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1. Efficient algorithms for calculating the probability distribution of the sum of hypergeometric-distributed random variables

Author

Arne Johannssen, Nataliya Chukhrova, and Philippe Castagliola

Subjects
Algorithm by De Pril, Approximation, Convolution, Hypergeometric distribution, Hypergeometric np chart, MATLAB, Science
Abstract

In probability theory and statistics, the probability distribution of the sum of two or more independent and identically distributed (i.i.d.) random variables is the convolution of their individual distributions. While convoluting random variables following a binomial, geometric or Poisson distribution is a straightforward procedure, convoluting hypergeometric-distributed random variables is not. The problem is that there is no closed form solution for the probability mass function (p.m.f.) and cumulative distribution function (c.d.f.) of the sum of i.i.d. hypergeometric random variables. To overcome this problem, we propose an approximation for the distribution of the sum of i.i.d. hypergeometric random variables. In addition, we compare this approximation with two classical numerical methods, i.e., convolution and the recursive algorithm by De Pril, by means of an application in Statistical Process Monitoring (SPM). We provide MATLAB codes to implement these three methods for computing the probability distribution of the sum of i.i.d. hypergeometric random variables in an efficient way. The obtained results show that the proposed approximation has remarkable properties and may be helpful in all fields, where the problem of convoluting hypergeometric-distributed random variables occurs. Therefore, the approximation considered in this paper is well suited to make a change over established practices. • This article presents theoretical bases of three methods for determining the probability distribution of the sum of i.i.d. hypergeometric random variables: (1) direct convolution, (2) recursive algorithm by De Pril, (3) approximation. • We provide associated MATLAB codes (including context-specific customizations) for direct implementation of these methods and discuss technical aspects and essential details of the tweaks we have made. • A representative application example in SPM shows that the proposed approximation is considerably simpler in application than both other methods and it ensures a remarkable high accuracy of the results while reducing computational time considerably.

Published
2021
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2. The Cusum Median Chart for Known and Estimated Parameters

Author

Philippe Castagliola, Fernanda Otilia Figueiredo, and Petros E. Maravelakis

Subjects
average run length, CUSUM chart, estimated parameters, median, order statistics, Statistics, HA1-4737, Probabilities. Mathematical statistics, QA273-280
Abstract

The usual CUSUM chart for the mean (CUSUM-X¯) is a chart used to quickly detect small to moderate shifts in a process. In presence of outliers, this chart is known to be more robust than other mean-based alternatives like the Shewhart mean chart but it is nevertheless affected by these unusual observations because the mean (X¯) itself is affected by the outliers. An outliers robust alternative to the CUSUM-X¯ chart is the CUSUM median (CUSUM-X˜) chart, because it takes advantage of the robust properties of the sample median. This chart has already been proposed by other researchers and compared with other alternative charts in terms of robustness, but its performance has only been investigated through simulations. Therefore, the goal of this paper is not to carry out a robustness analysis but to study the effect of parameter estimation in the performance of the chart. We study the performance of the CUSUM-X˜ chart using a Markov chain method for the computation of the distribution and the moments of the run length. Additionally, we examine the case of estimated parameters and we study the performance of the CUSUM-X˜ chart in this case. The run length performance of the CUSUM-X˜ chart with estimated parameters is also studied using a proper Markov chain technique. Conclusions and recommendations are also given.

Published
2019
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4. An EWMA sign chart for dispersion with exact run length properties

Author

Theodoros Perdikis, Stelios Psarakis, Philippe Castagliola, Vicent Giner-Bosch, Petros E. Maravelakis, Athanasios C. Rakitzis, Department of statistics, AUEB, Athens University of Economics and Business (AUEB), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Nantes Université (Nantes Univ), Universitat Politècnica de València (UPV), and University of Piraeus

Subjects
Statistics and Probability, [STAT]Statistics [stat], Sign statistic, variability, Applied Mathematics, Modeling and Simulation, Markov chain, distribution-free Sign statistic Markov chain EWMA control chart variability, EWMA control chart, Statistics, Probability and Uncertainty, distribution-free
Abstract

The EWMA Sign control chart is a distribution-free scheme used for monitoring shifts in the location parameter during process monitoring. In this work, we propose a modified Phase II EWMA chart based on a general Sign statistic, capable of monitoring shifts in the process variability. Regarding the determination of the proposed chart's in-and out-of-control Run Length properties, Markov chain methods are used in combination with a continuous transformation of the suggested general Sign statistic. Our results show the power of the proposed method regarding the proposed chart's exact Run Length properties and its efficiency in detecting shifts in the process variability.

Published
2023

8. An exponentially weighted moving average control chart based on signed ranks for finite horizon processes

Author

Stelios Psarakis, Philippe CASTAGLIOLA, Giovanni Celano, Theodoros Perdikis, Athens University of Economics and Business (AUEB), Università degli studi di Catania = University of Catania (Unict), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and Nantes Université (Nantes Univ)

Subjects
[SPI.OTHER]Engineering Sciences [physics]/Other, [STAT.AP]Statistics [stat]/Applications [stat.AP], distribution-free, Markov processes, quality control, statistical process monitoring, Wilcoxon signed rank statistic, Safety, Risk, Reliability and Quality, Industrial and Manufacturing Engineering
Abstract

International audience; Distribution-free control charts are an efficient quality monitoring tool to inspect lots of parts manufactured within a finite production horizon. In this work, the performance of the Exponentially Weighted Moving Average chart based on the Wilcoxon signed rank statistic is investigated for on-line monitoring of finite production runs. The chart's on-target performance is evaluated through a specific non-homogeneous Markov chain model under different process scenarios. A numerical analysis is conducted for determining its optimal design and a performance comparison with other available schemes is presented for different symmetric distributions of observations. Finally, an illustrative example is presented to show a practical implementation of the investigated chart.

Published
2023

10. On designing an optimal SPRT control chart with estimated process parameters under guaranteed in-control performance

Author

J.W. Teoh, W.L. Teoh, Michael B.C. Khoo, Philippe Castagliola, W.H. Moy, Heriot-Watt University (Malaysia), Universiti Sains Malaysia (USM), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and Nantes Université (Nantes Univ)

Subjects
[STAT]Statistics [stat], Guaranteed in-control performance, General Computer Science, SPRT control chart, Average extra quadratic loss Guaranteed in-control performance Markov chain Parameter estimation SPRT control chart Statistical process control, Average extra quadratic loss, Markov chain, General Engineering, Parameter estimation, Statistical process control
Abstract

International audience; Being one of the most sophisticated control charts, the sequential probability ratio test (SPRT) chart possesses fast detection ability across a broad range of process shifts. The SPRT chart has the advantage of sampling only a modest number of observations. Thus far, the SPRT chart has been developed under the assumption that the process parameters are known. As process parameters are often unknown in practice, this article reveals that parameter estimation from a limited amount of Phase-I data, leads to excessive false alarms and unstable chart's performances. To counter these problems, this article advocates the use of adjusted control limits to ensure that a sufficiently high proportion of the in-control conditional average time to signal value, is greater than a pre-specified level. This increasingly prevalent design of control charts is known as Guaranteed In-Control Performance (GICP). In this article, we propose an optimization design for the SPRT chart with estimated process parameters, by minimizing the expected value of the average extra quadratic loss under the GICP framework. Theoretical derivations by means of the Markov chain approach are developed in this article to evaluate the run-length properties of the SPRT chart with estimated process parameters. Results show that the overall performance of the proposed optimal SPRT chart is almost twice as good as the optimal CUSUM chart over a given range of process mean shifts. Finally, an implementation of the proposed optimal SPRT chart is demonstrated with real industrial data obtained from an epitaxial process.

Published
2022

11. Finite Horizon Process Monitoring

Author

Giovanni Celano, Philippe Castagliola, George Nenes, and Subhabrata Chakraborti

Subjects
Mathematical optimization, Computer science, Process (computing), Finite horizon
Published
2021

12. Phase II exponential charts for monitoring time between events data: performance analysis using exact conditional average time to signal distribution

Author

Subha Chakraborti, Nirpeksh Kumar, Philippe Castagliola, Banaras Hindu University [Varanasi] (BHU), University of Alabama [Tuscaloosa] (UA), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and Nantes Université (Nantes Univ)

Subjects
Guaranteed IC performance, Statistics and Probability, Distribution (number theory), Applied Mathematics, Phase (waves), Quality control, Signal, Conditional average, Exponential function, [STAT]Statistics [stat], Equal-tailed and ATS-unbiased exponential chart, Modeling and Simulation, Exact distribution, Statistical physics, Statistics, Probability and Uncertainty, Conditional and Unconditional perspectives, Mathematics
Abstract

International audience; In this paper, we study the performance properties of the phase II exponential chart with an unknown in-control (IC) rate parameter, used to monitor high-yield processes. The average time to signal (ATS) is used as the chart performance criterion instead of the usual average run length (ARL). Based on the IC conditional ATS (CATS) distribution, we examine the properties of both the equal-tailed and the ATS-unbiased exponential charts with estimated control limits and adjust the limits so that a nominal IC ATS performance is achieved. Two perspectives are investigated: the unconditional, under which the average of IC CATS distribution is set equal to a nominal ATS and, the conditional so that the IC CATS is set to or exceed a nominal ATS with a high probability. It is shown that the ATS-unbiased exponential chart under the conditional perspective has a better IC performance.

Published
2021

13. A one-sided exponentially weighted moving average control chart for time between events

Author

FuPeng Xie, Xuelong Hu, Philippe Castagliola, YuLong Qiao, Jinsheng Sun, School of Automation [Nanjing] (NJUST), Nanjing University of Science and Technology (NJUST), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Nantes Université (Nantes Univ), and Nanjing University of Posts and Telecommunications [Nanjing] (NJUPT)

Subjects
Statistics and Probability, Markov chain, Time-between-events, Estimation theory, Computer science, Control chart, Parameter Estimation, Exponentially weighted moving average, Process (computing), Early detection, Articles, [STAT]Statistics [stat], Markov chain model, One sided, EWMA chart, Statistics, Probability and Uncertainty, EWMA, Algorithm
Abstract

International audience; Exponentially weighted moving average (EWMA) control charts for time-between-events (TBE) are commonly suggested to monitor high-quality manufacturing processes for the early detection of process deteriorations. In this study, an enhanced one-sided EWMA TBE control chart is developed for rapid detection of increases or decreases in the process mean. The use of the truncation method helps to improve the sensitivity of the proposed scheme in the process mean detection. Moreover, by taking the effects of parameter estimation into account, the proposed scheme with estimated parameters is also investigated in this paper. Both the average run length (ARL) and standard deviation of run length (SDRL) performances of the proposed scheme with known and estimated parameters are studied using the Markov chain method, respectively. Furthermore, an optimal design procedure is developed for the recommended one-sided EWMA TBE chart based on ARL. Numerical results show that the proposed optimal one-sided EWMA TBE chart is more sensitive than the existing optimal one-sided exponential EWMA chart in monitoring both upward and downward mean shifts. Meanwhile, it also performs better than the existing comparative scheme in resisting the effect of the parameter estimation. Finally, two illustrative examples are considered to show the implementation of the recommended one-sided EWMA TBE scheme for simulated and real datasets. For the real dataset of F-16 aircraft, the accident occurrences of F-16 are very low, in which case monitoring the time between two successive F-16 accidents is more efficient than the traditional monitoring schemes. Moreover, the usage of the truncation method makes the proposed one-sided EWMA TBE chart more appropriate for monitoring those two datasets with known shift directions, and the operation of the proposed scheme is simple which does not need to predetermine the reflecting boundary of the existing comparative scheme.

Published
2022

14. Distribution-free mixed GWMA-CUSUM and CUSUM-GWMA Mann–Whitney charts to monitor unknown shifts in the process location

Author

Jean-Claude Malela-Majika, Sandile Charles Shongwe, Kutele Mabude, Philippe Castagliola, University of South Africa (UNISA), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and Nantes Université (Nantes Univ)

Subjects
Statistics and Probability, Distribution free, Mixed CUSUM-GWMA scheme, Nonparametric statistics, Process (computing), Mixed GWMA-CUSUM scheme, Exact control limits, CUSUM, Asymptotic control limits Distribution-free Exact control limits Mann-Whitney U statistic Mixed GWMA-CUSUM scheme Mixed CUSUM-GWMA scheme Phase I Phase II, Phase II, Test (assessment), Mann-Whitney U statistic, [STAT]Statistics [stat], Phase I, Modeling and Simulation, Statistics, Mann–Whitney U test, Asymptotic control limits, Distribution-free, Mathematics
Abstract

International audience; The Mann-Whitney (MW) test is one of the most important nonparametric tests used in the comparison of the location parameters of two populations. Unlike the t-test, the MW test can be used when the assumption of normality fails to hold. In this paper, the MW U statistic is used to construct two efficient distribution-free monitoring schemes, namely the mixed generally weighted moving average-cumulative sum (GWMA-CUSUM) MW U scheme (denoted as U-MGC) as well as its reversed version, i.e. the CUSUM-GWMA MW U scheme (denoted as U-MCG). The performances of the proposed schemes are investigated using the average run-length (ARL) and average extra quadratic loss (AEQL) values through extensive simulations. The newly proposed charts are found to be superior in small shifts detection than their competing (existing and others that are briefly introduced here) distribution-free Shewhart, EWMA, CUSUM, mixed EWMA-CUSUM, mixed CUSUM-EWMA and GWMA MW U charts in many situations. A real-life example is used to demonstrate the design and implementation of the new schemes.

Published
2022

16. Design of attribute EWMA type control charts with reliable run length performance

Author

Philippe Castagliola, Athanasios C. Rakitzis, Petros Maravelakis, and Shu Wu

Subjects
Statistics and Probability, c-chart, Markov chain, Binomial (polynomial), Computer Science::Software Engineering, Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing), Poisson distribution, Binomial distribution, symbols.namesake, Modeling and Simulation, np-chart, Statistics, symbols, Control chart, EWMA chart, Mathematics
Abstract

Attribute control charts assuming a Poisson (c chart) or a binomial distribution (np chart) are usually used when the quality characteristic cannot be measured on a continuous scale. For equivalent...

Published
2021

17. Double sampling monitoring schemes: a literature review and some future research ideas

Author

Jean-Claude Malela-Majika, Philippe Castagliola, Collen M. Motsepa, and Sandile Charles Shongwe

Subjects
Statistics and Probability, Acceptance sampling, Double sampling, Modeling and Simulation, Statistics, Process (computing), Control chart, Industrial engineering, Field (computer science), Mathematics
Abstract

Adapted from the acceptance sampling field, the double sampling monitoring schemes implement a two-stage strategy to decide whether the process being monitored is in-control or out-of-control. That...

Published
2021

19. Optimal one‐ and two‐sided adaptive EWMA scheme for monitoring Poisson count data

Author

Xuelong Hu, Philippe Castagliola, Xiaojian Zhou, Anan Tang, Nanjing University of Posts and Telecommunications [Nanjing] (NJUPT), Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Scheme (programming language), 021103 operations research, Markov chain, Computer science, 0211 other engineering and technologies, 02 engineering and technology, Markov Chain, Management Science and Operations Research, Poisson distribution, 01 natural sciences, Poisson Count Data, [STAT]Statistics [stat], 010104 statistics & probability, symbols.namesake, symbols, EWMA chart, Adaptive EWMA chart, 0101 mathematics, Safety, Risk, Reliability and Quality, Algorithm, computer, Count data, computer.programming_language
Abstract

International audience; The Poisson distribution assumption often arises in several industrial applications for modeling defects or non-conformities. In this work, we investigate the one-and two-sided performance of a new adaptive EWMA (Exponentially Weighted Moving Average)-type chart for monitoring Poisson count data. An appropriate discrete-state Markov chain technique is provided to compute the exact ARL (Average Run Length) properties. Moreover, comparative studies are conducted to demonstrate the higher sensitivity of the proposed chart in the detection of shifts with various magnitudes. Advices on how to select the appropriate chart parameters are provided and an illustrative numerical example is proposed.

Published
2021

23. A one-sided adaptive truncated exponentially weighted moving average scheme for time between events

Author

FuPeng Xie, Philippe Castagliola, JinSheng Sun, AnAn Tang, XueLong Hu, Nanjing University of Science and Technology (NJUST), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Nantes Université (Nantes Univ), and Nanjing University of Posts and Telecommunications [Nanjing] (NJUPT)

Subjects
[STAT]Statistics [stat], Adaptive truncated EWMA chart, General Computer Science, Markov chain model, Average run length, Time-between-events, General Engineering, Parameter estimation
Abstract

International audience; In order to provide a balanced protection against a range of shift sizes in high-quality processes, a new one-sided adaptive truncated exponentially weighted moving average (ATEWMA) control chart with known and estimated parameters is developed for monitoring time between-events (TBE) data. A dedicated Markov chain model is established for evaluating the run length properties in known and estimated parameters operating conditions. Furthermore, a two-stage optimal design procedure of the proposed scheme is developed based on the average run length (ARL) criteria. Simulation results show that the one-sided ATEWMA TBE scheme with known parameters is superior to its competitors in detecting both upward and downward shifts. Finally, two real data applications are employed to show the implementation of the recommended scheme in the monitoring of TBE data.

Published
2022

24. Generally weighted moving average monitoring schemes: Overview and perspectives

Author

Philippe Castagliola, Jean-Claude Malela-Majika, Kutele Mabude, Sandile Charles Shongwe, University of South Africa (UNISA), Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)

Subjects
[SPI.OTHER]Engineering Sciences [physics]/Other, Scheme (programming language), Run-length, Computer science, 0211 other engineering and technologies, 02 engineering and technology, Management Science and Operations Research, 01 natural sciences, Generally weighted moving average, 010104 statistics & probability, Moving average, EWMA chart, 0101 mathematics, Safety, Risk, Reliability and Quality, Parametric statistics, computer.programming_language, Flexibility (engineering), 021103 operations research, Monte Carlo Simulation, Function (mathematics), Weighting, [STAT]Statistics [stat], Kurtosis, Memory-type scheme, Algorithm, computer, GWMA
Abstract

International audience; An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided. A GWMA scheme is an extended version of the exponentially weighted moving average (EWMA) scheme with an additional adjustment parameter that introduces more flexibility in the GWMA model as it adjusts the kurtosis of the weighting function so that the GWMA scheme can be designed such that it has an advantage over the corresponding EWMA scheme in the detection of certain shift values efficiently. The parametric and distribution-free GWMA schemes to monitor various quality characteristics and its existing enhanced versions (i.e. double GWMA, composite Shewhart-GWMA, mixed GWMA-CUSUM and mixed CUSUM-GWMA) have better performance than their corresponding EWMA counterparts in many situations; hence, all such existing research works discussing GWMA-related schemes (i.e. 61 publications in total) are documented and categorized in such a manner that it is easy to identify research gaps. Finally, a number of possible future research ideas are provided.

Published
2020

25. One-sided precedence monitoring schemes for unknown shift sizes using generalized 2-of-(h+1) and w-of-w improved runs-rules

Author

Philippe Castagliola, Jean-Claude Malela-Majika, Sandile Charles Shongwe, University of South Africa (UNISA), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and Nantes Université (Nantes Univ)

Subjects
Statistics and Probability, Distribution free, Statistics::Theory, Distribution (number theory), Markov chain, 0211 other engineering and technologies, Precedence statistic, 02 engineering and technology, 01 natural sciences, 010104 statistics & probability, Phase I, Order statistic, Applied mathematics, Distribution-free, 0101 mathematics, Mathematics, Parametric statistics, 021103 operations research, Runs-rules, Nonparametric statistics, Phase II, [STAT]Statistics [stat], One sided, Case U
Abstract

International audience; Parametric monitoring schemes are expected to perform better than their nonparametric counterparts when the assumption of a specific form of a distribution such as the normal is met. In practice, such assumption is often violated. Consequently, the performance of parametric schemes deteriorates considerably. To solve this problem, more efficient and flexible monitoring schemes based on nonparametric tests are recommended. In this paper, efficient and robust one-sided monitoring schemes are developed using generalized {1-of-1 or 2-of-(h+1)} and {1-of-1 or w-of-w} improved runs-rules (IRR) without any distributional assumption in the zero-and steady-states modes. Moreover, the zero-and steady-states run-length properties of the resulting one-sided IRR schemes are formulated and empirically evaluated using the Markov chain technique. Comparisons with other well-known one-sided Shewhart-type nonparametric schemes (e.g. basic precedence scheme and precedence scheme with standard runs-rules) indicate that the proposed schemes have a better performance. Real data are used to demonstrate the design and implementation of the one-sided improved runs-rules precedence schemes. Finally, a discussion on the two-sided IRR precedence schemes is also provided.

Published
2020

26. A multivariate CUSUM control chart for monitoring Gumbel's bivariate exponential data

Author

Anan Tang, Jinsheng Sun, FuPeng Xie, Xuelong Hu, Philippe Castagliola, Nanjing University of Science and Technology (NJUST), Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Nanjing University of Posts and Telecommunications [Nanjing] (NJUPT), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Multivariate statistics, 021103 operations research, 0211 other engineering and technologies, 02 engineering and technology, Bivariate analysis, Management Science and Operations Research, Statistical process control, 01 natural sciences, Cusum control chart, Exponential function, 010104 statistics & probability, Gumbel distribution, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Statistics, Control chart, 0101 mathematics, Safety, Risk, Reliability and Quality, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

International audience

Published
2020

27. Optimal design of one-sided exponential EWMA charts based on median run length and expected median run length

Author

Jinsheng Sun, Philippe Castagliola, YuLong Qiao, Xuelong Hu, School of Automation [Nanjing] (NJUST), Nanjing University of Science and Technology (NJUST), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Nantes Université (Nantes Univ), and Nanjing University of Posts and Telecommunications [Nanjing] (NJUPT)

Subjects
Statistics and Probability, Optimal design, 021103 operations research, Expected median run length, 0211 other engineering and technologies, Exponential chart, 02 engineering and technology, Median run length, Exponentially weighted moving average chart, 01 natural sciences, Exponential type, Exponential function, [STAT]Statistics [stat], 010104 statistics & probability, One sided, Applied mathematics, EWMA chart, 0101 mathematics, Mathematics
Abstract

International audience; Exponential type charts are useful tools to monitor the time between events in high-quality processes with a low defect rate. Most studies on exponential charts are 1 designed with the average run length (ARL) metric. The only use of ARL in the design of control charts is sometimes criticized because the shape of the run length (RL) distribution of control charts changes with the shift size. In fact, the RL distribution of the exponential exponentially weighted moving average (EWMA) chart is skewed, especially when the process is in-control. Hence, the median run length (M RL) serves as a more meaningful indicator. Moreover, in some situations, the shift size in the process is unknown in advance. Under this case, the expected median run length (EM RL) can be used as the metric. In this paper, the RL properties of both the upper-and lower-sided exponential EWMA charts are studied through a Markov chain approach. Two optimal design procedures are developed for one-sided exponential EWMA charts based on the M RL and EM RL, respectively. The choices of reflecting boundaries for one-sided exponential EWMA charts are discussed through many numerical studies. The M RL and EM RL performances of the one-sided exponential EWMA charts are investigated.

Published
2020

28. A new distribution‐free adaptive sample size control chart for a finite production horizon and its application in monitoring fill volume of soft drink beverage bottles

Author

Sajal Saha, Philippe Castagliola, Michael B. C. Khoo, Mahfuza Khatun, American International University-Bangladesh (AIUB), Universiti Sains Malaysia (USM), International University of Business Agriculture and Technology (IUBAT), Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
021103 operations research, Markov chain, Short run, 0211 other engineering and technologies, Nonparametric statistics, Process (computing), 02 engineering and technology, truncated average run length, Management Science and Operations Research, 01 natural sciences, General Business, Management and Accounting, Standard deviation, finite production horizon, variable sample size, [STAT]Statistics [stat], 010104 statistics & probability, Chart, Sample size determination, Modeling and Simulation, Control chart, nonparametric, 0101 mathematics, Algorithm, Mathematics
Abstract

International audience; Nonparametric control charts have received increasing attention in process monitoring. In this paper, a new nonparametric sign (SN) control chart with variable sample size (VSS) for a finite horizon process is developed. The novelty of this research lies in the incorporation of the VSS technique into the nonparametric SN chart for a finite horizon process, hence, resulting in the development of a more sensitive nonparametric short run chart. The statistical performance of the new nonparametric VSS SN control chart is evaluated and compared with the existing fixed sample size (FSS) SN chart for a finite horizon process. The charts' performances are compared using the truncated average run length (TARL) and truncated standard deviation of the run length (TSDRL) criteria. The results obtained show that the nonparametric VSS SN short run chart is always quicker than the FSS SN short run chart in detecting process shifts for various underlying process distributions, hence, reducing scrap and rework cost. Finally, an application of the proposed control charting scheme is shown through a real-life example on the fill volume of soft drink beverage bottles.

Published
2020

29. On‐line monitoring of extreme values of geometric profiles in finite horizon processes

Author

Philippe Castagliola, Giovanni Celano, University of Catania [Italy], Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)

Subjects
0209 industrial biotechnology, Computer science, control chart, generalized extreme value distribution, random Gaussian process, statistical performance, Geometry, control chart, 02 engineering and technology, Finite horizon, statistical performance, Management Science and Operations Research, 01 natural sciences, generalized extreme value distribution, [STAT]Statistics [stat], 010104 statistics & probability, 020901 industrial engineering & automation, random Gaussian process, 0101 mathematics, Line (text file), Safety, Risk, Reliability and Quality, Extreme value theory, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2020

30. A variable parameters multivariate control chart for simultaneous monitoring of the process mean and variability with measurement errors

Author

Amirhossein Amiri, Philippe Castagliola, Hamed Sabahno, Shahed University [Téhéran], Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
021103 operations research, Observational error, Markov chain, Computer science, 0211 other engineering and technologies, Process (computing), 02 engineering and technology, Management Science and Operations Research, Multivariate control charts, 01 natural sciences, [STAT]Statistics [stat], 010104 statistics & probability, Variable (computer science), Statistics, 0101 mathematics, Safety, Risk, Reliability and Quality, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2020

31. The new synthetic and runs-rules schemes to monitor the process mean of autocorrelated observations with measurement errors

Author

Sandile Charles Shongwe, Philippe Castagliola, and Jean-Claude Malela-Majika

Subjects
Statistics and Probability, 021103 operations research, Observational error, Steady state (electronics), Markov chain, Autocorrelation, 0211 other engineering and technologies, Process (computing), 02 engineering and technology, 01 natural sciences, 010104 statistics & probability, Zero state response, Control theory, 0101 mathematics, Additive model, Mathematics
Abstract

The use of the 2-of-(H + 1) runs-rules and synthetic schemes to improve the performance of the currently available X¯ schemes in monitoring the process mean under the combined effect of measurement...

Published
2020

32. An adaptive variable-parameters scheme for the simultaneous monitoring of the mean and variability of an autocorrelated multivariate normal process

Author

Hamed Sabahno, Amirhossein Amiri, Philippe Castagliola, Shahed University [Téhéran], Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, Scheme (programming language), 021103 operations research, Markov chain, Applied Mathematics, Lag, Autocorrelation, 0211 other engineering and technologies, Process (computing), Sampling (statistics), Multivariate normal distribution, 02 engineering and technology, 01 natural sciences, [STAT]Statistics [stat], 010104 statistics & probability, Variable (computer science), Modeling and Simulation, Statistics, 0101 mathematics, Statistics, Probability and Uncertainty, computer, ComputingMilieux_MISCELLANEOUS, computer.programming_language, Mathematics
Abstract

Due to advances in technology, sampling procedures and short lag times between successive sampling, autocorrelation among the measured data has become common in most applications. Neglecting autoco...

Published
2020

33. Optimal designs of the exponentially weighted moving average (EWMA) median chart for known and estimated parameters based on median run length

Author

Zhi Lin Chong, Wei Lin Teoh, Michael B. C. Khoo, K. L. Tan, Philippe Castagliola, Universiti Sains Malaysia (USM), Universiti Tunku Abdul Rahman (UTAR), Heriot-Watt University (Malaysia), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and Nantes Université (Nantes Univ)

Subjects
Statistics and Probability, Optimal design, median run length (MRL), exponentially weighted moving average (EWMA) median chart, Exponentially weighted moving average, Measure (mathematics), [STAT]Statistics [stat], Zero state response, Chart, Modeling and Simulation, Statistics, Control chart, Estimated parameters, EWMA chart, known parameters, steady-state, zero-state, Mathematics
Abstract

International audience; In the literature, the sole dependence on the ARL as the performance measure of a control chart has received much criticism. This is because interpretation based on the ARL alone can be misleading, as the shape and skewness of the run-length distribution vary according to the magnitude of the process mean shift. Therefore, we consider the median run length (MRL) performance measure for optimal EWMA median chart when process parameters are known and estimated. We provide an illustrative example to show the application of the optimal EWMA median chart based on expected median run length (EMRL).

Published
2020

34. A side-sensitive double sampling X¯ monitoring scheme with estimated process parameters

Author

Philippe Castagliola, Sandile Charles Shongwe, Collen M. Motsepa, Jean-Claude Malela-Majika, University of South Africa (UNISA), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and Nantes Université (Nantes Univ)

Subjects
Statistics and Probability, Scheme (programming language), 021103 operations research, overall performance measures, estimated process parameters, 0211 other engineering and technologies, Process (computing), 02 engineering and technology, 01 natural sciences, Phase II, [STAT]Statistics [stat], 010104 statistics & probability, Double sampling scheme, Phase I, Distribution (mathematics), Double sampling, Modeling and Simulation, Statistics, side-sensitive double sampling scheme, Statistical process monitoring, 0101 mathematics, computer, Algorithm, Mathematics, computer.programming_language
Abstract

In statistical process monitoring (SPM), most of the monitoring schemes are designed assuming that the process parameters for the underlying distribution are known (i.e., Case K). In a variety of c...

Published
2020

35. Exponentially weighed moving average charts for monitoring zero-inflated proportions with applications in health care

Author

Petros E. Maravelakis, Athanasios C. Rakitzis, and Philippe Castagliola

Subjects
Statistics and Probability, Health Information Management, Epidemiology, Humans, Public Health Surveillance, Delivery of Health Care, Markov Chains
Abstract

In the context of public health surveillance, the aim is to monitor the occurrence of health-related events. Among them, statistical process monitoring focuses very often on the monitoring of rates and proportions (i.e. values in [Formula: see text]) such as the proportion of patients with a specific disease. A popular control chart that is able to detect quickly small to moderate shifts in process parameters is the exponentially weighed moving average control chart. There are various models that are used to describe values in [Formula: see text]. However, especially in the case of rare health events, zero values occur very frequently which, for example, denote the absence of the disease. In this paper, we study the performance and the statistical design of exponentially weighed moving average control charts for monitoring proportions that arise in a health-related framework. The proposed chart is based on the zero-inflated Beta distribution, a mixed (discrete-continuous) distribution, suitable for modelling data in [Formula: see text]. We use a Markov chain method to study the run length distribution of the exponentially weighed moving average chart. Also, we investigate the statistical design as well as the performance of the proposed charts. Comparisons with a Shewhart-type chart are also given. Finally, we provide an example for the practical implementation of the proposed charts.

Published
2022

36. The performance of the hypergeometric n p chart with estimated parameter

Author

Philippe Castagliola, Nataliya Chukhrova, Arne Johannssen, Université de Hambourg, Conception, Pilotage, Surveillance et Supervision des systèmes (CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and Nantes Université (Nantes Univ)

Subjects
Information Systems and Management, General Computer Science, 0211 other engineering and technologies, attribute control charts, 02 engineering and technology, Management Science and Operations Research, 01 natural sciences, Industrial and Manufacturing Engineering, Convolution, 010104 statistics & probability, Chart, np-chart, fraction nonconforming, Applied mathematics, convolution, Control chart, 0101 mathematics, Mathematics, 021103 operations research, Quality control, Hypergeometric distribution, [STAT]Statistics [stat], Modeling and Simulation, Probability distribution, run length properties, p-chart, Random variable
Abstract

Although it is well known that the performance of attribute control charts decreases significantly when the assumption of known process parameters is invalid, this assumption is prevalent in the pertinent literature. However, in most practical applications, the process parameters have to be estimated from a finite in-control Phase I sample, and therefore the performance of attribute control charts should be evaluated from the perspective of estimated process parameters. In this paper, we compare the run length properties of the hypergeometric n p chart in both the known and estimated parameter cases. In particular, we investigate the required number of Phase I samples and new specific chart parameters that allow the hypergeometric n p chart with estimated parameter p to have approximately the same in-control performance as in the known parameters case. Moreover, we perform a comprehensive in-control and out-of-control comparison of the hypergeometric n p chart with its binomial counterpart. In order to achieve these objectives, we also present a new approach to effectively compute the probability distribution of the sum of independent and identically hypergeometric-distributed random variables. The proposed approximation reduces the computational effort to a few seconds while keeping a remarkable high accuracy with only negligible deviations compared to the exact distribution obtained via convolution.

Published
2022

37. Revised triple sampling X̄ control charts for the mean with known and estimated process parameters

Author

Sajal Saha, Philippe Castagliola, Michael B. C. Khoo, Faijun Nahar Mim, Universiti Sains Malaysia (USM), International University of Business Agriculture and Technology (IUBAT), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and Nantes Université (Nantes Univ)

Subjects
Average run length, Strategy and Management, Process (computing), Sampling (statistics), Management Science and Operations Research, estimated process parameters 1. Introduction, Industrial and Manufacturing Engineering, [STAT]Statistics [stat], known process parameters, Double sampling, Chart, Statistics, triple sampling, Control chart, double sampling, control charts, Sampling control, Mathematics
Abstract

The primary aim of this research is to propose a revised triple sampling (TS) X¯ chart, where the derivations of new formulae for computing the average run length of the triple sampling (TS) X¯ chart correctly are provided. The secondary aim is to develop the revised TS X¯ chart with estimated process parameters. The revised TS X¯ charts are compared with the double sampling (DS) X¯, two stage adaptive sample size (AS2) X¯ and three stage adaptive sample size (AS3) X¯ charts when process parameters are known and estimated using the average run length (ARL), average number of observations to signal (ANOS), average of the average run lengths (AARL), standard deviation of the average run lengths (SDARL), average of the average number of observations to signal (AANOS) and standard deviation of the average number of observations to signal (SDANOS) criteria, where the revised TS X¯ charts are found to be superior. Additionally, a table giving the minimum number of Phase-I samples for estimating the process mean so that the revised TS X¯ chart with estimated process parameters has the desired in-control AARL and AANOS performances is provided.

Published
2022
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38. One-sided Adaptive Truncated Exponentially Weighted Moving Average X Schemes for Detecting Process Mean Shifts

Author

FuPeng Xie, Philippe Castagliola, Zhonghua Li, JinSheng Sun, XueLong Hu, School of Automation [Nanjing] (NJUST), Nanjing University of Science and Technology (NJUST), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Nantes Université (Nantes Univ), Nankai University (NKU), and Nanjing University of Posts and Telecommunications [Nanjing] (NJUPT)

Subjects
[STAT]Statistics [stat], Information Systems and Management, Adaptive EWMA X control chart, Markov chain model, Truncation method, Management of Technology and Innovation, Industrial relations, Variable sampling interval, Management Science and Operations Research, Business and International Management, One-sided type scheme, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; One-sided type schemes are known to be more appropriate for monitoring a process when the direction of a potential mean shift can be anticipated. Furthermore, if the magnitude of the potential mean shift is unknown, it is desired to design a control chart to perform well over a wide range of shifts instead of only optimizing its performance in monitoring a particular mean shift level. The one-sided adaptive truncated exponentially weighted moving average (ATEWMA) X scheme recommended in this paper is a control chart that combines a Shewhart X scheme and a new one-sided EWMA X scheme together in a smooth way for rapidly detecting the upward (or downward) mean shifts. The basic idea of the recommended one-sided ATEWMA X scheme is to truncate the observations (i.e., the sample means X) first, and then to dynamically weight the past observations according to a suitable function of the current prediction error. This helps to improve the sensitivity of the proposed one-sided ATEWMA X scheme for detecting both small and

Published
2022

39. A number‐between‐events control chart for monitoring finite horizon production processes

Author

Nataliya Chukhrova, Philippe CASTAGLIOLA, Giovanni Celano, Arne Johannssen, University of Hamburg, University of Catania [Italy], Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and Nantes Université (Nantes Univ)

Subjects
[STAT]Statistics [stat], finite horizon processes, nite horizon processes, fraction nonconforming, negative hypergeometric control chart, statistical process monitoring, Management Science and Operations Research, control charts, Safety, Risk, Reliability and Quality, control charts, finite horizon processes, fraction nonconforming, negative hypergeometric control chart, number-between-events, statistical process monitoring, number-between-events
Abstract

International audience; In this paper, we present a number-between-events (NBE) control chart for monitoring the fraction nonconforming in nite horizon production (FHP) processes and related specic performance measures. When monitoring fractions nonconforming in FHP processes, the common binomial p-chart has two crucial limitations: the underlying distributional assumptions are violated when dealing with low-volume production and a scarce eciency in the case of processes characterized by a low fraction nonconforming. Thus, an ecient monitoring of FHP processes requires the selection of the correct underlying statistical model: in this case, a distribution from the hypergeometric family of discrete statistical distributions. An ecient statistical monitoring of processes with low fractions nonconforming can be achieved by means of discrete time-between-events (TBE) control charts, which count the number of units up to the appearance of a xed number of nonconforming units in the sample. Here, we present a discrete TBE-chart, denoted as NBE-chart, based on the negative hypergeometric distribution that meets numerous requirements of ecient monitoring of FHP processes. The proposed control chart can be conveniently used for both low-volume and mass production in processes with frequent changeovers.

Published
2022

42. Guaranteed conditional performance of the median run length based EWMA X¯ chart with unknown process parameters

Author

Xuelong Hu, Jianlan Zhong, Anan Tang, Philippe Castagliola, Nanjing University of Posts and Telecommunications [Nanjing] (NJUPT), Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Fujian Agriculture and Forestry University (FAFU), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)

Subjects
Statistics and Probability, 021103 operations research, 0211 other engineering and technologies, Process (computing), 02 engineering and technology, standard deviation of median run length, 01 natural sciences, [STAT]Statistics [stat], 010104 statistics & probability, Chart, EWMAX chart, Moving average, Modeling and Simulation, Statistics, median run length, average median run length, EWMA chart, 0101 mathematics, \bar x and R chart, Mathematics, estimated parameters
Abstract

International audience; Exponentially weighted moving average (EWMA) type charts are very popular and efficient in monitoring various kind of statistics. Much researches have been done on the EWMAX chart with known process parameters. But, in practice, the process parameters used to set the control chart limits are often unknown and they need to be estimated from different Phase I samples. Moreover, because the shape of the run length distribution for the EWMAX chart changes with the mean shift, the median 1 run length (M RL) can serve as a good alternative to evaluate the performance of the EWMAX chart. In this article, we will investigate the conditional properties of the EWMAX chart with unknown process parameters based on the M RL metric. In order to investigate the chart's properties, the average M RL (AM RL) and the standard deviation of M RL (SDM RL) will be used together when the process parameters are unknown. To prevent too many lower in-control M RL values, the adjusted control limits of the M RL based EWMA chart are obtained by using a bootstrap type approach and the results show that the adjusted control limits can give a good tradeoff between the in-control and out-of-control M RL performances.

Published
2021

43. Evaluation of Shewhart time‐between‐events‐and‐amplitude control charts for correlated data

Author

Philippe Castagliola, Michael B. C. Khoo, Dorra Rahali, Hassen Taleb, Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Université de Tunis Carthage, Universiti Sains Malaysia (USM), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
021103 operations research, Computer science, 0211 other engineering and technologies, 02 engineering and technology, Management Science and Operations Research, Amplitude control, 01 natural sciences, 010104 statistics & probability, Amplitude, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Statistics, Statistical process monitoring, 0101 mathematics, Safety, Risk, Reliability and Quality, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2021

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

Author

Sandile Charles Shongwe, Tokelo Irene Letshedi, Philippe Castagliola, Jean-Claude Malela-Majika, University of South Africa (UNISA), Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)

Subjects
Distribution free, Run-length, Double EWMA chart, Wilcoxon signed-rank test, 0211 other engineering and technologies, 02 engineering and technology, Overall performance, Management Science and Operations Research, 01 natural sciences, 010104 statistics & probability, Statistics, Triple EWMA, Control chart, EWMA chart, 0101 mathematics, Safety, Risk, Reliability and Quality, Statistic, Mathematics, 021103 operations research, Process (computing), [STAT]Statistics [stat], Feature (computer vision), Nonparametric chart, Fast initial response
Abstract

International audience; 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.

Published
2021

45. New adaptive control charts for monitoring the multivariate coefficient of variation

Author

Khai Wah Khaw, Philippe Castagliola, Michael B. C. Khoo, M.A. Rahim, Universiti Sains Malaysia (USM), School of Mathematical Sciences, Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), and University of New Brunswick (UNB)

Subjects
0209 industrial biotechnology, Multivariate statistics, Adaptive control, General Computer Science, Markov chain, General Engineering, 02 engineering and technology, Statistical process control, 01 natural sciences, Standard deviation, [STAT]Statistics [stat], 010104 statistics & probability, 020901 industrial engineering & automation, Chart, Sample size determination, Statistics, Sensitivity (control systems), 0101 mathematics, ComputingMilieux_MISCELLANEOUS
Abstract

An adaptive control chart is one of the most effective techniques in Statistical Process Control (SPC). The coefficient of variation (CV) is common in many real life applications, especially in manufacturing and materials engineering, finance, medical and biological sciences. This paper proposes three adaptive charts to monitor the multivariate coefficient of variation (MCV), in order to improve the sensitivity of the standard MCV chart, in detecting small and moderate MCV shifts. The proposed charts are designed using the Markov chain approach and they are compared with the existing standard MCV chart using the average time to signal (ATS), standard deviation of the time to signal (SDTS) and expected average time to signal (EATS) criteria. The performance comparison shows that the proposed adaptive MCV charts, particularly the variable sample size and sampling interval (VSSI) MCV chart, outperform the existing MCV charts, in terms of the ATS and EATS criteria. By allowing the sample size and sampling interval to be varied in the VSSI MCV chart, process engineers will have better control in process monitoring and at the same time are able to detect an out-of-control signal quicker. Illustrative examples are presented by considering the VSSI MCV chart to show the chart’s implementation.

Published
2018

46. On the performance of the adaptive EWMA chart for monitoring time between events

Author

YuLong Qiao, Jianlan Zhong, Anan Tang, Philippe Castagliola, Xuelong Hu, Nanjing University of Posts and Telecommunications [Nanjing] (NJUPT), Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Fujian Agriculture and Forestry University (FAFU), Nanjing University of Information Science and Technology (NUIST), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, 021103 operations research, Distribution (number theory), Average run length, Applied Mathematics, 0211 other engineering and technologies, 02 engineering and technology, 01 natural sciences, [STAT]Statistics [stat], 010104 statistics & probability, Order (business), Modeling and Simulation, Statistics, Gamma distribution, EWMA chart, 0101 mathematics, Statistics, Probability and Uncertainty, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

In high-quality processes, events related to non-quality rarely occur and the times between these events (TBE) is likely to follow a skewed distribution like the gamma distribution. In order to mon...

Published
2021

47. An EWMA signed ranks control chart with reliable run length performances

Author

Philippe Castagliola, Petros Maravelakis, Stelios Psarakis, Theodoros Perdikis, Athens University of Economics and Business (AUEB), Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), University of Piraeus, Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)

Subjects
[SPI.OTHER]Engineering Sciences [physics]/Other, 021103 operations research, Wilcoxon signed-rank test, Markov chain, Nonparametric control chart, 0211 other engineering and technologies, Sample (statistics), 02 engineering and technology, Management Science and Operations Research, 01 natural sciences, [STAT]Statistics [stat], 010104 statistics & probability, Chart, Control chart, EWMA chart, EWMA control chart, 0101 mathematics, Safety, Risk, Reliability and Quality, Algorithm, Wilcoxon signed rank statistic, Statistic, Mathematics, Sign (mathematics)
Abstract

International audience; During the design phase of a control chart, the determination of its exact run length properties plays a vital role for its optimal operation. Markov chain or integral equation methods have been extensively applied in the design phase of conventional control charts. However, for distribution-free schemes, due to the discrete nature of the statistics being used (such as the sign or the Wilcoxon signed rank statistics, for instance), it is impossible to accurately compute their run length properties. In this work, a modified distribution-free phase II exponentially weighted moving average (EWMA)-type chart based on the Wilcoxon signed rank statistic is considered and its exact run length properties are discussed. A continuous transformation of the Wilcoxon signed rank statistic, combined with the classical Markov chain method, is used for the determination of the average run length in the in- and out-of control cases. Moreover, its exact performance is derived without any knowledge of the distribution of sample observations. Finally, an illustrative example is provided showing the practical implementation of our proposed chart.

Published
2021

48. The EWMA sign chart revisited: performance and alternatives without and with ties

Author

Philippe Castagliola, Theodoros Perdikis, Petros Maravelakis, Stelios Psarakis, Athanasios C. Rakitzis, Athens University of Economics and Business (AUEB), Conception, Pilotage, Surveillance et Supervision des systèmes (LS2N - équipe CPS3), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Nantes Université (Nantes Univ), University of the Aegean, and University of Piraeus

Subjects
Statistics and Probability, Sign statistic, Nonparametric control chart, Markov chain, Computer science, Nonparametric statistics, Articles, [STAT]Statistics [stat], Nonparametric control chart Sign statistic Markov chain EWMA control chart Rounding-off errors, Chart, Rounding-off errors, Econometrics, Control chart, EWMA control chart, EWMA chart, Statistics, Probability and Uncertainty, Sign (mathematics)
Abstract

International audience; The EWMA Sign control chart is an efficient tool for monitoring shifts in a process regardless the observations' underlying distribution. Recent studies have shown that, for nonparametric control charts, due to the discrete nature of the statistics being used (such as the Sign statistic), it is impossible to accurately compute their Run Length properties using Markov chain or integral equation methods. In this work, a modified nonparametric Phase II EWMA chart based on the Sign statistic is proposed and its exact Run Length properties are discussed. A continuous transformation of the Sign statistic, combined with the classical Markov Chain method, is used for the determination of the chart's in-and out-of-control Run Length properties. Additionally, we show that when ties occur due to measurement rounding-off errors, the EWMA Sign control chart is no longer distribution-free and a Bernoulli trial approach is discussed to handle the occurrence of ties and makes the proposed chart almost distribution-free. Finally, an illustrative example is provided to show the practical implementation of our proposed chart.

Published
2021
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49. Efficient algorithms for calculating the probability distribution of the sum of hypergeometric-distributed random variables

Author

Nataliya Chukhrova, Philippe Castagliola, Arne Johannssen, University of Hamburg, Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Independent and identically distributed random variables, MATLAB, Science, Clinical Biochemistry, Poisson distribution, 01 natural sciences, Algorithm by De Pril, 010104 statistics & probability, symbols.namesake, Probability theory, 0502 economics and business, Probability mass function, Applied mathematics, 0101 mathematics, Approximation, Statistical process monitoring, Mathematics, 050208 finance, Cumulative distribution function, 05 social sciences, Hypergeometric distribution, Hypergeometric np chart, Method Article, Convolution, [STAT]Statistics [stat], Medical Laboratory Technology, symbols, Probability distribution, Random variable
Abstract

Highlights • This article presents theoretical bases of three methods for determining the probability distribution of the sum of i.i.d. hypergeometric random variables: (1) direct convolution, (2) recursive algorithm by De Pril, (3) approximation. • We provide associated MATLAB codes (including context-specific customizations) for direct implementation of these methods and discuss technical aspects and essential details of the tweaks we have made. • A representative application example in SPM shows that the proposed approximation is considerably simpler in application than both other methods and it ensures a remarkable high accuracy of the results while reducing computational time considerably., Graphical abstract, In probability theory and statistics, the probability distribution of the sum of two or more independent and identically distributed (i.i.d.) random variables is the convolution of their individual distributions. While convoluting random variables following a binomial, geometric or Poisson distribution is a straightforward procedure, convoluting hypergeometric-distributed random variables is not. The problem is that there is no closed form solution for the probability mass function (p.m.f.) and cumulative distribution function (c.d.f.) of the sum of i.i.d. hypergeometric random variables. To overcome this problem, we propose an approximation for the distribution of the sum of i.i.d. hypergeometric random variables. In addition, we compare this approximation with two classical numerical methods, i.e., convolution and the recursive algorithm by De Pril, by means of an application in Statistical Process Monitoring (SPM). We provide MATLAB codes to implement these three methods for computing the probability distribution of the sum of i.i.d. hypergeometric random variables in an efficient way. The obtained results show that the proposed approximation has remarkable properties and may be helpful in all fields, where the problem of convoluting hypergeometric-distributed random variables occurs. Therefore, the approximation considered in this paper is well suited to make a change over established practices.•This article presents theoretical bases of three methods for determining the probability distribution of the sum of i.i.d. hypergeometric random variables: (1) direct convolution, (2) recursive algorithm by De Pril, (3) approximation.•We provide associated MATLAB codes (including context-specific customizations) for direct implementation of these methods and discuss technical aspects and essential details of the tweaks we have made.•A representative application example in SPM shows that the proposed approximation is considerably simpler in application than both other methods and it ensures a remarkable high accuracy of the results while reducing computational time considerably.

Published
2021

50. A variable parameters auxiliary information based quality control chart with application in a spring manufacturing process: The Markov chain approach

Author

Nger Ling Chong, Sajal Saha, Philippe Castagliola, Michael B. C. Khoo, Faijun Nahar Mim, Universiti Sains Malaysia (USM), Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), International University of Business Agriculture and Technology (IUBAT), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)

Subjects
[SPI.OTHER]Engineering Sciences [physics]/Other, [STAT.AP]Statistics [stat]/Applications [stat.AP], 021103 operations research, expected average time to signal, Markov chain, 0211 other engineering and technologies, 02 engineering and technology, Bivariate analysis, control chart, auxiliary information, 01 natural sciences, Industrial and Manufacturing Engineering, Standard deviation, 010104 statistics & probability, Chart, Sample size determination, Statistics, Control chart, average time to signal, EWMA chart, 0101 mathematics, variable parameters, Safety, Risk, Reliability and Quality, Statistic, Mathematics
Abstract

International audience; In this paper, a new variable parameters chart for the process mean with a statistic that integrates information from the study and auxiliary variables is proposed. The proposed variable parameters chart with auxiliary information (AI) (abbreviated as VP-AI) is optimally designed to minimize the out-of-control steady-state (i) average time to signal (ATS1) and (ii) expected average time to signal (EATS1) values when the mean shift sizes are known and unknown, respectively. The Markov chain approach is adopted to derive the formulae of the performance measures ATS1, standard deviation of the time to signal (SDTS1) and EATS1. The VP-AI chart significantly outperforms the standard VP chart; thus, justifying the incorporation of auxiliary information to enhance the ability of the VP chart. The VP-AI chart is also compared with the Shewhart AI, synthetic AI, exponentially weighted moving average (EWMA) AI, run sum AI and variable sample size and sampling interval (VSSI) AI charts. The VP-AI chart significantly outperforms the Shewhart AI, synthetic AI and VSSI AI charts for all levels of shifts. Meanwhile, the VP-AI chart outperforms the EWMA AI and run sum AI charts for most shifts. The VP-AI chart is found to be more robust than the EWMA-AI chart when the correlation coefficient is misspecified or the bivariate normality assumption is violated as long as the size of the shift is moderate or large. A real application which monitors spring elasticity is used to illustrate the VP-AI chart’s implementation.

Published
2021

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