects of this paper.

II. THE CURRENT CHALLENGES OF THE MOROCCAN HOSPITAL SYSTEM

This part presents the main problems that impact the hospital sector in Morocco:

A. Lack of financial and human resources:

The Moroccan hospital sector suffers from insufficient spending compared to other countries. According to the statistics shown by the Global Health Organization, the health expenditure in Morocco represents just 6% of GDP, while in other countries such as France; the healthcare budget represents 11.6% of GDP and over 15% in the US [START_REF]Health expenditure ratios of all countries at[END_REF]. As regards the lack of human resources, Moroccan hospitals are unable to cover the needs of the entire population that tops 33 million by the available number of doctors and nurses. According to data provided by the Health Ministry in 2012, the annual average number of visits per doctor is 1015 [START_REF]Studies and health information service[END_REF], Morocco has just 46 doctors per 1000 people. This lack of medical staff is affecting the quality of services provided to citizens and increasing their waiting time in public hospitals.

B. Lack of medical staff motivation:

In addition to the lack of financial and human resources, a lack of motivation is a big problem too. In the health sector, several strikes were done in the aim of increasing doctors salaries. In addition, there is no remuneration system based on the workplace, this problem causes an unbalanced geographical distribution of the personnel, 44% of doctors are located between Rabat and Casablanca [START_REF]Studies and health information service[END_REF].

C. Disastrous hospitalization conditions:

Hospitalization conditions in Morocco are disastrous, a big number of citizens have not the possibility to benefit from the medical care due to the absence of health insurance. According to preliminary results of the survey "Panel de ménages" conducted by the National Human resources Development ONDH1 in 2012 and presented at a seminar in Rabat January 28, 2015 [START_REF]Panel de ménages[END_REF], only 23.3% of the population was covered in 2012 by a health insurance. The investigation showed that the inability to bear the costs of consultation is the cause number one not allowing to access to health care with a proportion of 60.2%. Despite the launch of health services plan for the economically disadvantaged persons (RAMED) 2 , the number of citizens receiving no basic medical coverage remains very high, and even people benefiting from RAMED complain about its inefficiency. It does not allow them to enter all forms of medical care. As regards the health of mother and child, figures are alarming: an average of 5 women and 20 children died every month (statistical data released by the mother-child hospital at Marrakech in 2014). The situation of pregnant women is critical too. Some pregnant women, at the moment of their childbirth, wait to be supported by medical staff in vain. Some of them give birth on the floor of the hospital without any doctor intervention, but the health plan launched by Morocco the 13 November 2013 suggests a better future for the woman and child [START_REF]Plan d'action 2012 -2016 pour accélérer la réduction de la mortalité matérnelle et néonatale[END_REF]. According to a paper published on the website of the World Health Organization: This plan aims to improve the quality of care and reduce by 2015 the mortality of children under five years of 70% and the mortality of mothers 82% compared to 1990 levels [START_REF]Le Maroc adopte un nouveau plan en faveur des mères et des enfants[END_REF].

In accordance with the objectives of this plan, our paper aims to improve the performance of a hospital specialized on mother and children treatment and to minimize their waiting time, and more precisely, mother's one. For this, a modeling and simulation of the mother pathway is necessary for the understanding of the distribution of waiting times on healthcare activities. The following part presents a literature review of some researches in hospital management based in modeling and simulation of the patient pathway.

III. LITTERATURE REVIEW

Many researchers are interested in studying the hospital system trying to improve its performance. For the purpose of the development of an understanding of the functioning of the complete system and the patient's needs, the first step of any study is supposed to be mapping the patient pathways [START_REF] Mould | The evolution of the pathway and its role in improving patient care[END_REF]. It's used at many researches in the hospital sector. Jihène J., El Mhamedi A. and Chabchoub H. propose a new approach that allows the patient pathway modelling at an emergency department [START_REF] Jihène | Modélisation et analyse du parcours de patient dans le Service d'Urgence : Cas de l'hôpital de Sfax[END_REF]. In order to reduce waiting time in an emergency department (ED) and improve the doctor's efficiency, T Wong, A Guinet, A Belaidi and B Bésombes represent a modelling and simulation of the patient pathway using ARIS and ARENA. In their model, authors assume that the patient's arrival can be approximately considered as stochastic event independent of time and then it follows a Poisson distribution. The results obtained prove that the waiting time could be largely reduced and doctor's efficiency improved, and further healthcare costs reduced. They give also a comparison between the two business process re-engineering (BPR) software tools: ARIS and Arena. They conclude that arena is better when it's about a simulation-oriented modelling [START_REF] Wang | Modelling and simulation of emergency services with ARIS and Arena. Case study: the emergency department of Saint Joseph and Saint Luc Hospital[END_REF]. For the same purpose, El oualidi, J. Saadi, L. El hiki, A.

SUMMARY OF SOME HOSPITAL MANAGEMENT RESEARCHES USING MODELLING AND SIMULATION AND THEIR OBJECTIVES

Objectives

References Improving the decisionmaking organization and reducing the duration of hospitalization [START_REF] Gérard | Analyse et modélisation du parcours du patient, Logistique et management[END_REF] Reducing the waiting time in emergencies [START_REF] Wang | Modelling and simulation of emergency services with ARIS and Arena. Case study: the emergency department of Saint Joseph and Saint Luc Hospital[END_REF], [START_REF] Moulay | Modélisation et analyse du flux des patients au service des urgences. Cas de l'hôpital Ibn Rochd à Casablanca[END_REF], [START_REF] Miller Ferrin | Fixing the emergency department: a transformation journey with EDsim[END_REF] Reducing the patient time spent in the emergency services and improving its performance [START_REF] Navas | Construction et simulation d'un modèle de flux de patients dans le service d'urgences d'un hôpital colombien[END_REF] Restructuring of a hospital [START_REF] Romeyer | Modélisation par les processus : une méthode préalable indispensable à la mise en oeuvre d'un système d'information communicant centré sur le patient[END_REF] treatment of medical personnel assignment problem [START_REF] Ma El Oualidi | Problème d'affectation des infirmières: un état de l'art et modélisation. Cas du service des urgences de l'hôpital Ibn Roch de Casablanca[END_REF] Minimizing the pharmaceutical logistics expenditures [START_REF] Di Martinelly | Chaîne logistique en milieu hospitalier : modélisation des processus de distribution de la pharmacie[END_REF] a. hospital management researches using modelling and simulation and their objectives

Once the system modeled, then comes simulation, one of the popular methods in the study of complex systems such as hospital systems in order to present the dynamic aspect of the system. It allows evaluating the performance of the existing process and realizing impossible tests or ones that are very expensive to perform in reality. This step requires a well studied model for reliable results.

A model of the patient pathway in an emergency department was proposed and simulated using Aris to detect bottlenecks in the system and make it faster [START_REF] Wang | Modélisation et simulation du processus de passage des patients aux urgences à l'aide d'ARIS : Étude de cas au SAU du Centre Hospitalier Saint Joseph et Saint Luc[END_REF]. L. Trilling performs a simulation of a medico-technical platform process to determine staffing requirements and hire an overall performance improvement of the plate process [START_REF] Lorraine | Aide à la décision pour le dimensionnement et le pilotage des ressources humaines mutualisées en milieu hospitalier[END_REF]. Queuing theory is also used in a variety of studies analyzing the patient pathways in different types of healthcare processes. De Bruin, A. M., van Rossum, A. C., Visser, M. C Koole, and G. M., (2007) applied it to model the flow of hospitalized patients suffering from cardiac pathology [START_REF] De Bruin | Modelling the emergency cardiac in-patient flow: an application of queuing theory[END_REF]. J-S Tancrez, Roland, Cordier, and Riane, (2011) are based on Markov chains to study the disruption caused by emergencies in the operating theater. The modelling and simulating of the hospitalized patient flow in emergencies help identify the impact of emergencies unpredictable arrival and operations times on the original schedule of operations [START_REF] Jean-Sébastien | Étude de la perturbation par les urgences du planning opératoire[END_REF].

This short literature review shows that modelling and simulation of the patient pathway are used for the treatment of a multitude of healthcare problems. Thereby, table I shows some researches in this context and their desired objectives.

In the same context, our research presents a modelling and simulation of the mother pathway in the mother-child hospital at Marrakech. For this, we are based on the queuing theory.

IV. THE PATIENT PATHWAY STUDY:

Figure 1. The mother pathway model in the mother-child hospital at Marrakech

The real challenge of hospitals is to improve the quality of care and to allocate staff resources reasonably in order to make the patient pathway faster and efficient [START_REF] Wang | Modelling and simulation of emergency services with ARIS and Arena. Case study: the emergency department of Saint Joseph and Saint Luc Hospital[END_REF]. As mentioned before, one of the big problems faced by Moroccan hospitals is insufficient human resources. This problem affects the quality of care offered to patients and generates their dissatisfaction. This lack of resources is very critical in mother services, where the speed of decision making and the availability of medical personnel are required. To determine the optimal number of human resources needed in the services involved, a model of the mother's pathway is needed to better understand hospital processes and to better control its development. This control allows determining different forms of waste present in the hospital, reducing patients waiting time and furthering to satisfying them. The achievement of the results of our study will reduce the burden on the medical staff, making it satisfied and more efficient. The figure 2 presents the procedure followed in our study, it consists of four steps: analysis, modeling, simulation and discussion.

A. System analysis

In the following paragraphs, our system will be limited to the mother's pathway from her access to the mother-child hospital at Marrakech until its exit. Once at the hospital, the mother goes through admission, where she makes registration and constitution of his medical file, and then she goes to billing, then she goes to desired healthcare service. Finally, she goes through the administration service before leaving the hospital. The figure 1 presents the mother pathway in the mother-child hospital.

Our system studied is limited, in addition to the emergency service, to four services namely: gynecology and obstetrics, maternity, radiology and analyzes laboratory. This system is characterized by the following properties:

-Discipline of services: in a queue, it is the priority rule followed when choosing the next patient to serve; in our case, it is the FCFS (First Come First Served). The emergency service is an exception that follows another discipline called IAO. It consists on prioritizing the urgent cases of patients -System Capacity: the number of patients that can be simultaneously present in the system, it may be finite or infinite. A finite capacity "c" means that if a patient comes and •it allows discoving the system ; it contains the description of the system and its properties; Analysis •it's the representation of the system in a specific language; Modeling • it consists on studying the process according to performance goals

Simulation

•it allows the analysis and discussion of results of the simulation.

Discussion

finds "c" patients in the queue, he left immediately without getting the desired service. These are called lost customers. In our case, it is assumed that no patient is lost. We say that the system capacity is infinite.

B. System modelling

The modelling of the patient pathway requires the knowledge of laws followed by the patients' arrival at the hospital and the services in question. According to a study conducted by Dehas and al (2006) [START_REF] Dehas | Evaluation des Performances d'un Système de Santé : Cas de l'Hôpital Khellil Amrane (Béjaïa)[END_REF], the patient arrival process follows a Poisson law while healthcare services follow the exponential law. In what follows, we'll assume that result and validate by statistical tests then we'll calculate parameters of arrival and services processes.

Arrival process:

The hospital mother child receives an average of 45 mothers daily. We consider the event "patient arrival" which occurs on average λεR per unit of time.

X is the random variable representing the number of times the event occurs per unit of time. The patient arrival process satisfies the following conditions:  The probability of arrival at time s> t does not depend on what happened before time t. This is the so-called property "without memory."

 The numbers of arrivals recorded in two separate intervals of the same length follow the same probability distribution. This is the so-called property "stationary".

 X (0)=0 The three conditions above present the case of Poisson process with a parameter λ.

To confirm that result, we time arrivals in the intensive care unit, and note for each arrival the time corresponding.

(1) L: the sum of frequencies. f n : the occurrence of the number of patients n during L. After calculating durations between every sequential arrival, we calculate the distribution average λt given by the equation [START_REF]Health expenditure ratios of all countries at[END_REF].

Using data presented on the table II, λt=1.4

The use of a statistical test is necessary to verify if the distribution of the arrival process follows a Poisson law or not. One of the most used tests is χ2. This test consists on calculating theatrical frequencies using the formula (2). We calculate χ2 and we compare it to the one that we'll identify in the khi-deux table.

(

) 2
For that, we need to calculate the dof (degree of freedom) using the following formula:

dof= c-p-1 (3)
C: the number of clusters (in our case 5)

p: the number of parameters gotten from the distribution ( 1 and it's the average λt) So dof=5-1-1=3

According to the χ2 table, for 3 degrees of freedom, χ 2 0.9 =0.5844. Since the χ2calculated in the table III is lower than χ 2 0.9 , then the distribution is following the Poisson low with a parameter λ=1.4/day.

Services processes

We consider a sequence of random variables Y1, Y2... Yi is where the patient's service time (i = 1, 2 ...). The variables Y1, Y2 ... are independent and identically distributed; it is the case of an exponential distribution with parameter μ. 1 / μ is the average time of patients' pathway in the service.

The table V shows the average number of patients served per unit of time. We'll take the example of the service of maternity to show steps followed to calculate different parameters of services processes distribution. The table IV clusters the service durations in 7 clusters and present the occurrence of the event (patient served in the maternity) in each cluster.

Using the data of the table IV, the average of the distribution is: m=(0.5*61+1.5*32+2.5*15+3.5*6+4.5*3+5.5)/61+32+15+6+4 m=1.32

Using the test of χ2, we will be able to know if the service distribution follows an exponential law with a parameter μ=0.75 (μ=1/m). The χ2 calculated equals 0.86; the χ2 identified from the khideux table with dof=4 is equals to 1.0636 and is superior than the one calculated; so the distribution of the service of maternity follows the exponential low. The performance:

The literature shows a multitude of indicators to assess the performance of a service such as hospital bed occupancy rates, utilization of human resources, the period of appointment, the waiting time, the mortality rate, average length of stay, etc ... The aim of our research is to minimize the waiting time of the mother in the mother-child hospital in Marrakech. For this, we'll try to model the average waiting time in what follows.

A patient waiting time is the sum of waiting times at each activity in his pathway in the hospital. To model the waiting time, we will classify the activities of the value chain in two categories: non-value-added activities for the patient (secondary activities: reception, invoicing and administration) and those with added value (gynecology and obstetrics, maternity, radiology and laboratory) which represent the heart of the hospital business.

The average waiting time is:

This term is to minimize,so two key performance indicators are chosen to evaluate the performance of the hospital processes. The first one is the average rate of waiting, in other words, it's the percentage of waiting time compared to the total time spend by the patient within the hospital.

The second one is the percentage of time spent on non-added value activities. It's defined as follows:



C. System simulation:

The stage of the simulation of the patient's pathway in the mother-child hospital in Marrakech will allow to evaluate the performance and further to offer a solution to improve it in terms of human resources. The inputs of the simulation are the number and work schedule of medical and paramedical staff and the laws of distribution of arrivals time and services and their parameters.

The simulation is done under the following assumptions:

 It is assumed that there are no medical machines failures in the considered services.

 There is no medical personnel absence throughout the simulation.

 The deterioration of the performance is equal to 0.7; which means that 70% of the medical staff time spent in the hospital is a value-added time.

 According to the statistical data collected in the unit of statistics of the hospital, patients are approximately distributed within the hospital as follows: emergencies (30%), consultations (15%), laboratory (20%), radiology (8%), and maternity (27%).

The report of the simulation gives a standby rate of 68%, i.e the patient spends 68% of his time in the hospital waiting to be served. In addition, I 2 =0.07, that means that 7% of the patient time is spent at the NAV activities. To reduce the first rate, it is proposed initially to increase the number of medical and paramedical staff. Several simulations are performed to determine the optimal number of human resources within hospital services in question, we changes in each simulation the number of human resources in the different services. At the end of each simulation, we compare the performance indicators with predetermined objectives. The simulation shows that this is effectively a lack of human resources in the maternity service. Increasing the medical staff in this service may decrease the number of trips to the emergency and perhaps the number of death concerning women. In order to confirm the simulation results, it's necessary to compare them with the data that represent the real situation. The figure 3 presents the number of patients treated by each service during a month that are closed to the simulation results.

D. Discussion of results:

After many simulations, we conclude that there are two services that affect the most the patient waiting time, which are: the invoicing and maternity services. According to the simulation results, it's possible to reduce the standby rate to only 15% just by adding two people in the invoicing service and two others in the maternity service. But this solution assumes that the staff are well motivated and did its job efficiently, which is not true in the case in public hospitals due to the big workload that they're facing every day. Besides, increasing the number of staff also implicates rising material resources within the concerned service, which requires a significant financial budget; and as it is very tight in the Moroccan hospital sector, this solution is not adequate to the situation.

In order to minimize the waiting time for patients, we must explore another improvement way which is to follow a methodology of Lean implementation to manage motion, time and workload of the staff of this service and increase its performance; this approach starts from the modeling of the patient pathway to detect bottlenecks of the system, and proposes solutions using different tools with a continuous improvement spirit.

V. CONCLUSION:

To evaluate the performance of the hospital system, two steps must be followed: the modeling and the simulation. The first step helps us to have a general vision of the system and relationships between its components. Also, it's necessary to obtain good results on the simulation. In fact, the modeling requires also laws followed by arrival and service distributions. In this paper, we were able to find the different laws and parameters of distributions that are present in the patient (women) pathway in the mother-child hospital at Marrakech. The second step allows studying the system in a long period, detect bottlenecks and search solutions to improve the global performance. In a health network where resources are limited, a good governance of the existing means is required; small improvements such as the reduction of overtreatment of waste (e.g switch to radiology to detect the problem before performing the visual stage) or medication waste, etc ... provide significant and lasting time and money.

The healthcare sector requires a new spirit of working for continuous improvement and listening to employees to benefit from their ideas and potential skills. A Lean approach well adapted to the specificities of the hospital sector will be very beneficial. We note as prospects of our work, the proposal of a Lean healthcare approach and its implementation in a Moroccan hospital.

  2 RAMED : Régime d'Assistance MédicaleArtiba, (2009) conducted a model of patient flow within the hospital Ibn Rochd of Casablanca through the SADT method[START_REF] Moulay | Modélisation et analyse du flux des patients au service des urgences. Cas de l'hôpital Ibn Rochd à Casablanca[END_REF].

Figure 2 .

 2 Figure 2. The procedure followed to study the patient pathway

Figure 3 .

 3 Figure 3. The number of patients on each service per month in the motherchild hospital at Marrakech

TABLE I .

 I

TABLE II .

 II

	NUMBER OF PATIENTS ARRIVED PER A DAY DURING A MONTH
	Number of patients per a day occurrence of the number of
		patients at a month
	0	21
	1	32
	2	24
	3	11
	4	4
	5	0
	b. number of arrivals per a day

TABLE III .

 III

		THE Χ	2 TEST TO THE IDENTIFICATION OF THE LAW FOLLOWED
				BY THE ARRIVAL PROCESS
	N	f n	f th	Іf th -f n І	Іf th -f n І 2 / f th
	0	21		23	2	0.17
	1	32		34	2	0.12
	2	24		25	1	0.04
	3	11		12	1	0.008
	4	4		4	0	0
					χ2	0.41
		c. calculation of the χ2

TABLE IV .

 IV

	DURATIONS OF THE MATERNITY SERVICE
	Service duration (d)	Number of services observed
	d<1 hour	61
	1<d<2 hours	32
	2<d<3 hours	15
	3<d<4 hours	6
	4<d<5 hours	3
	5<d<6 hours	1
	6 hours<d	0
	d. durations of the maternity service

TABLE V .

 V

	SERVICES PROCESSES DISTRIBUTION PARAMETERS
	Service i	μ i
	Gynecology and obstetrics	0.35
	(extern consultations)
	Maternity	0.75
	Laboratory	0.87
	Radiology	0.36

e. parameters of the services distribution

ONDH : Observatoire National de Développement Humain Xème Conférence Internationale : Conception et Production Intégrées, CPI

2015, 2-4 Décembre 2015, Tanger -Maroc. Xth International Conference on Integrated Design and Production, CPI 2015, December 2-4, 2015, Tangier -Morocco.


Adil Aramja
email: adil.aramja@gmail.com

Oualid Kamach
email: okamach@yahoo.fr

Samir Chafik
email: s_chafik@yahoo.fr

Creating a baseline model of Manufacturing Execution Systems using Petri nets : Literatture overview

Keywords: MES, benchmark, baseline model, survey, modeling, Petri

the current economical context is pushing companies to do more with less, with better quality, to do it faster and most of all in a cost effective manner. Apart from creating economies of scales, ensuring operational efficiencies is also of a paramount importance. To do so, many companies strive to implement lean processes and best practices and amongst other alternatives, implementing IT software solutions such as Manufacturing Execution Systems (MES). Such tools can help manufacturing companies shorten the manufacturing cycle, improve the process performances and increase therefore the company competitiveness in a very challenging market landscape. Acquiring such tools would be most of the times very expensive especially for small and medium businesses that are very cautious about their CAPEX/OPEX spending. This is mainly because MES solutions are offered as a package of several modules and their integration with the existing systems and infrastructure imply additional cost and burden for this type of companies.

In this paper, we are presenting the literature view on modeling MES solution systems which will be as a guideline for our approach to assist small and medium industries with a baseline model of MES solutions. The intended model will be established by first of all setting a benchmark of the MES solutions in European market, second a survey will be distributed to different Industrial companies in Moroccan market in order to grasp their needs and finally making a reference model using modeling tools such as Petri nets.

I. GENERAL OVERVIEW OF M.E.S

The manufacturing Execution Systems (MES) are software systems intended to manage, control and coordinate the different tasks defined at the production and manufacturing level in order to improve the company's operational performances.

The development of MES solutions has gone through different stages. According to Rondeau (2011), there were five stages that witnessed the evolution and development of manufacturing planning and control systems:

-Reorder Point Systems (ROP), which consisted in a continuous monitoring of available warehouse stock of a given product. While using materials from the warehouse, the system checks if this use will lead the stock level to reach the reorder level usually indicated as ROP.

-Materials Requirement Planning (MRP) approach is based on determining the number of parts, components and materials to produce each end item. MRP systems also provide the schedule specifying when each item should be ordered or produced [START_REF] Chase | The McGraw-Hill/Irwin Series[END_REF].

-MRP II systems which stands for Manufacturing Resource Planning is just a direct evolution of MRP Systems. This evolution was mainly driven by the evolution the development of the information processing technology. MRP II systems control the entire system from order entry through scheduling, inventory control, finance, and accounting [START_REF] Chase | The McGraw-Hill/Irwin Series[END_REF].

Fig. 1. Evolution of manufacturing planning and control systems [START_REF] Rondeau | Evolution of manufacturing Planning and control systems: from reorder point to enterprise ressource planning[END_REF] The MES solutions encompass nowadays several components of the CIM model such as CAP (Computer Aided Planning), CAM (Computer Aided Manufacturing), CAQ (Computer Aided Quality Assurance), PDA (Production Data Acquisition), MDA (Machine Data Acquisition), and PTR / T&A (Personnel Time Recording, Time & Attendance) [START_REF]Manufacturing Execution Systems: Industry Specific requirements and solutions[END_REF]. As a result of this integration, MES plays a key role being the single data repository for the different production departments and also by giving a consolidated and customized reports that can be used by the business and management systems such as ERPs.

A. MES norms and Guidelines

Norms and guidelines represent the outcome of efforts established by different industrial groups and eventually normalization bodies. These efforts are meant to offer the different industry players a standardized model of MES solutions which will help not only vendors to create solutions quickly increasing therefore the adoption rate of these solutions, but also reducing risks for customers related mainly to the financials, technical integration and interoperability with existing systems [START_REF] Ferrazzi | Manufacturing Execution Systems: A case study in the aerospace industry[END_REF]. In this section, we are going to focus mainly on the models defined by MESA and ISA.

In 1997, MESA has developed a very compact model which encompasses eleven function of a MES system. These functions are linked to each other and connected to other software solutions at the upper level [START_REF] Ferrazzi | Manufacturing Execution Systems: A case study in the aerospace industry[END_REF].

MESA has later on defined what is called C-MES (Collaborative MES) which focus on how core operations interact with business operations considering factors such as increased competition, outsourcing, supply chain optimization, and asset optimization [START_REF] Ferrazzi | Manufacturing Execution Systems: A case study in the aerospace industry[END_REF].

The other model that we are going to address was defined by ISA, the International Society of Automation (ISA). ISA is using more the term manufacturing operation system. Besides the terminology and definitions, the ISA-95 standard aims at defining which information has to be exchanged between systems for sales, finance and logistics and systems for production, maintenance and quality. This information is structured using UML models which are the basis for the development of standard interfaces between ERP and MES systems.

B. Advantages and benefits of using MES systems

The adoption of Manufacturing Execution Systems was initially noticed within several discrete, batch and continuous process manufacturing industries, especially aerospace, automotive, semiconductor, pharmaceuticals and petrochemicals.

Market reports show that they are increasingly being applied in sectors such as metals, plastics and medical equipment.

We can summarize the main advantages of using MES in the following [START_REF]The benefits of MES: A report from the field[END_REF]:

-Better integration of information that is all the information need to be collected from machinery are stored in a single database.

-More reliable data about the production environment.

-Collecting the information in a real-time basis, allowing better decision making.

-Reducing paper work and improving documentation management -Reducing manufacturing cycle times -Reduction of errors and defects by permanent computer-based monitoring of all important production parameters.

-Reduction of production costs and better utilization of plant capacity as a result of computer-based production planning and scheduling.

-Reduction of set-up times by optimization of plant allocation.

-Inventory reduction (raw materials, finished products) by improved planning, and more flexible and demandoriented production.

-Effective organization, monitoring, and documentation of processes which are subject to regulatory compliance

C. Investment decision in M.E.S

In order to argument the investment in M.E.S solutions for upper level management, a business case should be established. Traditional analysis gives more emphasize to financial criteria and indicators such as the NPV (Net Present Value), IRR (Internal Rate of Return), Payback period or even the TCO (Total cost of ownership). However, another nonfinancial criteria should also be considered such as the enterprise culture, i.e. the resistance factor that might arise from the employees.

Reference [START_REF] Chao | Manufacturing Execution Systems (MES) assessment and investment decision study[END_REF] suggested a methodology that may assist companies in making the right decision for MES solution based on a general decision model called BOCR (Benefits -Opportunities -Costs -Risks) and ANP (Analytical Network Process). ANP is very practical for decision making based on multi-criteria and it has been used in several cases related to IT projects.

The way how decision is taken can also vary depending on the size of companies. Large companies often consider investment in IT systems as strategic decision therefore carrying out an assessment is viewed as unnecessary. On the other hand for smaller companies which lacks time and personnel, making a comprehensive assessment is a complex task.

II. MES SYSTEMS MODELLING

Manufacturing systems are complex: they are comprised of people, processes, products, information systems and data, and material processing and handling systems. In order to design effective and efficient systems and integrate the various Components, manufacturing systems modeling is required.

Because of system complexity however, systems must be modeled using various views, e.g., functional, informational, physical, control, etc. [START_REF] Krishnamurthy | hybrid manufacturing system modeling environment using VRML[END_REF] There quite many different modelling techniques and methods and each modelling method has its specific characteristics and may have different focuses on application systems. Nevertheless, these methods didn't succeed in reporting the full description of manufacturing process information and the complex internal relations [START_REF] Qiao | Manufacturing process modelling using process specification language[END_REF].

In this section we are going to shed some lights on some work and efforts associated with the modelling of MES systems.

The modelling of Manufacturing Execution Systems is an interdisciplinary challenge. Actually, the information required for setting up the MES model requirements are spread among different stakeholders within the company. That is, people at the production process level have different view on the technical and the business process then operators and Management personnel might have [START_REF] Ricken | Modeling of Manufacturing Execution Systems: an Interdisciplinary Challenge[END_REF]. Moreover they have different interests and requirements regarding the MES functionalities.

This fragmentation of the information would have consequences both on MES vendors and customers: The formers would experience difficulties to locate the different data points and report accurately the different performance indicators as specified by the customer since data are needed in different details from different stakeholders and for the latters, this will lead to a suboptimal cooperation and islands of knowledge among co-workers and thus to a non-efficient use of information potentially available [START_REF] Ricken | Modeling of Manufacturing Execution Systems: an Interdisciplinary Challenge[END_REF].

Same problem was also reported by companies in industries working with low variety batches and relatively longer lead times MTO (Make-to-Order) Projects such as the aerospace industry. These type of organizations are working on islands of automation making it very difficult to carry out any analysis of the available data. Various functions are working independently and are unable to share information with each other [START_REF] Muhammad | Manufacturing Execution System for a Subsidiary of Aerospace Manufacturing Industry[END_REF].

In order to overcome this problem and to have a simple communication method and easily understandable by different stakeholders, it was argued that using understandable graphic modeling notations would be a very efficient solution. A new notation model was developed called "SpeziMES" which not only fulfills all essential requirements but also compliant with existing modeling standards [START_REF] Ricken | Modeling of Manufacturing Execution Systems: an Interdisciplinary Challenge[END_REF]. MES specification requires at least three types of information and their relation to each other: information about the technical system, information about the production process and information about the required MES functions. The MES model represents the core of this modeling framework. It displays the functions of MES embedded in interacting IT functionalities and systems. For a complete modeling of MES, all possible timing descriptions like discrete event-driven, time-discrete and time-continuous need to be expressed. In MES, synchronous, asynchronous and concurrent processes could take place, so that an appropriate modeling language allows the modeling of all of these three types of process synchronization [START_REF] Ricken | Modeling of Manufacturing Execution Systems: an Interdisciplinary Challenge[END_REF].

Other researches pointed Petri nets as an efficient modeling tool. The rationale behind this choice was that MES systems were a complex DEDS (Discrete Event Dynamic System) as such there were many random factors and unstructured problems in it and second Petri nets was a good tool for modeling and analyzing the dynamic system of discrete matters [START_REF] Jiwei | The research of Manufacturing Execution System Modeling based on colored Petri nets[END_REF].

Petri nets development was motivated mainly by the need to model industrial systems. They have been used extensively to represent simple production lines with buffers, automotive production systems, flexible manufacturing systems, Just in Time and Kanban manufacturing systems [START_REF] Zurawski | Petri Nets and Industrial Applications : A tutorial[END_REF].

Reference [START_REF] Jiwei | The research of Manufacturing Execution System Modeling based on colored Petri nets[END_REF] showed how petri nets can be applied for modelling MES systems in a hybrid industry. The case study was taken from the manufacturing process of cotton yarn.

The first step was to understand the different steps of the production process of cotton yarn, this will give a clear overview on the flow of the different objects. Secondly, the establishment process of the production plan and how MES fits into it. Actually the production data is transferred using MES and if production has been modified, MES will respond accordingly. Therefore, the tasks that need to be modelled are the relationship between the different production activities.

The author used what is called colored Petri nets where color concept is applied to basic petri nets. The principle is as follow: same class individuals are endowed with same color, different class individuals are endowed with different color. In this way, one place can comprise several objects or one composite condition, and one transition can also denote different changes. At the same time, the token has been appended color, and can be used to depict the attribute information of object. Therefore it can simplify the complexity of the system model. The colored petri nets model of production process can be built based on the production process characteristics of cotton spinning industry and the rules of colored petri nets.

III. CONCLUSION

In this paper, we tried to give a general overview on the previous works attempting to model MES systems. The functional model defined by ISA seems to be the main reference model used by different authors and industrial players. Petri nets and its variants are the most used techniques for modeling MES solutions as they are widely tested and experimented in industrial and manufacturing sectors.

Fig. 2 .

 2 Fig. 2. Eleven functionnalities of M.E.S as defined by MESA

Fig. 3 .

 3 Fig. 3. MES specification framework models

Fig. 4 .

 4 Fig. 4. The colored petri net model for the production process.

Xème Conférence Internationale : Conception et Production Intégrées, CPI 2015, 2-4 Décembre 2015, Tanger -Maroc. Xth International Conference on Integrated Design and Production, CPI 2015, December 2-4, 2015, Tangier -Morocco. Identify applicable sponsor/s here. If no sponsors, delete this text box (sponsors).


Jonathan Seybold
email: seybold@hsg-imat.de

Ulrich Kessler
email: kessler@hsg-imat.de

Karl-Peter Fritz
email: fritz@hsg-imat.de

Heinz Kück

Precision Micro Assembly of Optical Components on MID and PCB

Keywords: Optical module, laser diode, VCSEL, sensor, rotary encoder, precision assembly, low cost, miniaturization, MID

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Indroduction

Micro assembly of optical elements often requires high precision joining operations during the assembly of the components. In this contribution the assembly of the optical components of a module for rotary encoders is described. Rotary encoders are used in many industrial applications for positioning and motion control. Thereby, optical encoders are usually used for high precision measurements [START_REF] Schaeffler | Magnetisch versus optisch; Winkel-Mess-Systeme für Rundtischachsen im Vergleich[END_REF].

In this case, an optical encoder was designed and built up with an alternative functional principle, which was newly developed at HSG-IMAT. The first feature is the precisely micro structured plastic disc as solid measure similar to a compact disc (CD) or digital versatile disc (DVD). The disc of the encoder is made of polycarbonate and is manufactured by injection moulding at low manufacturing costs.

The second feature is that the encoder contains an optical module with a laser diode, a lens and photo diodes. The assembly of this optical module is described in this paper. The motivation of the research is to reach a plug and play assembly of the encoder itself which leads to a low cost encoder but in spite of this, the encoder has also a high resolution [START_REF] Hopp | Inkrementale und absolute Kodierung von Positionssignalen diffraktiver optischer Drehgeber[END_REF]. To achieve this objective, a relative positioning accuracy of ±10 µm between laser diode and lens is required in the optical module. The reason for this is, that all critical tolerances than are included in the optical module itself.

To achieve the required accuracy of ±10 µm between laser diode and lens two different approaches were proposed. On the one hand an encoder with a MID optical module was designed and built up [START_REF] Nr | ZN: Untersuchungen zu einem hochauflösenden optischen Drehwinkelsensor in Low-Cost-Bauweise[END_REF]. In this case, the challenge is to reach the required accuracy during the assembly process of the laser diode. On the other hand the optical components were directly assembled on PCB with automated assembly processes [START_REF] Nr | 349 ZN: Untersuchungen zu kostengünstigen absolut und inkremental kodierten optischen Drehgebern mit justagefreier Endmontage und mikrostrukturierter diffraktiver Maßverkörperung aus Kunststoff[END_REF]. In this case, the challenge is to reach the required accuracy during the assembly process of the lens.

Optical Module on MID

The first optical module was based on Moulded-Interconnect-Device (MID) technology using the LPKF LDS® process [START_REF] Mid E | 3D-MID Technologie[END_REF]. The optical module contains one laser diode (VCSEL), one lens and five photo diodes. First, the laser diode was manually attached exactly to the center of the MID-header within the required tolerance of ±10 µm using a Finetech Fineplacer. Accordingly, the five photodiodes were manually attached whereby the cathode was connected with conductive adhesive. All dies were wirebonded directly to the MID-substrate to connect the anode. Afterwards, the lens was assembled manually with form closure on the MID-header. In the final step, the optical module was connected by conductive adhesive to a PCB on which the electrical processing of the signals was performed. Fig. 1 shows on the left side the assembled and wire-bonded dies on the MID-substrate and below the assembled lens. The right side shows the completely assembled optical module together with the PCB. The photo diodes with an edge length of 1.4 mm can be used as scale.

The contour of the lens has been designed to fit on the MID-header at the bottom and to carry an aperture at the top. The lens was made of PMMA and was manufactured by ultra-precise diamond turning. For larger quantities the lens can also be manufactured by injection moulding. At first, different vacuum pick up tools for the assembly of the laser diode were tested. The best results were achieved with a pick-up tool with conical shape which holds the laser diode at its edges. Thereby the laser diode is held in a defined position in the tool through a self centering effect because of the conical shape of the tool [START_REF]Die Attachment and Fluid Dispensing[END_REF]. This allows to assemble the laser diode without a bottom side referencing step. It has become evident, that a bottom side referencing of the laser diode leads to a loss of positioning accuracy due to the poor quality of the bottom side edges in combination with an insufficient resolution of the inspection system. Fig. 2 shows on the left side the laser diodes on blue tape in the state as delivered. The right side schematically shows the pick-up process of the laser diodes from the blue tape.

The assembly process of the laser diode runs fully automatic in several steps. First the reference marks on the PCB are detected with the inspection camera. Subsequently the conductive adhesive is applied to the target position by a stamping process.

Afterwards the respective pick-up position of the laser diode on blue tape is detected exactly with the inspection camera and the laser diode is picked up and held in the pick-up tool by vacuum. After moving to the target position and the assembly the vacuum is switched off and the pick-up tool moves to the starting position. Finally, the thermal curing process of the adhesive is carried out in an oven.

The other studied tools were either made from rubber or metal and had flat surfaces, so that the tool touches the top side of the chip. With the metal tool the surface of the laser diode was damaged and with the rubber tool no stable pick-up and positioning process was possible due to the small rubber tip, which proved to be too instable.

Positioning Accuracy of the Laser Diode

To investigate and optimize the positioning accuracy several 3x3 laser diode arrays were assembled on an experimental PCB using different setups. In detail the shape and size of the reference marks on the PCB were varied and also the procedure of the camera inspection of the laser diode before the pick-up process from blue tape. Fig. 3 shows such an assembled laser diode array.

It could be shown, that the automatic inspection works best with rectangular or linear contrast transitions. Therefore rectangular reference marks should be preferred over circular or crosswise marks. Accordingly the inspection of the laser diode works better when the rectangular structures of the surface are used instead of the circular alignment marks. Furthermore it has been shown that for highly precise assembly it can be advantageous to use the reference marks on the PCB only for assembly of the first die if there is more than one chip to be assembled. For the subsequent assembly steps it is then possible to use the first assembled die as reference mark. In this way, the more precise lithographic structures of the die instead of the etched reference marks on the PCB, which are less precise, are used to achieve the required accuracy.

The 3x3 laser diode array in Fig. 3 was assembled according to this principle. The first laser diode was assembled in relation to the reference mark on PCB. The other laser diodes were assembled in relation to the first laser diode, whereby for each laser diode a new inspection step of the reference laser diode was done. In order to investigate the quality of the optical referencing, the PCB was loaded to and unloaded from the machine between the assembly of each laser diode. The positions of the facets of the laser diodes were measured before and after the curing process on a coordinate measuring machine und compared with the intended target positions. The diagram in Fig. 4 shows the measured displacement of the facets of the laser diodes from their target positions. After curing, the maximum displacement was found to be ±7 µm, the standard deviation was < 3.5 µm. Altogether five 3x3 laser diode arrays were assembled.

The die attach of the photo diodes is easier due to their larger size. In addition, the sensor concept doesn't require the same level of accuracy as it is with the laser diode and lens. The assembly could therefore be done using a rubber tool.

Assembly of the lens

The assembly of the lens has similar requirements concerning the accuracy like the laser diode. First, UV curable adhesive is transferred by a ring-shaped stamp to the PCB. Then the lens is picked up with a conical pick-up tool which assures the defined alignment of the lens in the pick-up tool. The target position of the lens on the PCB equates to the facet of the laser diode. Therefore an inspection step of the laser diode is done. Then the lens is assembled and the adhesive is cured through UV radiation.

To ensure the correct distance between laser diode and lens, on the bottom side of the lens a gap for the adhesive is defined. Fig. 5 shows schematically the assembly process of the lens on the PCB. The challenge in this case is to find the center of the lens before the pick-up step. Because of the clear optical surfaces, it is difficult for the inspection camera to find sufficient contrast at the edges. For this case, a ring at the top side of the lens was designed. When manufacturing the lens by injection moulding, the ring shaped plane can be arranged with a mat surface to enhance the contrast.

Fig. 5. Schematic assembly process of the lens on PCB

The assembled optical module on PCB is shown in Fig. 6. Visible are the PCB with the electronic components, which were assembled first, the photo diodes and the lens. The laser diode is located below the lens. The photo diodes with an edge length of 1.4 mm can be used as scale.

Fig. 6. Complete assembled optic module on PCB

The misalignment between laser diode and the assembled lens is determined as the difference between the center of the lens, measured by optical inspection and the centre of the facet of the laser diode which can be seen as image through the lens in its focal plane. Another method is to consider the beam profile of the spot. Fig. 7 shows on the left side the beam profile with a correctly aligned lens and on the right side a misaligned lens. Shown is the relative intensity of the laser beam in its beams waist plane in which is the encoder disc with its solid measure too. A misaligned lens causes of course poor signal quality or even total failure of the rotary encoder when the misalignment is too large.

Conclusion and Outlook

A miniature optical module for a rotary encoder was designed and built up first based on MID and further on PCB. The optical module includes one laser diode, one lens and several photo diodes. The positioning accuracy of the assembled optical components was analysed. The result is that assembly within ±10 µm is possible under the described circumstances. Further investigations should be done under the condition of large scale manufacturing to confirm this result. HSG-IMAT will continue to work in the field of precision assembly. For example automated active alignment of the lens by beam control and a higher resolution of the inspection camera of the 3-D assembly machine are two issues, which will bring further progress in precision assembly.

In addition, it is planned at HSG-IMAT to investigate and develop forward the 3-D assembly on MID. This enables to use the advantage of the MID-technology in reference to the degree of freedom in 3-D. From this point of view, this technology allows to design mechanical joining elements which can be used for the purpose of alignment or also actuators and sensors with functions based on 3-D, for example 3-D magnetic field sensors.

Fig. 1 .

 1 Fig. 1. a) MID-substrate with assembled laser diode and photo diodes; b) MID-substrate with assembled lens; c) MID module inclusive the assembled aperture connected to the PCB

Fig. 2 .

 2 Fig. 2. a) Laser diodes on blue tape; b) Schematic pick-up process from blue tape

Fig. 3 .

 3 Fig. 3. 3x3 Laser diode array on PCB

Fig. 4 .

 4 Fig. 4. Frequency distribution of the displacement in x-and y-direction

Fig. 7 .

 7 Fig. 7. Beam profile of a correct assembled lens (a) and of a misaligned lens (b)


Sebastian Haag
email: sebastian.haag@ipt.fraunhofer.de

Tobias Müller

Christoph Pallasch

Christian Brecher

Integrated Tool-chain Concept for Automated Micro-optics Assembly Full Paper, IPAS

The work presented in this paper aims for a significant reduction of process development and production ramp up times for the automated assembly of micro-optical modules and systems. The approach proposed bridges the gap between the product development phase and the realization of automation control through integration of established software tools such as optics simulation and CAD modeling as well as through introduction of novel software tools and methods to efficiently describe active alignment strategies. The focus of the paper is put on the formalized specification of product configurations as a basis for the engineering of automated assembly processes. The concepts are applied to industrial use-cases. The paper concludes with an overview of the application of the concepts in an engineering tool-chain as well as an outlook on the next development steps.

Introduction

Photonics technologies are key technologies of the 21 st century enabling innovative applications in demanding and societal relevant domains. In many cases, photonic applications belong to the field of high-technology applications with small and medium production volumes. In order to respond to increasing competitive pressure in production of micro-optical systems and lasers, flexible, autonomous, and efficient solutions for assembly systems have to be developed [START_REF]Integrative production technology for high-wage countries[END_REF]. Competitive small and medium size volume production can only be achieved based on an increased degree of automation as automation can reduce costs while realizing highly reliable processes and high product quality as well as improved working conditions. However, a high degree of automation still correlates negatively with the flexibility of a production system which can lead to a major negative impact on the return on investment calculation. Recently, promising progress has been made developing modular and reconfigurable assembly systems [START_REF] Müller | Reconfigurable Self-optimising Handling System[END_REF][START_REF]Changeable and Reconfigurable Manufacturing Systems[END_REF]. There is a significant lack of corresponding software solutions to allow for an efficient exploitation of the available flexibility as promised by computer-aided process planning (CAPP). In order to fulfil precision requirements and due to manufacturing tolerances and finite accuracy of the positioning systems, the assembly of micro-optical systems requires the use of sensor-guided processes such as vision-based component pickup, passive alignment exploiting geometrical features through image-processing, and active alignment optimizing the optical function towards a desired value. The use of sensors requires the processing and analysis of signals and in some cases reasoning in order to extract information from it which drastically increases the complexity of process planning and commissioning. Thus, the required engineering time is high and nullifies the benefit of automation. This is the motivation for ongoing research activities which intends to develop and validate an integrated development environment (IDE) for automated precision assembly processes bridging the gaps between computer-aided product development, virtual process planning and assembly execution by means of methods and software tools for implementing complex sensor-based handling and alignment processes. The assembly of micro-optical systems is still dominated by manual operations. Feasibility of automation has been proven for many cases such as resonator mirror alignment, focus optics alignment, fast-axis collimator alignment for diode laser bars as well as for multi-single emitter diode laser modules ( [START_REF] Brecher | Automated alignment of optical components for high-power diode lasers[END_REF][START_REF] Brecher | Automated assembly of VECSEL components[END_REF][START_REF] Garlich | SCALAB. Scalable Automation for Emerging Lab Production[END_REF][START_REF] Miesner | High-power diode laser technology and applications VII. 26-27[END_REF][START_REF] Pierer | High-power diode laser technology and applications IX. 23-25[END_REF]). Investment and implementation costs are still high and mean a high risk -especially for small and medium sized companies. An engineering gap regarding the information transfer from product development to the subsequent engineering phases of process development and assembly system configuration and commissioning can be stated. This gap needs to be overcome in order to allow automation technology to achieve a breakthrough in the production of optical systems such as lasers. The work presented in this paper strives for closing the identified engineering gap by proposing a standardized and yet flexible approach for engineering such assembly solutions supported by corresponding software tools which do not exist in the domain of laser system production. The main task identified by the authors is the introduction of a flexible engineering methodology for planning and commissioning the automated assembly of optical systems and therefore the integration of existing tools and the conceptual design and the prototypal implementation of novel tools for bridging existing engineering gaps.

Concept of Hybrid Assembly Process Planning for Optical Systems

This paper proposes a hybrid approach for assembly process planning for optical systems in which parts of the engineering can be automated as in CAPP and other engineering tasks are implemented or optimized by Integrated Tool-chain Concept for Automated Micro-optics Assembly Full Paper, IPAS 2014 operators. ElMaraghy defines in [START_REF]Changeable and Reconfigurable Manufacturing Systems[END_REF] the term of micro-process planning as the specification of detailed parameters for individual operations. This definition corresponds with the intent of the proposed approach which integrates well-established engineering tools (for CAD modeling, optical simulation, PLC and robot programming) as well as novel software modules for the specification of sensor-guided process parameters through standardized communication interfaces and data formats. An iterative approach of virtual and physical engineering steps is proposed in order to provide sufficient flexibility during the process planning phase. Virtual engineering steps comprise offline and computer-aided development efforts. Physical engineering steps stand for development efforts carried out physically, e.g. the refinement of an active alignment process using real laser and camera (instead of simulation). The term 'online' is avoided because the authors use that term for activities in the actual production system.

Fig. 1: Overview of engineering elements for hybrid planning and commissioning the automated assembly of optical systems

Fig. 1 provides an overview of the elements of the proposed engineering platform. Product design (PD) is usually carried out using computer-aided (virtual) methods. Early physical realization of the product as a prototype allows evaluation of the design and possibly design improvements. For process planning and commissioning the authors propose a two-stage approach analogue to model-driven engineering approaches for maximizing re-usability [START_REF] Gašević | Model driven engineering and ontology development[END_REF]. The first stage is a platform-independent view (xPIxx) on the task while the second stage is platform-specific (xPSxx). Furthermore, process planning and commissioning are both proposed to be subdivided in a virtual as well as a physical branch. This framework leads to four engineering elements:

• Virtual platform-independent process planning (vPIPP): This engineering step carries out top-to-bottom (T2B) specification of key characteristics in a formal way and uses that information for deriving an assembly sequence. For the development and verification of specific assembly steps, tools such as the proposed alignment-in-the-loop can be used to virtually specify and verify complex tasks offline. • Physical platform-independent process planning (pPIPP): On a dedicated prototyping platform individual process steps such as active alignment pre-planned in the virtual environment can be executed and validated. Discrepancies between ideal models and the real world can be identified and compensated this way. A possible solution to overcome such discrepancies is the integration of visible reference marks for local referencing between model and hardware. • Virtual platform-specific process commissioning (vPSPC): For mapping the assembly task specification consisting of an assembly sequence and virtually planned process steps to an assembly platform, the concept proposes the use of Virtual Production Systems (VPS). VPS's can be used for teaching coordinates in the model environment. High-precision tasks require the use of sensor-guidance based on visible reference marks. • Physical platform-specific process commissioning (pPSPC): The final step of commissioning takes place on the production platform in a drastically reduced way complexity and ramp up time.

Fig. 2 depicts the engineering phases of product development, process planning, and commissioning of the assembly task in a slightly different way than in the previous section. Here, the paths of information exchange are illustrated by arrows. For an efficient engineering process, it must be ensured that all phases have welldefined interfaces for passing on and exchanging information between each other. Note, that no direct links for information exchange are depicted between the physical engineering steps (PP, pPIPP and pPSPC). Information must be fed back to the virtual environment in the models in order to refine the model-driven approach.

Integrated Tool-chain Concept for Automated Micro-optics Assembly Full Paper, IPAS 2014

Overview of the integrated tool-chain

For the development of the photonic products, established software tools are available such as optical simulation tools and CAD modeling tools (Fig. 3, left column). Assembly process planning for micro-optical systems comprises the sequence of assembly steps and the planning of processes such as part feeding and alignment. The product configurator edits formalized representation of the liaison diagram and therefore bridges the gap between product development and process planning (Fig. 3, middle column). In the VPS resources are assigned and the assembly sequence is verified regarding logic and collisions (Fig. 3, right column).

Fig. 3: Overview of tools in IDE

Formalization of the product configuration

Product development consists of several phases. In a first step, functional and non-functional requirements are defined from a customer point of view. In a second step, the defined requirements are transformed into technical requirements specifications. In a third step, for optical systems, an optical model is created and assembly tolerances are analyzed through simulation. As a result of this step the optical elements are chosen and the product can be designed in CAD regarding its outer and inner dimensions. Furthermore, the mechanical design of laser systems is optimized regarding its thermal behavior by means of thermal analysis. Professional and wellestablished software is available for all of these steps.

In the case of optical systems, special attention needs to be paid to the high precision demands often reaching in the sub-micrometer domain. Process steps such as handling, alignment and bonding of parts in many cases need sensor-based strategies compensating for inaccuracies induced by unavoidable mechanical tolerances. Therefore, in case of optical systems, the authors adapted ideas of classical process planning in an intermediate step describing the desired geometric and especially the desired optical relations of the product parts for bridging the gap between product development and assembly execution. According to the terminology defined in [START_REF] Whitney | Mechanical assemblies. Their design, manufacture, and role in product development[END_REF] for mechanical assemblies, constraints or requirements on geometric and mechanical relations are named key characteristics (KC's). KC's express the objectives and constraints of individual assembly steps as well as a quality measure for the whole assembly. This paper proposes to additionally include optical functions in the set of key characteristics. One important difference compared to plain mechanical assemblies is that constraints can be defined by parts that do not have a direct physical linkage. The modeling environment needs to support these circumstances. Furthermore, this paper shows how to formally define dependencies between KC's allow the derivation of the sequence of assembly steps (assembly sequence graph or precedence graph) and therefore the generation of platform independent assembly logic. KC's defining the desired relation between certain parts can be modeled hierarchically in order to derive mechanical constraints from optical ones. This information completes the assembly logic. Extending UML allows the use of standard computer-aided software engineering (CASE) tools. State-of-the-Art UML tools allow the application of text templates on such diagrams for generating machine readable code which can be processed further within the subsequent engineering tool-chain. By definition in this paper, one KC physically links two product features (PFLinkItem). Furthermore, a KC defines a geometric or a functional relationship. In order to describe such a relationship two more product features are referenced as key characteristic items (KCItem). KCItems and PFLinkItems can be the same product features as depicted in Fig. 4Fehler! Verweisquelle konnte nicht gefunden werden., left. This is the case when, for example, an optical element is bonded onto a carrier plate using geometric features such as parallelism and distance of edges. Sometimes it is necessary to physically link two product features while the key characteristic such as an optical function is defined by other items. Fig. 4Fehler! Verweisquelle konnte nicht gefunden werden., right, shows a configuration where Object1 (carrier) holds Object2 (lens) and Object2 is attached to Object3 (e.g. heat sink of a laser diode bar). The constraint on the physical linkage between Object1 and Object3 is determined by the optical function between Object3 and Object2. The alignment of micro-optical components fulfilling optical constraints often requires multiple steps. Firstly, the positioning system places the optical component using machine accuracy (pre-positioning). Secondly, the component is aligned according to geometric features (passive alignment) using machine vision and e.g. edge detection. Thirdly, many optical components require active alignment for directly optimizing the desired optical function. Fig. 5 shows an optical KC which is refined by other key characteristics (KCRefinement).

Fig. 5: Refinement of key characteristics (KCRefinement) and dependencies between key characteristics

Using the proposed UML profile, dependencies between key characteristics can be expressed. This is required for describing multi-step alignment (pre-positioning, passive alignment, active alignment). The combination of the features of refinement and dependency allows the expression of highly complex assembly constraints carrying all relevant information for subsequent assembly execution. Based on the formalized product configuration description the assembly sequence can be derived as explained in the following section.

Derivation of the assembly sequence and commissioning

The assembly sequence can be derived from the dependencies between key characteristics by evaluating the KCRefinement and KCDependency relation stereotypes in the formalized liaison diagram. The resulting Integrated Tool-chain Concept for Automated Micro-optics Assembly Full Paper, IPAS 2014 assembly sequence describes the assembly task in a platform-independent way because the assembly platform is not part of this description (vPIPP) and therefore no platform specific information is available. Neither resources such as manipulators and grippers nor coordinates are specified yet. Active alignment routines and other complex process steps are represented by placeholders at first. Within the context of the work presented, different tools are under development for efficiently planning sensor-based processes in a hybrid assembly process planning system. Once an alignment strategy is referenced as a subroutine by the placeholder its functionality is verified by an alignment-in-the-loop software tool. This tool uses the application programming interface of the commercial optical modelling and simulation software for manipulating the position and orientation of the lens under inspection. Output of the simulation is a simulated intensity profile of the optical setup which is processed by the alignment routine calculating corrective values for manipulating the lens. For the verification of alignment strategies, the lens under inspection is initialized randomly regarding its position and orientation and then the steps of processing the intensity profile, calculating the corrective value, and manipulating the lens virtually are carried out in a loop until the termination criteria is reached.

The transfer to a production platform requires two major steps: 1. teaching of coordinates in the VPS, 2. assigning reference mark detection routines. Teaching and planning based on a VPS minimizes standstill times of the physical production system. Fig. 6 shows different shapes of reference marks which can be detected in a standard way. This allows a mapping between model data and real world data during process execution.

Exemplary assembly specification

This section illustrates the application of the proposed formalism for specifying the assembly task of a collimation module for diode laser systems. The optical system consists of a fast-axis collimation lens (FAC) and a slow-axis collimation lens (SAC). The optics have to be aligned in a specific distance in order to fulfill the optical function of the module. Two side tabs are used for holding the optical components. The side tabs do not have an optical function. Fig. 7 shows the target configuration of the collimation module as a wire frame model (middle) and its representation in a liaison diagram (left).

Conclusion and outlook

This paper introduced a formal notation for specifying target configurations of micro-optical systems. The notation includes information about key characteristics which determine the optical function of the system as well as the constraints of each assembly step. Key characteristics can be refined in order to match the multistep alignment approach for optical systems comprising the steps of pre-positioning, passive alignment, and active alignment. Furthermore, the definition of dependencies between key characteristics can be exploited in order to generate a platform-independent assembly sequence. Future work will be dedicated to the realization of a tool-chain by implementing software tools for specifying the individual assembly steps in a level of detail which allows their execution through an assembly platform. The focus will be put on the specification of strategies for sensor-guided process steps and especially active alignment processes as the engineering of such processes is currently the bottleneck regarding the planning and commissioning of micro-optical assembly.

Fig. 2 :

 2 Fig. 2: Engineering phases for the assembly of micro-optical systems. Arrows indicate flow of information.

Fig. 4 :

 4 Fig. 4: Formalized target configuration patterns as liaison diagram and as formalized liaison diagram: key characteristic directly specifying the constraints on a physical linkage between two product features (left), key characteristic specifying the constraints on a physical linkage between two product features using a third product feature (right).

Fig. 3Fehler !

 3Fehler Fig. 3Fehler! Verweisquelle konnte nicht gefunden werden. shows two patterns of describing physical linkages between product features such as gluing areas or optical surfaces. Two types of representations are used in the figure. One representation (liaison diagram) uses a number code representing a product feature. The solid line connecting two product features stands for a physical linkage, the double line stands for a key characteristic specifying the constraints of the physical linkage. A constraint could be a specific geometric relation or an optical function. This kind of representation is applicable for intuitively sketching out target configurations. The second representation introduced by the authors is a formal representation of a liaison diagram (formalized liaison diagram) and it uses a newly defined UML profile and is semantically equivalent to the first one.Extending UML allows the use of standard computer-aided software engineering (CASE) tools. State-of-the-Art UML tools allow the application of text templates on such diagrams for generating machine readable code which can be processed further within the subsequent engineering tool-chain. By definition in this paper, one KC physically links two product features (PFLinkItem). Furthermore, a KC defines a geometric or a functional relationship. In order to describe such a relationship two more product features are referenced as key characteristic items (KCItem). KCItems and PFLinkItems can be the same product features as depicted in Fig.4Fehler! Verweisquelle konnte nicht gefunden werden., left. This is the case when, for example, an optical element is bonded onto a carrier plate using geometric features such as parallelism and distance of edges. Sometimes it is necessary to physically link two product features while the key characteristic such as an optical function is defined by other items. Fig.4Fehler! Verweisquelle konnte nicht gefunden werden., right, shows a configuration where Object1 (carrier) holds Object2 (lens) and Object2 is attached to Object3 (e.g. heat sink of a laser diode bar). The constraint on the physical linkage between Object1 and Object3 is determined by the optical function between Object3 and Object2. The alignment of micro-optical components fulfilling optical constraints often requires multiple steps. Firstly, the positioning system places the optical component using machine accuracy (pre-positioning). Secondly, the component is aligned according to geometric features (passive alignment) using machine vision and e.g. edge detection. Thirdly, many optical components require active alignment for directly optimizing the desired optical function. Fig.5shows an optical KC which is refined by other key characteristics (KCRefinement).

Fig. 6 :

 6 Fig. 6: Samples of reference marks with corresponding results from image-processing (from [4]).

Fig. 7 :

 7 Fig. 7: Representation of the target configuration of a collimation module. The wire frame sketch (middle) illustrates the optical system. The left column shows the formal representation.

Fig. 8 Fig. 8 :

 88 Fig.8depicts the assembly sequence of the collimation module. The additional nodes (A) and (B) represent mechanical end stops used for passive referencing. The dashed lines represent temporal linkages used during assembly. In step (a), the side tab is aligned temporarily using the mechanical endstops (A) and (B). In step (b), the FAC is inserted temporarily. In (c), the linkage is controlled by a key characteristic applying geometric constraint. In (d), the SAC is assembled regarding a geometric constraint between FAC and SAC. Steps (e) and (f) add the second side tab to the module. Picture (g) represents the final product with the fulfilled constraint.

Acknowledgement

The authors would like to thank the German Federal Ministry of Education and Research (BMBF) for the support of the work by financing the MANUNET-DeLas project (funding code 02PJ2542).