Aurélien Bénel

Sylvie Calabretto

Andréa Iacovella

Jean-Marie Pinon

Porphyry 2001: Semantics for scholarly publications retrieval

Keywords: Patron-augmented digital libraries, user interfaces and visualization systems, semantic nets, browsing/reading/annotating

We describe the design and algorithms of Porphyry 2001, a scholarly publication retrieval system. This system is intended to meet library user studies which advocate human interpretation and social interactions. The metaphors we used are annotations and publication (making public). We first discuss about different philosophical approaches to semantics and choose the more suited to scholarly work: the one considering a transitory, hypothetical and polemical knowledge construction. Then we propose an overview of Porphyry 2001: an hypertext system based on a dynamic structure of user annotations. The visualization and evolution of the structure (a dynamic directed acyclic graph) is made more efficient by the use of an ad hoc browsing algorithm.

Introduction

Our study is related to a digitalization project by the French school of archaeology in Athens 1 . This project aims at giving online access to one of its main periodical publications: "La Chronique des fouilles", an archeological excavations and findings yearly survey. This corpus has been chosen since although its size is reasonable (about 12,000 pages), it is nearly exhaustive in regards to the past 80 years of archaeological activity in Greece and Cyprus. Besides, the "Chronique" is daily read in libraries throughout the world.

We must stress that the information retrieval problem is not new concerning the "Chronique". Publishers have tried for 80 years to make it easier to consult. It is made of small independent parts (about 50,000) which are hierarchically structured and indexed according to artifact location, dating and typology. Archaeologists who have tried retrieval systems based on automatic indexing or manual indexing using thesauri are satisfied by none of them. The former is said to be inadequate because it deals with out-of-context terms. The latter is considered to be hard to manage over time by the indexing team since it needs periodic updates of both thesauri and indexes in order to reflect science progress. As a first example, there has been several years ago a polemic between two archaeologists about determining in ambiguous cases whether the border of a mosaic was black or white. An automatic indexing system would have extracted only the point of view in the text. Moreover, without knowing whom point of view it is, the index could not have been interpreted. As a second example, when the Copper Age has been inserted in the chronology between the Neolithic Period and the Bronze Age, a thesaurus-based system would have needed plenty of documents to be reinterpreted and re-indexed. Therefore, we had to study the most theoretical aspects of information retrieval (even philosophical aspects), to find an alternative for our system.

From semantics theories to workstations

Information retrieval (IR) as defined by Cornelis J. van Rijsbergen [START_REF] Van Rijsbergen | A new theoretical framework for information retrieval[END_REF] aims at matching relevant documents with user information needs. In order to be "computed", this matching has to be transmuted from the content space into the form space. Since computers cannot match the meaning of the information needs with the meaning of the documents, IR techniques tend to translate information needs into formal queries and documents into formal descriptions (also called "logical views" [START_REF] Baeza-Yates | Modern Information Retrieval[END_REF]). So one of the challenges in IR should be to minimize the gap due to this translation: the gap between signifiers and signified. This question is a central one in linguistic semantics.

Linguistic theroies of semantics

As stated by the French linguist François Rastier [START_REF] Rastier | Encyclopédie philosophique universelle[END_REF], there have been, among the various theories of semantics, mainly two streams: the first one (widely spread) from the logic community, the second one (nearly unknown) from the hermeneutic community. Whereas the former focuses on representation, the latter focuses on communication. Whereas, in the former, properties of a sign occurrence are inferred from relations between types (see "type hierarchies" in John F. Sowa [START_REF] Salton | Automatic Information Organization and Retrieval. Chapter: "Retrieval models[END_REF]), in the latter, there are only "source occurrences" and "revisited occurrences". Whereas the former makes the Aristotelian assumption of an ontology (from the Greek word "ontos" for "being"), the latter considers a transitory and hypothetical knowledge construction.

Since the system we want to design is for scientists, we will adopt the hermeneutical view of semantics (see our prior work [START_REF] Bénel | Truth in the digital library: from ontological to hermeneutical systems[END_REF]). Indeed, this approach is more adapted to modern science by highlighting the constructivist nature of scientific knowledge (see Karl R. Popper [START_REF] Popper | Objective Knowledge: an Evolutionary Approach[END_REF] and Thomas S. Kuhn [START_REF] Kühn | The Structure of Scientific Revolutions[END_REF]).

It is worth noting that the need for both interaction and communication has been highlighted in experimental studies about traditional library users.

Kenton O'Hara et al. [START_REF] O'hara | Student readers' use of library documents: implications for library technologies[END_REF] studied the document-related research activities of PhD students during a working day. The induced model characterized the work carried out by university library users as going beyond the traditional searching and retrieving of information. In that way, note making, photocopying, bibliographic searching, reading, annotating, information reviewing, and documents writing should be considered as a whole.

In a different setting, Andreas Paepcke [START_REF] Paepcke | Digital libraries: Searching is not Enough. What we learned on-site[END_REF] interviewed engineers involved for example in customer support or in design in order to learn about their information needs and habits. He concluded that even if retrieving information is central, it is interwoven with discovering, managing, interpreting and sharing information and that all of these activities need the communication between humans.

But oddly enough, very few digital library systems at this time support social interactions [START_REF] Tochtermann | A first step toward communication in virtual libraries[END_REF] and patron-augmentation [START_REF] Goh | Patron-augmented digital libraries[END_REF] (see [START_REF] Röscheisen | Beyond browsing: shared comments, soaps, trails and on-line communities[END_REF] also).

Because science carries more than interactions among individuals, systems should go one step further by supporting groups. Scientific groups (from working groups to colloquiums) are important for knowledge construction in the process of becoming more objective.

Knowing the knowledge of each individual, the question becomes: "What is the knowledge of the group?" Expressed in a different way: "How do we get a syntactic and semantic coherence from these different (and even contradictory) models?" If these questions are opened for Knowledge Managing in general, they have got an answer for years in the scientific praxis: publication.

In the traditional publication process, the "publishers" (real publishers, reviewers, committees…) check submitted papers regarding form and contents in order to ensure its validity for the group. Then the authority given to the publishers is transferred to the papers themselves. As a result we propose that in our system scientists can choose to join groups headed by "publishers" they consider as authorities and that their knowledge representations can be "published" through a reviewing process just like in the physical world.

Porphyry 2001 overview 2

Porphyry 2001 is a client-server system aiming at creating, retrieving and sharing documents and annotations. Its architecture (see Figure 1) is grounded on the distinction between content and structure.

The content server is a classic web server with an ad hoc "servlet". Given extraction parameters, it is able to deliver fragments from web accessible documents (only plain-text and JPEG images for now).

The structure server use a database server to store and retrieve data and meta-data. Both are handled in the same way: they are filtered by the structure server and formalized through the same directed acyclic graph model. In this model, if, for two descriptors D 1 and D 2 , D 1 → D 2 , then any document described by D 2 is described by D 1 too. It is worth mentioning that only edges and nodes have significance for the 2 The Porphyry Project Page: http://lisi.insa-lyon.fr/projets/descrippr27.htm system. But, so that users can interpret the graph, we store labels too. Node labels contain short descriptions and edge labels contain information (see the edge popup label in Figure 2 at the center) about their creation (user, date) and publication (group, date). As long as the formal signification of this framework is kept, users are free to use it in order to represent (see Figure 3): specialization, composition, attributes, attribute values, relations…. The graph being accessed by a user can be split into different sub-graphs depending on their ownership and performance considerations.

Context and structure are combined either by the native client (see Figure 2) or by the web interface server (so that a classic web client can access it). Although the web interface is dedicated on browsing, the native client allow the researcher to upload new documents, to define new fragments, and to modify also his/her own corpus structure.

Scenario of user interactions

In this section, we will trace step by step an example of computer-human interactions involved in document retrieval. Our schema (Figure 4) will show both the annotation graph as displayed by Porphyry 2001 and the user actions. As shown in the Figure 4, let us navigate in the Figure 3 indexing graph…

• Step #1.
The global corpus deals with "vestige typé". More specialized corpora exist dealing with "daté" or "épigraphique" or "instrumenta/mobilier" but not with "architectural" (since this descriptor corresponds to no document). When the user selects "instrumenta/mobilier", the system jumps to step #2.

• Step #2.

The selected corpus deals with "vestige de type instrumenta/mobilier". This describes exactly the document which has the identifier "2". More specialized corpora deal with "mobilier paléochrétien" or "vase" but neither with "architectural" nor with "épigraphique". When the user selects "vase", the system jumps to step #3.

• Step #3.

The selected corpus deals with both "vestige de type vase (instrumenta/mobilier)" and "vestige daté". Please note that "daté" is automatically inferred (since all documents dealing with "vase" deals also with "daté"). More specialized corpora deal with "mobilier paléochrétien", "vase paléochrétien", "vase archaïque", "paléochrétien" or "archaïque" but not with "architectural", "épigraphique", "classique" or "2". When the user selects "archaïque", the system jumps to step #4. • Step #4.

The selected corpus deals with "vestige de type vase (instrumenta/mobilier) daté de l'époque archaïque". This corpus contains only one document, the one with "5" as its identifier. Step # 1 :

Step # 3 :

Step # 4 :

Step # 2 :

Algorithms

In the two preceding scenari, the annotation graph was filtered. As a matter of fact, most of interactive information retrieval systems (see Marti Hearst [START_REF] Hearst | User interfaces and visualization[END_REF]) focus on reducing cognitive load by filtering information. In our system, the filtering algorithm is a valuable help in navigating through corpora. Since searching and indexing are both corpora discriminations, our filter can be seen as an assistant for both refining a query and reusing descriptors for a new indexing. We will now explain our algorithm in detail. Gerard Salton in the late 60's [START_REF] Salton | Automatic Information Organization and Retrieval. Chapter: "Retrieval models[END_REF] defined a set-theoretical model of information retrieval. It deals with a set of "descriptors" and a set of documents. In that way, we can draw the corpus inclusion (see Figure 5) and the request conjunction graphs (see Figure 6). Then, from the mapping of documents with descriptors (see Table 1), we can deduce the mapping of requests with documents corpora (see Table 2). From that point, we can figure out that several corpora can't be obtained by any request (e.g. {B,C}) and that the same corpus can be obtained by different requests (e.g. request a AND b with request b). Although these results are widely known, they have been, as far as we know, rarely used as interaction media. Table 1. Sample mapping of documents A, B, C, D with descriptors a, b, c.

Descriptors

a b c A X X B X X C X Documents D X
Table 2. Mapping of requests with documents corpora (computed from Table 1). Claudio Carpineto et al. [START_REF] Carpineto | Dynamically bounding browsable retrieval spaces: an application to Galois lattices[END_REF] used Boolean logic results by removing from the corpus inclusion graph every inaccessible corpora in order to get a static generalization/specialization diagram of documents classes (see Figure 7).

TRUE

In our approach (see our prior works [START_REF] Bénel | Vers un outil documentaire unifié pour les chercheurs en archéologie[END_REF] for more details) we preferred to join together, in the requests graph, requests which describe the same corpus. By doing so, we get a state-chart diagram (see Figure 8) in which states correspond to corpora and transitions correspond to elementary requests. These one-descriptor-requests on transient corpora can be seen as the addition of a descriptor to the global request: a kind of query refinement.

Owing to the preceding state-chart, in a given state (result of the selection of a set of descriptors) any refinement can be said:

• Impossible: if it leads from the current corpus to the empty corpus (e.g. descriptor c in state {B} see Figure 8), • Known: if it leads from and to the current corpus (e.g. descriptor a in state {B}, descriptor b in state {B} see Figure 8), • Possible: otherwise. The filter consists in showing only known descriptors and their "children" and in assigning its corresponding state to any showed descriptor. The scenari shown in Figure 4 illustrates the use of this filter on a simple example. We can also have a look at real size examples in Figure 1.

Discussion

At this point, a few aspects should be discussed about Porphyry 2001 system.

Starting from scratch

The digital library system we have presented is based on patron-augmentation. But, for such an evolutionary approach, the question is: "Evolution? From what?". Can we give an "empty box" to users? If document retrieving is based on annotations, how could the first annotator of a document retrieve it?

As a matter of fact, some information can be automatically loaded in the descriptor graph:

• The title hierarchy of the semi-structured document (since this structure describes each section), • Manual (or intellectual?) controlled indexes stored in document appendices, • Automatically extracted key-words or key-phrases (structured for example regarding alphabetical order or formal clusters). One should note that there are neither thesauri, nor "ontologies", nor even concepts which are approved by the whole archaeological community. Therefore we cannot reuse them as a bootstrap for our sytem. But, on the contrary, the collaborative use of Porphyry 2001 system could lead archaeologists to normalize such definitions. From an archeological point of view, this is one of the main challenge of using the system.

Combinatory explosion

Another important question deals with the algorithmic complexity of our graph filter. On the one hand the system must give results in less than a few seconds (in order to remain usable in an interactive process). On the other hand it is difficult to evaluate the theoretic complexity of the algorithm since there are a very few constraints on the partial order structure.

To find a practical answer, we must consider the use of the system. As we saw, the graph which is browsed by a given user, is made of its personal graph and the graphs from the groups he/she has registered.

Firstly, these graphs are connected only by the "root" descriptor and by identifiers. They are independent indexing dimensions. That is what information sciences call "facets". Because of their independence, the complexity of n groups is only n times the complexity of 1 group and, moreover, the algorithm can be run in parallel on n servers (one per group) so that the computing time for n graphs is nearly the same as for 1 graph.

Secondly, the nature of personal graphs and group graphs are quite different. The latter are rather bigger than the former and is updated much less often (only during the publication process). So it is interesting to make pre-computation of the group graphs. In fact the involved algorithms consist in recursively deducing relations and in doing basic set operations. We chose to do in advance recursive computations only and to do "on the fly" set operations (database management systems are good for it). It seems to be a good compromise between mass memory use and response time.

The two proposed optimizations (multiple servers and pre-computation) have been implemented and used. We plan for the next months to test them with huge real data.

Evaluating interactive information retrieval

Let us study a few epistemological aspects. Since science is based on falsification (see Karl R. Popper [START_REF] Popper | Objective Knowledge: an Evolutionary Approach[END_REF]), a theory must be testable to be said "scientific". A test is an experiment that can make the theory getting false (by deduction modus tollens). A test result is particular but not singular: it must be obtained and obtained again at anytime by anybody at anyplace. A succeeding test result is a result that "breaks" the theory. Moreover, since methods are based on the domain paradigms (see Thomas S. Kuhn [START_REF] Kühn | The Structure of Scientific Revolutions[END_REF]), testing protocols must be validated by the scientific community.

We would like to stress a few points. First, the scientist must propose a test but shouldn't lead the test. The community should test it. A testable theory is "objective" and doesn't need anymore the subject who have invented it. By the way, it is psychologically difficult for a human to break his/her own work… On the contrary, it is so great to break somebody else's work! Second, because we work on interactive information retrieval and so with human individuals, it seems to be difficult to get particular results. Does it make sense to compare the activity of two users, especially when each of them is the world expert in his/her domain? Does it make sense to compare activities of a same user with two interactive systems (knowing that he/she may have learned "something" during the first activity)?

For us, it would be important if this kind of methodological aspects were discussed by the IR community. If these points were clearer, then we could ask the community to validate or invalidate the following protocol.

Our protocol (its setup is in progress) relies on the "reality" of the test: real users doing their own activities with real information and for a long time. Firstly, we propose to compare two interfaces to access the same data (250,000 records of archeological photographs descriptions): the classical QBE interface (query by example) and ours. Secondly, we propose to log over time the growing of the descriptors graph (for "La Chronique des fouilles") in order to know if the evolution we hope for is real or not.

Conclusion

The system we have presented proposes a framework for free descriptors created either by machines (words or phrases occurrences…) or by human (categories, annotations…). Most of all, owing to collaboration and dynamics, it can be used as a debate media. Every annotation is dated and authored, so that it can be interpreted, contradicted by another annotation, or considered as obsolete.

We aim at giving the user a system just like the "memex" Vannevar Bush [5] dreamt of. The reader could retrieve his/her former mind "trails" and others' ones (colleagues, tutors, librarians…). The automatic system would be there to assist the reader in his task by ridding him of repetitive aspects of his/her activity, so that he/she could focus on creative and intuitive aspects of his/her work.

Fig. 1 .

 1 Fig. 1. Corpus consulting through Porphyry multi-tiers architecture.

Fig. 2 .

 2 Fig. 2. Porphyry client screenshot.

Figure 3 -

 3 Figure 3 -Sample index structure.

Figure 4 -

 4 Figure4-Retrieval scenario (see index structure in Figure3).

Figure 5 -Figure 6 -

 56 Figure 5 -Lattice structure of documents space. Legend C1 C2 : C2 ⊂ C1

Fig. 7 .

 7 Fig. 7. Class diagram [18] derived from documents space.

Fig. 8 .

 8 Fig. 8. State-chart diagram [18] derived from descriptors space.

Ecole française d'Athènes (http://www.efa.gr)


Gerd Behrmann
email: behrmann@cs.aau.dk

Agnès Cougnard

Alexandre David
email: adavid@cs.aau.dk

Emmanuel Fleury
email: fleury@labri.fr

Kim Guldstrand Larsen

Didier Lime
email: didier.lime@irccyn.ec-nantes.fr

UPPAAL-Tiga: Time for Playing Games!

à la diffusion 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.

Introduction

For more than a decade timed, priced and hybrid games have been proposed and studied by various researchers [START_REF] Asarin | Controller Synthesis for Timed Automata[END_REF][START_REF] De Alfaro | Symbolic Algorithms for Infinite-State Games[END_REF][START_REF] Maler | On the Synthesis of Discrete Controllers for Timed Systems[END_REF][START_REF] Bouyer | Optimal Strategies in Priced Timed Game Automata[END_REF]. Though several decidability results and algorithms have been presented, so far only prototype tools have been developed [START_REF] Altisen | Tools for controller synthesis of timed systems[END_REF]. Uppaal-Tiga 1 is the first efficient tool supporting the analysis of timed games allowing synthesis of controllers for control problems modelled as timed game automata and with safety or liveness control objectives.

What Can Be Done with Uppaal-Tiga?

Control Problems. The modeling formalism of Uppaal-Tiga consists of a network of timed game automata [START_REF] Maler | On the Synthesis of Discrete Controllers for Timed Systems[END_REF] (NTGA). A timed game automaton is a timed automaton [START_REF] Alur | A Theory of Timed Automata[END_REF] in which the set of actions is partitioned into controllable actions and uncontrollable actions. The former are actions that can be triggered by the controller, the latter by the environment/opponent. The opponent has priority over the controller. Given a NTGA, we are mainly interested in two types of control objectives:

The reachability objective: Is it possible to find a strategy for the triggering of controllable actions guaranteeing that a given set of (goal) states of the system is reached regardless of what and when uncontrollable actions are taken?

The safety objective: Is it possible to find a strategy for the triggering of controllable actions guaranteeing that a given set of (bad) states of the system are never reached regardless of what and when uncontrollable actions are taken?

Formally, control objectives are formulated as "control: P", where P is TCTL formula specifying either a safety property (

A[] φ or A[φ 1 W φ 2 ]) or a live- ness property (A<> φ or A[φ 1 U φ 2 ]
). Given a control objective "control: P" the search engine of Uppaal-Tiga will provide a strategy (if any such exists) under which the behaviour will satisfy P. Here a (winning) strategy is simply a function describing for each state of the system what the controller should do either in terms of "performing a particular controllable action" or to "delay".

1 2 3 4 Goal 5 x ≤ 1;c1 x > 1;u1 x < 1 u2 x := 0 x ≥ 2;c2 x < 1 u3 c3 x ≤ 1;c4

Fig. 1. Timed game automaton example

Example. To illustrate the use of Uppaal-Tiga, consider the example in Fig. 1, consisting of a timed game automaton A with one clock x. It has two types of edges: controllable (c i ) and uncontrollable (u i ). A defines the rules of the game. In our current example (Fig. 1), we define the simple reachability objective "control: A<> A.Goal". Uppaal-Tiga searches for a winning strategy on this game using the algorithm proposed in [CDF + 05]. Each winning condition, entered in Uppaal-Tiga as a regular query, is marked as "satisfied " if there exists a winning strategy and "not satisfied " if none exists. Hence, in our example, the query "control: A<> A.Goal" will be marked "satisfied ". Moreover, the tool can output the corresponding strategy from the command line or let the user play against it in the simulator as shown in Fig. 2. For controllable games (here), Uppaal-Tiga plays the controller and the user is the opponent. The first transition is for the controller (Uppaal-Tiga), the second for the opponent (user), and the third is for the opponent but it will be countered by the controller (Uppaal-Tiga takes the transition to 2 ), hence it is greyed -the opponent cannot take this action.

Applications. Uppaal-Tiga has recently been used for an industrial case study with the company Skov A/S specializing in climate control systems used for modern pig and poultry stables [START_REF] David | Guided Controller Synthesis for Climate Controller Using UPPAAL-TIGA[END_REF]. The synthesis capability of the tool has been combined with Simulink and Real-Time Workshop to provide a complete tool chain for synthesis, simulation, and automatic generation of production code.

Uppaal-Tiga has also been recently applied to check for (bi-)simulation between timed automata and timed game automata [START_REF] Chatain | Playing Games with Games[END_REF]. Given two timed Fig. 2. View of the simulator when playing a strategy automata, the tool can check if one (bi-)simulates the other and similarly for timed game automata with applications for controller synthesis with partial observability. This technique has been applied to the compositional verification of the ZeroConf protocol.

Our tool is being used in the AMAES project2 , a French national project on Advanced Methods for Autonomous Embedded Systems. Uppaal-Tiga has been successfully applied for controlling the autonomous robot Dala [START_REF] Lemai-Chenevier | IxTeT-eXeC: planification, réparation de plan et contrôle d'exécution avec gestion du temps et des ressources[END_REF] in charge of taking pictures and transmitting them back to Earth during limited transmission windows. It is desirable in such control problems to optimize the moves to save power.

What Is New?

Input Language. The new generation of Uppaal-Tiga inherits the enriched input language of Uppaal-4.0, with the only exception of priorities. The user has now access to C-like syntax to declare functions, custom types, etc. In addition, users can now define more complex winning conditions by means of logical formulas in the indicated subset of TCTL.

Strategies. Uppaal-Tiga is able to generate a strategy for the controller, which ultimately corresponds to a control program, or a "counter-strategy" for the opponent as a proof that the controller cannot win. These strategies can now be output as decision graphs (hybrid BDD/CDD graphs). The discrete part of the states is represented as a BDD and the symbolic part as a CDD [START_REF] Larsen | Clock Difference Diagrams[END_REF]. Finally, Uppaal-Tiga allows the user to play against the strategy in both the GUI3 and CLI.

Performances. Uppaal-Tiga is faster by several orders of magnitude on large examples (more than 1000 times faster) and consumes much less memory (100 times less) than the first prototype presented at CONCUR'05. This comes from the full integration of the algorithm in the Uppaal-4.0 [BDH + 06]4 framework. This brings to Uppaal-Tiga some of the reliability and performances achieved by years of Uppaal developments. Also improvements have been made on the DBM library, in particular on subtractions, partitions, federations, specific operations for timed games (e.g. the computation of controllable predecessors w.r.t. delay), and the essential operation of merging several difference bound matrices (DBMs) into one.

Conclusion

Uppaal-Tiga is a new (and the only efficient) tool for controller synthesis for control problems modeled as timed game automata. Its performance and usability has greatly been improved by its integration with Uppaal-4.0. In a future version methods for preventing synthesis of strategies generating zeno behaviour will be provided. Also the computationally much more complex problem of synthesis under partial observability is under investigation.

http://www-verimag.imag.fr/∼krichen/AMAES/

This is a major new feature for the next major release.

http://www.uppaal.com


Tokelo I Letshedi

Jean-Claude Malela-Majika

Philippe Castagliola

Sandile C Shongwe
email: sandile@tuks.co.za

Distribution-free triple EWMA control chart for monitoring the process location using the Wilcoxon rank-sum statistic with fast initial response feature

Keywords: Double EWMA chart, EWMA chart, Fast initial response, Nonparametric chart, Overall performance, Run-length, Triple EWMA

The exponentially weighted moving average (EWMA) control chart is a memory-type chart known to be more efficient in detecting small and moderate shifts in the process parameter. The double EWMA (DEWMA) chart is an extension of the EWMA chart that is more effective than the latter in the detection of small-to-moderate shifts. This paper proposes a new distribution-free (or nonparametric) triple EWMA (TEWMA) control chart based on the Wilcoxon rank-sum (W) statistic to improve the detection ability in the process location parameter. Moreover, a new fast initial response (FIR) feature is added to further improve the sensitivity of the new TEWMA chart. The performance of the proposed TEWMA chart with and without FIR features is compared to those of the existing EWMA and DEWMA W charts. It is observed that the TEWMA chart with and without FIR features is superior to the competing charts in most situations. A real-life illustration is provided to show the application and implementation of the new chart.

Introduction

All production lines and service-rendering establishments are recommended to use statistical process monitoring (SPM) techniques. This will assist with producing or rendering high quality services or products that will meet needs of end users with low risk benefits. In applications where very little information is known about the underlying process, it is mostly advised to use nonparametric or distribution-free charts rather than the parametric ones. This is because they do not depend on any specific underlying distribution and they are generally in-control (IC) robust; see for instance, the arguments in Chakraborti and Graham [START_REF] Chakraborti | Nonparametric Statistical Process Control[END_REF] . For efficiency, memory-type control charts are usually used to detect small-to-moderate shifts of any process parameter. There are four different types of memory-type control charts in the SPM literature and these are: (i) Exponentially weighted moving average (EWMA) chart by Roberts 2 , (ii) Cumulative sum (CUSUM) chart by Page 3 , (iii) Generally weighted moving average (GWMA) chart by Sheu and Lin [START_REF] Sheu | The generally weighted moving average control chart for detecting small shifts in the process mean[END_REF] , and (iv) Homogeneously weighted moving average (HWMA) chart by Abbas [START_REF] Abbas | Homogeneously weighted moving average control chart with an application in substrate manufacturing process[END_REF] . For more detailed studies or literature reviews on the latter memory-type schemes, see Hawkins and Olwell 6 , Ruggeri et al [START_REF] Ruggeri | Exponentially weighted moving average (EWMA) control chart[END_REF] , Mabude et al [START_REF] Mabude | Generally weighted moving average monitoring schemes -Overview and Perspectives[END_REF] , Nawaz and Han 9 , Abid et al [START_REF] Abid | A mixed HWMA-CUSUM mean chart with an application to manufacturing process[END_REF] , Adegoke et al [START_REF] Adegoke | Efficient homogeneously weighted moving average chart for monitoring process mean using an auxiliary variable[END_REF] and Adeoti and Koleoso [START_REF] Adeoti | A hybrid homogeneously weighted moving average control chart for process monitoring[END_REF] . The focus of this paper is on improving the performance of the nonparametric EWMA-type charts to monitor the process location, especially during start-up period. Improving the performance of the EWMA-type control charts during start-up period has never been addressed for the nonparametric SPM context. For some recent contributions to nonparametric charts, refer for instance to Mukherjee et al [START_REF] Mukherjee | Comparisons of some distribution-free CUSUM and EWMA schemes and their applications in monitoring impurity in mining process flotation[END_REF] , Triantafyllou [START_REF] Triantafyllou | A new distribution-free control scheme based on order statistics[END_REF] , Chong et al [START_REF] Chong | Performance comparisons of distribution-free Shewhart-type Lepage and Cucconi schemes in monitoring complex process distributions[END_REF][START_REF] Chong | Some simplified Shewhart-type distribution-free joint monitoring schemes and its application in monitoring drinking water turbidity[END_REF] and Shafqat et al [START_REF] Shafqat | A nonparametric repetitive sampling DEWMA control chart based on linear prediction[END_REF] . Next though, a literature review of some related parametric research works are discussed and thereafter, the objective of this paper is outlined.

With an end goal to increase the responsiveness of the EWMA control charts to detect small shifts in a process mean, Shamma and Shamma [START_REF] Shamma | Development and evaluation of control charts using double exponentially weighted moving averages[END_REF] proposed the double EWMA (DEWMA) control chart. Originally not aware of the latter paper, Zhang and Chen [START_REF] Zhang | An extended EWMA mean chart[END_REF] also studied the performance of the DEWMA chart to monitor the process mean; note though, there are additional aspects that were considered in the latter paper but absent in the former. Some additional studies on the DEWMA charts in different contexts can be found in Hong et al [START_REF] Hong | DEWMA control chart for the coefficient of variation[END_REF] , Alkahtani [START_REF] Alkahtani | Robustness of DEWMA versus EWMA control charts to non-normal processes[END_REF] , Teh et al [START_REF] Teh | Comparing the median run length (MRL) performances of the max-EWMA and max-DEWMA control charts for skewed distributions[END_REF] , Chao et al [START_REF] Chao | An intelligent GA-nonparametric DEWMA sign chart for green chain management[END_REF] and, Alevizakos and Koukouvinos [START_REF] Alevizakos | Monitoring of zero-inflated binomial processes with a DEWMA control chart[END_REF] . Based on latter publications, it is generally accepted that the DEWMA charts are more sensitive than EWMA charts for small-to-moderate shifts. For the nonparametric case, Karakani et al [START_REF] Karakani | A double generally weighted moving average exceedance control chart[END_REF] showed that the DEWMA based on the exceedance statistic is superior to the EWMA one in detecting small shifts.

The focus of this paper is on the Wilcoxon rank sum statistic, denoted as . Note that Li et al [START_REF] Li | Nonparametric CUSUM and EWMA control charts for detecting mean shifts[END_REF] Therefore, the main objective of this paper is to improve further on the research works by Li et al [START_REF] Li | Nonparametric CUSUM and EWMA control charts for detecting mean shifts[END_REF] and Malela-Majika [START_REF] Malela-Majika | New distribution-free memory-type control charts based on the Wilcoxon rank-sum statistic[END_REF] , by proposing a new triple EWMA (TEWMA) chart to monitor the process location shifts and then compare its performance to that of EWMA and DEWMA charts. Note that there is no work in the SPM literature that addresses the use of TEWMA chart in a distribution-free context. To the best of authors' knowledge, Alevizakos et al [START_REF] Alevizakos | The triple exponentially weighted moving average control chart[END_REF][START_REF] Alevizakos | A triple exponentially weighted moving average control chart for monitoring time between events[END_REF] investigated the performance of the TEWMA chart for monitoring the process mean and time between events, respectively. Moreover, Alevizakos et al [START_REF] Alevizakos | The triple exponentially weighted moving average control chart[END_REF][START_REF] Alevizakos | A triple exponentially weighted moving average control chart for monitoring time between events[END_REF] compared the performance of each TEWMA chart against the corresponding EWMA and DEWMA charts, where it is observed that the TEWMA charts have better performance in most situations.

Note though, for thorough derivations of the run-length properties of the TEWMA chart for any independent and identically distributed (i.i.d.) process, readers are referred to Alevizakos et al [START_REF] Alevizakos | The triple exponentially weighted moving average control chart[END_REF] .

The fast initial response (FIR), initially suggested in the SPM literature by Lucas and

Crosier [START_REF] Alevizakos | A triple exponentially weighted moving average control chart for monitoring time between events[END_REF] , is a head-start feature with similar (but, slightly more pronounced) positive effects compared to the time-varying control limits as it identifies issues during the start-up period.

Thereafter, more researchers have used this enhancement technique at the start-up period of the monitoring process; see for instance Rhoads et al [START_REF] Rhoads | A fast initial response scheme for the exponentially weighted moving average control chart[END_REF] , Knoth 40 and Lu [START_REF] Lu | Applying fast initial response features on GWMA control charts for monitoring autocorrelation data[END_REF] . Note that Steiner 42 proposed the use of a more formal multiplicative factor expression that yields tighter control limits at start-up and converges to the standard control limits as time increases.

∑ ( ) (1)
Assuming that there are no ties (i.e. duplicated values in the combined observations), the mean and the variance of the statistic are respectively given by (see for instance Li et al [START_REF] Li | Nonparametric CUSUM and EWMA control charts for detecting mean shifts[END_REF] ): and

(2)

The EWMA W control chart

The EWMA chart was proposed by Li et al [START_REF] Li | Nonparametric CUSUM and EWMA control charts for detecting mean shifts[END_REF] and its charting statistic is defined by

where is a smoothing parameter and . After some basic algebraic manipulation, the mean and variance of (3) are respectively given by and (4)

( )
Hence, the upper and lower control limits of the EWMA chart are computed as follows:

(

where is the control limits coefficient which has to be calculated such that the attained IC ( ) is close or equal to the pre-specified nominal . Thus, the EWMA chart gives a signal if plots beyond the control limits.

The DEWMA chart

The DEWMA chart was proposed by Malela-Majika [START_REF] Malela-Majika | New distribution-free memory-type control charts based on the Wilcoxon rank-sum statistic[END_REF] and its charting statistic is given by (6) where is as given in (3) and . That is, the smoothing procedure is applied twice, i.e. the first smoothing is done in (3) and the second one is done in (6). After some basic algebraic manipulation, the mean and variance of ( 6) are respectively given by and ( 7)

[ ]

with

. Hence, the upper and lower control limits of the DEWMA chart are computed as follows:

where is the control limits coefficient which has to be calculated such that the attained is close or equal to the pre-specified nominal . Thus, the DEWMA W chart produces an OOC signal when value plots beyond the control limits in (8).

The design of the TEWMA chart with and without FIR features

TEWMA chart without FIR features

The TEWMA design entails applying the smoothing procedure three times; instead of twice as for the DEWMA or once as for the EWMA. Following on similar line of argument as Alevizakos et al [START_REF] Alevizakos | The triple exponentially weighted moving average control chart[END_REF] , it follows that the charting statistic of the TEWMA chart is given by (9) where is given in ( 6) and . From ( 3), ( 6) and ( 9): (10) that is, the original statistic in (1) goes through a smoothing procedure three times; hence, simplifying each expression in (10) leads to the following:

∑ ∑ ∑ (11)
Substituting into , and thereafter substituting into , then after some algebraic manipulations, the charting statistic of the TEWMA chart can also be re-written as

∑ ( ) (12)
For a more detailed algebraic derivation in the case of the parametric TEWMA ̅ chart, readers are advised to consult Alevizakos et al [START_REF] Alevizakos | The triple exponentially weighted moving average control chart[END_REF] . Hence, the mean and variance of ( 9) or (12) are respectively given by and ( 13)

( ∑ )
The simplified version of the is given in the Appendix. The upper and lower control limits are respectively given by (14) where is the control limits coefficient which has to be calculated such that the attained is close or equal to the pre-specified nominal . Thus, the TEWMA chart gives an OOC signal when value plots beyond the control limits in (14).

TEWMA chart with a basic FIR feature

To improve the sensitivity of the standard TEWMA chart in detecting shifts during startup, the basic FIR feature is added. This feature can be implemented to get an early alert at the beginning period of monitoring (when a change is suspected to be present) or after an OOC signal. The basic FIR feature proposed by Steiner [START_REF] Steiner | EWMA control charts with time-varying control limits and fast initial response[END_REF] is computed as

(15a)
where it is suggested to use and , with as a segment of an interval from a start-up value to the control limits. Based on the latter formulation, Steiner [START_REF] Steiner | EWMA control charts with time-varying control limits and fast initial response[END_REF] showed that the FIR feature has 'very little to none' effect in narrowing control limit of the time-varying control chart after the 20 th observation. Combining ( 14) and (15a) yields the control limits of the FIR-TEWMA chart:

(15b)

At time , the FIR-TEWMA chart produces an OOC signal when value plots beyond the control limits in (15b).

TEWMA chart with a MFIR feature

As an improvement to Steiner [START_REF] Steiner | EWMA control charts with time-varying control limits and fast initial response[END_REF] 's FIR feature, Haq et al [START_REF] Haq | Improved fast initial response features for exponentially weighted moving average and cumulative sum control charts[END_REF] introduced the MFIR feature. The MFIR is computed as

( ) ( ) (16a)
Combining ( 14) and (16a) yields the control limits of the MFIR-TEWMA chart:

(16b)

The MFIR-TEWMA chart produces an OOC signal at time when value plots beyond the control limits in (16b). Haq et al [START_REF] Haq | Improved fast initial response features for exponentially weighted moving average and cumulative sum control charts[END_REF] similarly showed that after the 20 th observation, the MFIR feature has a 'very little to none' effect on narrowing the control limits of the timevarying control chart.

TEWMA chart with a IMFIR feature

This paper also proposes a new FIR feature called the IMFIR feature where the power transformation factor is multiplied by square root of time. As it will be seen, the advantage of this new feature is that the sensitivity of the proposed TEWMA chart increases the ability to detect any shifts at start-up period of the process as soon as possible. That is, it allows time-varying control limits to be narrower at the early stages of the process to better detect start-up problems, while ensuring that the long-run properties of the time-varying monitoring scheme are not disturbed. The IMFIR feature is defined by

( ) √ ( ) (17a)
where the values of and are taken as 0.5 and 0.3, respectively. Combining ( 14) and (17a) yields the control limits of the IMFIR-TEWMA chart:

(17b)

The IMFIR-TEWMA chart produces an OOC signal when value plots beyond the control limits in (17b).

In Figure 1, the adjustment factors in (15a), (16a) and (17a) are compared against each other as time increases. This is an extension of Figure 1 in Haq et al [START_REF] Haq | Improved fast initial response features for exponentially weighted moving average and cumulative sum control charts[END_REF] to illustrate how the new IMFIR feature is an improvement of both FIR and MFIR features by Steiner [START_REF] Steiner | EWMA control charts with time-varying control limits and fast initial response[END_REF] and Haq et al [START_REF] Haq | Improved fast initial response features for exponentially weighted moving average and cumulative sum control charts[END_REF] . The adjustment factors of FIR, MFIR and IMFIR converge to unity as time increases;

based on Figure 1, it is apparent that those of FIR and MFIR does so at time point equal to 24, while that of IMFIR does so at time point equal to 32. Moreover, while the adjustment factor of MFIR is smaller than that of FIR whenever 15 and thereafter, they are equal; that of IMFIR is only equal to those of FIR and MFIR at sampling time 32 and onwards. This implies that the IMFIR feature reduces the control limits much further than the FIR and MFIR features at the start-up period (while not disturbing its long-run properties), and thus increase the detection capability of a time-varying TEWMA scheme.

The implementation of IMFIR-TEWMA charts

The IMFIR-TEWMA chart can be implemented as follows:

Step 1: Generate a phase I sample of size m, , from an IC process (e.g., from N(0,1)).

Step 2: Generate a phase II sample of size n, . When the process is IC, the distributions of the phases I and II are identical (i.e. 0). Otherwise, the distribution for the phase II sample is taken to be similar to that for the phase I sample, but with a change in the mean parameter ( 0) (e.g. from N( ,1)).

Step 3: The statistic is computed by combining the phase I and phase II samples using (1).

Step 4: Find the mean and variance of when the process is IC using (2). These are used in

Steps 5 and 6.

Step 5: Compute the plotting statistic using ( 9) or ( 12) and choose such that the attained 500. The time-varying control limits of the IMFIR-TEWMA chart are calculated using (17b).

Step 6: The IMFIR-TEWMA chart gives a signal if the plotting statistic computed is Step 5 plots beyond the control limits calculated in Step 5.

The FIR-TEWMA and MFIR-TEWMA charts can also be implemented in a similar way.

Performance analysis and comparisons of the proposed control charts 4.1 Performance metrics

The run-length (RL), ARL, standard deviation of the RL (SDRL) and expected ARL (EARL) characteristics are often used to explore how sensitive is the explored control chart. The RL refers to the number of charting statistics to be plotted on the chart before the first OOC signal. In this paper, Monte Carlo simulations are used with 20 000 replications to assess the TEWMA schemes with and without FIR features. When the overall performance is of interest, the EARL metric is recommended. The EARL is mathematically defined by

] ∑ (18)
where is the number of increments between the (lower limit of ) and (upper limit of ).

IC robustness

To study the robustness of the proposed charts, three distributions are considered, i.e., the standard normal (denoted as N(0,1)), Student's (v) (with v = 5, 15 and 30), Gamma ( ,

(denoted by GAM( ,1) with 1, 3 and 15) distributions are used. A control chart is considered to be IC robust when the characteristics of the IC RL are approximately the same across all continuous probability distributions (see for instance Chakraborti and Graham 1 ).

OOC performance

Table 2 shows that the OOC ARL of the TEWMA chart are lower for small values of , but increase as increases, indicating a deteriorating performance. For small and moderate shifts in the process location, the proposed chart performs better under the heavy-taileddistribution followed by the normal distribution. However, for large shifts, their performances under the different distributions are almost similar. For skewed gamma distribution, the higher the value of , the worse the performance; for instance, when 0.1, 0.9, under the GAM(3,1) distribution, the OOC ARL is equal to 534.8 (i.e. higher than the nominal value of 500, which implies that it is ARL-biased). Next, the EARL values increase as increases for each distribution in Table 2, indicating a deteriorating OOC performance. For instance, under the N(0,1) distribution, when 0.05, 0.5 and 0.9, then the corresponding EARL values are equal to 38.3, 45.4 and 61.7, respectively. In addition, Figure 3 studies the effect of Phase II sample size, i.e. {3,5,10}, on the OOC performance using the EARLs when {0.05, 0.5}. Figure 3 shows that as the Phase II sample size increases, the better the Phase II OOC performance becomes, thus indicating an improvement in the detection ability.

Similarly, Figure 4 shows that the larger the Phase I sample size ( ), the better the Phase II OOC performance. Figures 3 and4 show that the larger the smoothing parameter, the less sensitive is the TEWMA chart, since the EARLs become larger; especially for the skewed gamma distribution. ] and ] denote overall performance metrics defined in (18) for 'small', 'large' and 'small-to-large' shifts, respectively. Based on the OOC ARL performance illustrated in Table 3, it shows that the IMFIR-TEWMA chart is more sensitive than the standard TEWMA, FIR-TEWMA and MFIR-TEWMA charts for all shift values as well as in terms of the EARL values under symmetric distributions. However, for small shifts under skewed distributions, the IMFIR-TEWMA chart is outperformed by its competitors, see Table 3 Since the ARL values are spread over a wide range of values; hence, in Figure 5, they are displayed in a compact manner using the log scale, i.e. . From Figure 5, it is observed that, in general, the standard TEWMA chart will take longer to give a signal as compared to the FIR-TEWMA, MFIR-TEWMA and IMFIR-TEWMA charts for the majority of shifts. However, for most shifts, the IMFIR-TEWMA chart detects changes in the location parameter faster, with the MFIR-TEWMA and FIR-TEWMA charts, being the second and third best for the majority of shifts, respectively. In Tables 4 to 6, the proposed TEWMA chart is compared to the EWMA and DEWMA charts with and without FIR features when = 0.5, m = 100 and n = 5 under the N(0,1), t (5) and GAM (3,1), respectively. It is worth mentioning that the EWMA and DEWMA charts discussed in Li et al [START_REF] Li | Nonparametric CUSUM and EWMA control charts for detecting mean shifts[END_REF] and Malela-Majika [START_REF] Malela-Majika | New distribution-free memory-type control charts based on the Wilcoxon rank-sum statistic[END_REF] did not incorporate any of the FIR features discussed here. For control charts with no FIRs (i.e. labelled 'Standard' in Tables 4 to 6), the TEWMA chart has the best small as well as large shifts performance; however, the DEWMA chart has better moderate shifts performance. With respect to EARLs, the TEWMA chart has the best performance followed by the DEWMA chart and finally, the EWMA chart being the worst performing.

Next

Illustrative example

The implementation of the proposed TEWMA control chart with and without the IMFIR feature using a dataset on the size of piston rings from Montgomery [START_REF] Montgomery | Statistical Quality Control: A Modern Introduction[END_REF] for which a goodness of fit test for normality is not rejected since the p-value is equal to 0.4167. Setting an =500, we use =0.50 and =2.937, so that the attained value of the TEWMA W chart be equal to 500.14 for ( , )=(125,5). The TEWMA chart is shown in Figure 6 and no charting statistic plots beyond the control limits, i.e. it does not give a signal in the prospective phase. When the IMFIR feature is incorporated in the TEWMA chart, it is found that = 3.177 yields an attained value of 501.22. The IMFIR-TEWMA chart is also shown in Figure 6 where we observe that it gives a signal on the first sample in the prospective phase. Moreover, it is observed in Figure 6 that, the IMFIR adjustment factor narrows the control limits during the start-up period. This in turn, ensures that the IMFIR-TEWMA chart has a better detection ability than the TEWMA chart (without the IMFIR feature). Also, it can be seen that, as the time increases, the control limits of the IMFIR-TEWMA chart converges towards those of the TEWMA chart without the IMFIR, which shows that the effect of the IMFIR feature is only applicable during start-up only and gradually disappears as time increases. More importantly, the TEWMA chart outperforms the DEWMA and EWMA charts with and without the FIR features, especially for small shifts. However, the DEWMA chart has the best performance in detecting moderate shifts. Therefore, it can be said that the proposed TEWMA chart with IMFIR feature can be used over the DEWMA and EWMA charts as it is shown that it is more sensitive and results in earlier OOC signals in most situations as compared to its competitors.

For future research, we intend to propose the TEWMA chart to monitor variability using the Ansari-Bradley statistic (refer for instance to Zhou et al [START_REF] Zhou | A new nonparametric control chart for monitoring variability[END_REF] ) and also study the effect of the IMFIR feature.

Appendix

With the help of a formal calculus software, can equivalently be written as

( ∑ ) ( )
Another alternative formulation of the above expression is provided in Alevizakos et al [START_REF] Alevizakos | The triple exponentially weighted moving average control chart[END_REF] .

Figure 1 :

 1 Figure 1: Comparison of the FIR, MFIR and IMFIR adjustment factors with respect to time

2 .

 2 (a) TEWMA chart (with no FIR feature) (b) IMFIR-TEWMA chart Figure Robustness of the proposed charts when (100,5), 0.05 for a nominal =500 under different distributions

Figure 3 .Figure 4 .

 34 Figure 3. The effect of Phase II sample size on the performance TEWMA chart using the EARL when 100, {3, 5, 10}, {0.05, 0.5}, =0 and =2 with an increment of 0.1

  (a) N(0,1) distribution (b) t(5) distribution (c) GAM(3,1) distribution Figure 5. The OOC profile comparison of the proposed schemes when (100, 5), 0.05 for a nominal =500 under different distributions 4.4 Performance comparison of the EWMA, DEWMA and TEWMA charts

Figure 6 .

 6 Figure 6. Illustrative example of the standard TEWMA and IMFIR-TEWMA control charts using the piston ring data from Montgomery 45

  Tapang et al[START_REF] Tapang | Three nonparametric control charts based on ranked set sampling[END_REF] , Malela-Majika and Rapoo 30 , Chakraborti and Graham 1,31 , Triantafyllou 32 , Mabude et al 33 , Tercero-Gomez et al 34 and Qiu 35 .

presented the EWMA chart with measurements utilizing a simple random sampling method. A while later, Malela-Majika and Rapoo 27 presented the EWMA chart utilizing structured sampling techniques (i.e. based on rank set sampling method). More recently, Malela-Majika 28 proposed a DEWMA chart which is shown to have better out-of-control OOC performance in detecting small-to-moderate shifts in the process location than the EWMA chart. Other discussions on control charts based on the statistic can be found in

. The design of the EWMA and DEWMA charts 2.1 Wilcoxon rank sum test ( )

	samples. However, the distribution of the test samples is the same as the one of the reference
	sample with a difference in the location shift only. In other words,	, where
	represents the change (or shift) in the location parameter. Thus, when the process is in-
	control (IC),		0; hence,	. However, when	0, the process is said to be out-of-
	control (OOC). Wilcoxon 44 proposed the statistic by merging the reference observations
	with the observations of the	test sample together and re-arranging all values of the
		observations	in	an	ascending	order.	Let
						be the resulting ordered sample, where
	if is the smallest	value from the newly formed sample , also	if
	is the smallest	value from , this means that	{1, 2, …,	},	{1, 2, …, } and
	{1, 2, …, }.
	Let					be the sample of the indicators where
	1 if		and	0 if	. Then, at time , the statistic is defined by
	The rest of the paper is structured as follows: Section 2 provides some design background of
	the test statistic as well as the EWMA and DEWMA	charts. The design of the proposed
	TEWMA	charts with and without FIR features are discussed in Section 3. Section 4 gives
	an empirical performance of the proposed TEWMA	chart and some comparisons against
	the EWMA and DEWMA	charts. An illustrative example is given in Section 5 using real-
	life data. Finally, Section 6 provides some concluding remarks.
	2Assume that		{	1,2,…, } is an IC reference (i.e. Phase I) sample with unknown
	cumulative distribution function (c.d.f.),	, and	{ ,	1,2,3, …;	1,2,3, …, },
	simply denoted as , is a set of test samples with c.d.f.	. The observations from the
	reference sample are assumed to be independent from each other and from the ones in the test

The basic FIR feature in Steiner

[START_REF] Steiner | EWMA control charts with time-varying control limits and fast initial response[END_REF]

is denoted as FIR in this paper. Later, Haq et al

[START_REF] Haq | Improved fast initial response features for exponentially weighted moving average and cumulative sum control charts[END_REF]

, proposed a modified FIR (MFIR) feature which is shown to yield better OOC performance than the Steiner

[START_REF] Steiner | EWMA control charts with time-varying control limits and fast initial response[END_REF]

's FIR feature. Therefore, in addition to introducing the TEWMA chart; in this paper, a new improved MFIR (IMFIR) feature is incorporated to the TEWMA chart to improve its performance during the start-up period. For the sake of completeness and comparison purpose, the basic FIR and MFIR are also incorporated to the EWMA, DEWMA and TEWMA charts.

Table 1

 1 lower values than the ones with FIR features. Note that 5 th , 25 th , 50 th , 75 th and 95 th percentiles are denoted as P5, P25, P50, P75 and P95, respectively and are presented in Figure1. Moreover, it is shown in Figure2that the , P5, P25, P50 and P75 of the RL distribution are almost constant, while the ones of the and P95 have a slight (but insignificant) variation. Thus, based on Table1and Figure2, it can be deduced that the TEWMA chart with or without FIR features is IC robust. It is important to mention that the and P95 profiles of the TEWMA with the IMFIR feature are larger than the one with no FIR feature, see Figures2(a) and (b); a high IC is undesired as it may lead to a high probability of an OOC signal, when in fact the process is IC.

	shows the robustness of the TEWMA	charts with and without FIR features when
	(100, 5) and	{0.05, 0.5} for a nominal	=500. From Table 1, it can be
	noticed that, the attained IC	values are close to each other across different distributions

and similarly, the attained IC are also close to each other across different distributions. For instance, the attained IC are around 500 for all the distributions considered in this paper. In addition, it is observed that the TEWMA chart with no FIR feature has

Table 1 .

 1 Robustness of the TEWMA with and without FIR feature when

	=(100,5),

Table 2 .

 2 The

			profile of the TEWMA chart when		(100, 5),	{0.05, 0.5,
	0.9},	=0 and	=1.5 with an increment of 0.1 for a nominal	=500 under different
						distributions
				N(0,1)			t(5)		GAM(3,1)
	Shift		0.05	0.5	0.9	0.05	0.5	0.9	0.05	0.5	0.9
	0.1		355.3	369.1	408.3	304.5	360.0	401.9	339.9	435.2	534.8
	0.2		126.5	176.5	244.4	93.3	137.6	224.7	110.1	192.1	357.9
	0.3		36.7	63.6	121.9	24.1	39.9	103.9	28.9	63.9	184.6
	0.4		16.4	24.6	61.0	11.8	16.3	46.4	13.2	21.5	82.2
	0.5		9.7	12.2	32.8	7.5	8.9	23.4	7.6	10.3	42.1
	0.6		6.7	7.8	17.7	5.3	5.9	12.7	5.3	6.3	23.1
	0.7		4.9	5.4	10.9	3.9	4.5	7.8	3.9	4.6	12.4
	0.8		3.8	4.3	7.3	3.1	3.5	5.3	3.0	3.6	7.9
	0.9		3.1	3.5	5.3	2.5	2.9	3.8	2.4	3.0	5.4
	1.0		2.5	3.0	4.0	2.1	2.5	3.0	2.0	2.6	3.9
	1.1		2.1	2.6	3.2	1.8	2.3	2.5	1.7	2.3	2.9
	1.2		1.9	2.3	2.6	1.6	2.0	2.2	1.5	2.1	2.4
	1.3		1.6	2.1	2.3	1.4	1.8	1.8	1.4	1.9	2.1
	1.4		1.5	1.9	2.0	1.3	1.7	1.7	1.2	1.8	1.8
	1.5		1.3	1.7	1.8	1.2	1.5	1.5	1.1	1.6	1.6
		]	38.3	45.4	61.7	31.0	39.4	56.2	34.9	50.2	84.3
			2.321	2.933	2.851	2.321	2.933	2.851	2.321	2.933	2.851

Table 3 .

 3 The profile of the TEWMA with and without FIR features when (100, 5, 0.5) for a nominal =500 under different distributions

			N(0,1)			t(5)				GAM(3,1)
	Shift	TEWMA	FIR-TEWMA	MFIR-TEWMA	IMFIR-TEWMA	TEWMA	FIR-TEWMA	MFIR-TEWMA	IMFIR-TEWMA	TEWMA	FIR-TEWMA	MFIR-TEWMA	IMFIR-TEWMA
	0.1	369.1	371.8	373.9	357.5	360.0	351.5	340.6	328.2	435.2	428.9	452.9	478.5
	0.2	176.5	170.1	157.8	142.0	137.7	127.2	119.2	98.6	192.1	203.5	197.8	187.1
	0.3	63.6	51.7	47.2	35.7	40.0	30.5	28.2	18.0	63.9	59.0	56.6	39.4
	0.4	24.6	15.6	13.8	9.5	16.3	9.7	7.2	4.6	21.5	14.2	11.9	14.2
	0.5	12.2	6.6	4.9	3.0	9.0	4.7	3.0	2.1	10.3	5.6	3.8	2.3
	0.6	7.8	4.0	2.7	1.9	5.9	2.8	1.9	1.6	6.3	3.0	2.1	1.6
	0.7	5.4	2.7	1.9	1.5	4.5	2.1	1.5	1.3	4.6	2.1	1.5	1.3
	0.8	4.3	2.0	1.5	1.3	3.5	1.7	1.3	1.2	3.6	1.6	1.2	1.1
	0.9	3.5	1.7	1.3	1.2	3.0	1.4	1.2	1.1	3.0	1.3	1.1	1.1
	1.0	3.0	1.4	1.2	1.1	2.5	1.3	1.1	1.1	2.6	1.2	1.0	1.0
	1.1	2.6	1.3	1.1	1.1	2.3	1.2	1.1	1.1	2.3	1.1	1.0	1.0
	1.2	2.3	1.2	1.1	1.0	2.0	1.1	1.0	1.0	2.1	1.1	1.0	1.0
	1.3	2.1	1.1	1.0	1.0	1.8	1.1	1.0	1.0	1.9	1.0	1.0	1.0
	1.4	1.9	1.1	1.0	1.0	1.7	1.1	1.0	1.0	1.8	1.0	1.0	1.0
	1.5	1.7	1.1	1.0	1.0	1.6	1.0	1.0	1.0	1.6	1.0	1.0	1.0
	]	129.2	123.2	119.5	109.5	112.6	104.7	99.6	90.3	144.6	142.2	144.6	144.3
	]	2.1	1.2	1.0	1.0	1.9	1.1	1.0	1.0	1.9	1.0	1.0	1.0
	]	45.4	42.2	40.8	37.3	39.5	35.9	34.0	30.9	50.2	48.4	49.0	48.8
		2.933	2.995	3.126	3.2095	2.933	2.995	3.126	3.2095	2.933	2.995	3.126	3.2095

  , for control charts with FIR and MFIR features, the DEWMA and TEWMA charts seem to have the best small shifts performance, with the TEWMA chart having a slight EARL values from the columns, 'Standard' vs. 'FIR' vs. 'MFIR' vs. 'IMFIR': the feature that results in the lowest ARL and EARL values, correspond to the IMFIR. The latter shows that for each chart, the IMFIR feature yields the best performance in most situations.

	advantage based on the	] values. Note though, for moderate shifts, the DEWMA
	chart has better performance. For large shifts, i.e. for	1, the competing charts are almost
	equivalent, see the	] values in Tables 4 to 6.
	Finally, for control charts with IMFIR feature, the TEWMA	chart seems to have the best
	small shifts performance, see the	] values in Tables 4 to 6; with the DEWMA
	chart having the second best performance. Again, for moderate shifts, the DEWMA	chart
	has a better performance. For large shifts, all the competing charts are almost equivalent; see
	the	] values in Tables 4 to 6.
	In general, from Tables 4 to 6, it is observed that in most situations (with or without the FIR
	features), the TEWMA	chart has relatively better OOC performance for small and large
	shifts; however, the DEWMA	chart has excellent moderate shifts detection ability than its
	competitors. Moreover, comparing the EWMA, DEWMA and TEWMA	charts' ARL and

Table 4 .

 4 The

			OOC	profile comparison of the EWMA, DEWMA and TEWMA charts
		with and without FIR features when	(100, 5, 0.5) for a nominal	=500 under
						the N(0,1) distribution
			Standard			FIR			MFIR			IMFIR
	Shift	EWMA DEWMA TEWMA EWMA DEWMA TEWMA EWMA DEWMA TEWMA EWMA DEWMA TEWMA
	0.1	357.7	354.3	352.7	353.2	335.8	349.1	340.4	327.5	340.8	340.2	326.1	333.6
	0.2	142.5	128.5	118.0	132.3	117.6	120.6	116.6	116.5	108.2	117.7	110.9	99.2
	0.3	38.9	36.6	37.5	32.9	33.1	32.6	26.4	25.9	25.1	27.0	26.6	23.7
	0.4	15.6	14.2	15.6	12.7	11.7	13.0	9.2	9.0	9.1	9.1	8.1	9.3
	0.5	9.3	8.8	9.8	7.3	7.0	7.8	5.1	4.2	5.4	5.2	5.1	5.4
	0.6	6.5	6.1	6.7	5.0	4.7	5.2	3.3	2.8	3.8	3.4	3.3	3.6
	0.7	5.0	4.7	5.1	3.5	3.4	3.7	2.4	2.0	2.7	2.5	2.4	2.6
	0.8	4.0	3.6	3.8	2.7	2.6	2.7	1.8	1.5	2.0	1.9	1.9	2.0
	0.9	3.3	3.0	3.0	2.2	2.0	2.1	1.5	1.3	1.6	1.5	1.5	1.5
	1.0	2.9	2.5	2.5	1.8	1.7	1.7	1.3	1.2	1.4	1.3	1.3	1.3
	1.1	2.5	2.1	2.1	1.5	1.5	1.4	1.2	1.2	1.2	1.2	1.2	1.2
	1.2	2.2	1.9	1.9	1.3	1.3	1.2	1.1	1.1	1.1	1.1	1.1	1.1
	1.3	2.0	1.7	1.6	1.2	1.2	1.2	1.1	1.0	1.1	1.1	1.1	1.1
	1.4	1.9	1.5	1.5	1.1	1.1	1.1	1.0	1.0	1.0	1.0	1.0	1.0
	1.5	1.7	1.4	1.3	1.1	1.1	1.1	1.0	1.0	1.0	1.0	1.0	1.0
	]	112.8	108.5	106.7	107.7	101.0	104.6	99.5	96.6	97.7	99.8	95.4	94.2
	]	2.1	1.7	1.7	1.3	1.2	1.2	1.1	1.1	1.1	1.1	1.1	1.1
	]	39.7	38.1	37.5	37.3	35.0	36.3	34.2	33.1	33.7	34.3	32.8	32.5
		2.906	2.474	2.318	2.991	2.575	2.423	3.135	2758	2.624	3.12	2.75	2.623

Table 5 .

 5 The

			OOC	profile comparison of the EWMA, DEWMA and TEWMA charts with and
		without FIR features when		(100, 5, 0.5) for a nominal	=500 under the t(5)
							distribution
			Standard			FIR			MFIR			IMFIR
	Shift	EWMA DEWMA TEWMA EWMA DEWMA TEWMA EWMA DEWMA TEWMA EWMA DEWMA TEWMA
	0.1	337.5	318.7	306.3	322.3	316.1	308.7	320.1	300.1	315.3	324.5	293.8	277.4
	0.2	97.1	87.5	88.0	93.0	77.9	77.8	88.8	75.5	75.3	86.1	74.7	81.8
	0.3	26.5	22.2	25.1	21.4	21.5	23.3	15.2	16.4	13.9	17.2	15.6	15.9
	0.4	11.3	10.6	12.1	9.6	8.7	10.4	6.4	6.1	6.7	6.2	6.1	6.7
	0.5	7.3	6.7	7.5	5.8	5.4	6.0	3.8	3.7	4.2	3.9	3.7	4.1
	0.6	5.3	4.8	5.3	3.8	3.7	4.0	2.6	2.6	2.9	2.6	2.5	2.8
	0.7	4.1	3.7	4.0	2.8	2.7	2.8	2.0	1.9	2.1	1.9	1.9	2.0
	0.8	3.3	2.9	3.1	2.2	2.1	2.1	1.5	1.6	1.6	1.5	1.5	1.5
	0.9	2.8	2.4	2.5	1.8	1.7	1.7	1.3	1.3	1.4	1.3	1.3	1.3
	1.0	2.5	2.1	2.1	1.5	1.4	1.4	1.2	1.2	1.2	1.2	1.2	1.2
	1.1	2.2	1.8	1.8	1.3	1.3	1.3	1.1	1.1	1.1	1.1	1.1	1.1
	1.2	2.0	1.6	1.6	1.2	1.2	1.2	1.1	1.1	1.1	1.1	1.1	1.1
	1.3	1.8	1.5	1.4	1.1	1.1	1.1	1.0	1.0	1.0	1.0	1.0	1.0
	1.4	1.6	1.4	1.3	1.1	1.1	1.1	1.0	1.0	1.0	1.0	1.0	1.0
	1.5	1.5	1.3	1.3	1.1	1.1	1.0	1.0	1.0	1.0	1.0	1.0	1.0
	]	95.9	89.2	87.8	90.4	85.9	85.2	86.9	80.4	83.1	87.6	78.8	77.2
	]	1.8	1.5	1.5	1.2	1.1	1.1	1.1	1.1	1.1	1.0	1.0	1.0
	]	33.8	31.3	30.9	31.3	29.8	29.6	29.9	27.7	28.7	30.1	27.2	26.7
		2.906	2.474	2.318	2.991	2.575	2.423	3.135	2758	2.624	3.12	2.75	2.623

Table 6 .

 6 The

			OOC	profile comparison of the EWMA, DEWMA and TEWMA charts
		with and without FIR features when	(100, 5, 0.5) for a nominal	=500 under
						the GAM(3,1) distribution
			Standard			FIR			MFIR			IMFIR
	Shift	EWMA DEWMA TEWMA EWMA DEWMA TEWMA EWMA DEWMA TEWMA EWMA DEWMA TEWMA
	0.1	356.8	345.5	332.4	363.4	356.2	343.9	375.3	370.5	354.0	362.2	355.5	343.6
	0.2	133.3	111.3	110.0	131.8	112.7	110.0	109.5	101.3	104.8	120.8	116.6	116.5
	0.3	31.7	30.4	27.7	35.2	24.6	24.4	25.4	20.9	21.4	31.2	24.5	21.0
	0.4	12.2	11.9	12.2	10.8	9.4	10.1	8.5	6.9	7.8	8.4	6.8	7.1
	0.5	7.5	7.0	7.6	6.1	5.5	6.0	4.0	3.8	4.2	3.9	3.8	4.2
	0.6	5.4	4.8	5.3	4.0	3.6	3.8	2.5	2.4	2.7	2.5	2.5	2.6
	0.7	4.2	3.7	3.9	2.9	2.6	2.6	1.8	1.7	1.8	1.8	1.7	1.8
	0.8	3.4	2.9	3.0	2.1	1.9	1.9	1.4	1.3	1.4	1.4	1.3	1.3
	0.9	2.9	2.4	2.4	1.6	1.5	1.5	1.2	1.2	1.2	1.2	1.2	1.1
	1.0	2.5	2.1	2.0	1.4	1.3	1.2	1.1	1.1	1.1	1.1	1.1	1.1
	1.1	2.2	1.8	1.7	1.2	1.1	1.1	1.0	1.0	1.0	1.0	1.0	1.0
	1.2	2.0	1.6	1.5	1.1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
	1.3	1.8	1.4	1.3	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
	1.4	1.7	1.3	1.2	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
	1.5	1.6	1.2	1.1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
	]	108.3	101.2	98.0	109.4	101.7	98.9	104.5	100.7	98.4	105.3	101.4	98.5
	]	1.9	1.5	1.4	1.1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
	]	37.9	35.3	34.2	37.6	35.0	34.0	35.7	34.4	33.7	36.0	34.7	33.7
		2.906	2.474	2.318	2.991	2.575	2.423	3.135	2758	2.624	3.12	2.75	2.623