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1. Monitoring the Ratio of Two Normal Variables Based on Triple Exponentially Weighted Moving Average Control Charts with Fixed and Variable Sampling Intervals

Author

Xuelong Hu, Guan Sun, Fupeng Xie, and Anan Tang

Subjects
SPC, RZ, EWMA chart, TEWMA chart, VSI-TEWMA chart, Mathematics, QA1-939
Abstract

In statistical process control (SPC), the ratio of two normal random variables (RZ) is a valuable statistical indicator to be taken as the charting statistic. In this work, we propose a triple exponentially weighted moving average (TEWMA) chart for monitoring the RZ. Additionally, the variable sampling interval (VSI) strategy has been adopted to different control charts by researchers. With the application of this strategy, the VSI-TEWMA-RZ chart is then developed to further improve the performance of the proposed TEWMA-RZ chart. The run length (RL) properties of the proposed TEWMA-RZ and VSI-TEWMA-RZ charts are obtained by the widely used Monte-Carlo (MC) simulations. Through the comparisons with the VSI-EWMA-RZ and the VSI-DEWMA-RZ charts, the VSI-TEWMA-RZ chart is statistically more sensitive than the VSI-EWMA-RZ and the VSI-DEWMA-RZ charts in detecting small and moderate shifts. Moreover, it turned out that the VSI-TEWMA-RZ chart has better performance than the TEWMA-RZ chart on the whole. Furthermore, this paper illustrates the implementation of the proposed charts with an example from the food industry.

Published
2022
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2. On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion.

Author

XueLong Hu, AnAn Tang, YuLong Qiao, JinSheng Sun, and BaoCai Guo

Subjects
Medicine, Science
Abstract

Recent researches on the control charts with unknown process parameters have noticed the large variability in the conditional in-control average run length (ARL) performance of control charts, especially when a small number of Phase I samples is used to estimate the process parameters. Some research works have been conducted on the conditional ARL performance of different types of control charts. In this paper, by simulating the empirical distribution of the conditional ARL and especially using the exceedance probability criterion (EPC), we study the conditional ARL performance of the synthetic [Formula: see text] chart. Our results show that a large amount of Phase I samples is needed to obtain a specified EPC of the synthetic chart. For the available number of Phase I samples, the control limits of the synthetic chart are adjusted using the EPC method to improve its conditional in-control performance. It is shown that, for small mean shift sizes, a tradeoff should be made between the conditional in-control and out-of-control performances. For moderate to large shifts, the conditional performance of the synthetic chart using the adjusted control limits is generally satisfied. By comparing the results with the ones using the bootstrap approach, it can also be concluded that the conditional performances of both approaches are comparable. While the method proposed in this paper requires much less computation work than the bootstrap approach.

Published
2020
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26. 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
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27. 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
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30. 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
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32. Optimal design of the adaptive EWMA chart for the mean based on median run length and expected median run length

Author

Xuelong Hu, Anan Tang, Jinsheng Sun, 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), and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)

Subjects
Optimal design, 021103 operations research, Information Systems and Management, Steady state (electronics), 0211 other engineering and technologies, Process (computing), Magnitude (mathematics), Ranging, 02 engineering and technology, Management Science and Operations Research, 01 natural sciences, [STAT]Statistics [stat], 010104 statistics & probability, Chart, Management of Technology and Innovation, Industrial relations, Statistics, Range (statistics), EWMA chart, 0101 mathematics, Business and International Management, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

The Adaptive Exponentially Weighted Moving Average (AEWMA) chart, which combines the Shewhart and classical EWMA schemes, is usually designed using the Average Run Length () as the criterion to be optimized. The shape of the run length distribution is known to change according to the magnitude of the shift in the process mean, ranging from highly skewed when the process is in-control or nearly to approximately symmetric when the shift is large. Therefore, the Median Run Length () provides a more meaningful interpretation than the . In this paper, the is used as an alternative performance criterion, and the AEWMA chart is optimized for a wide range of mean shifts using zero and steady state modes. Comparative results show that the suggested AEWMA chart offers a more balanced protection for detecting both small and large shifts in the process mean than the classical EWMA chart, in terms of the performance. The construction of the -based AEWMA chart is also illustrated using an example, and it is com...

Published
2018
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33. The effect of measurement errors on the adaptive EWMA X¯ chart

Author

Xuelong Hu, Philippe Castagliola, Jinsheng Sun, and Anan Tang

Subjects
010104 statistics & probability, 021103 operations research, Observational error, Control theory, 0211 other engineering and technologies, 02 engineering and technology, EWMA chart, 0101 mathematics, Management Science and Operations Research, Safety, Risk, Reliability and Quality, 01 natural sciences, Mathematics
Published
2018
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34. Conditional median run length performance of the synthetic X¯ chart with unknown process parameters

Author

Xiaojian Zhou, Xuelong Hu, Philippe Castagliola, Anan Tang, Panpan Zhou, Nanjing University of Science and Technology (NJUST), 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), Nanjing University (NJU), Nanjing University of Science and Technology [Nanjing], Université de Nantes - Faculté des Sciences et des Techniques, Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - Faculté des Sciences et des Techniques, Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), and Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST)

Subjects
021103 operations research, 0211 other engineering and technologies, Process (computing), 02 engineering and technology, Management Science and Operations Research, 01 natural sciences, [STAT]Statistics [stat], 010104 statistics & probability, 0101 mathematics, Safety, Risk, Reliability and Quality, Algorithm, \bar x and R chart, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

International audience

Published
2020
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35. An adaptive EWMA median chart for monitoring the process mean

Author

Wu Shu, Xuelong Hu, Zhao Min, Huang Teng, and Anan Tang

Subjects
021103 operations research, Markov chain, Computer science, 0211 other engineering and technologies, Process (computing), Exponentially weighted moving average, 02 engineering and technology, Statistical process control, 01 natural sciences, 010104 statistics & probability, Chart, Control theory, EWMA chart, 0101 mathematics
Abstract

The Adaptive Exponentially Weighted Moving Average (AEWMA) chart is known to combine the Shewhart and the classical EWMA schemes in a smooth way. In this paper, we studied the run length properties of the AEWMA median chart using a Markov chain approach and the performance of the proposed chart is compared with the existing Shewhart and EWMA median charts. The comparative results show that the AEWMA median chart represents a good alternative to achieve a reasonable balance for various shift sizes.

Published
2019
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36. A new nonparametric adaptive EWMA control chart with exact run length properties

Author

Philippe Castagliola, Anan Tang, Jinsheng Sun, Xuelong Hu, 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 Science and Technology [Nanjing], Université de Nantes - Faculté des Sciences et des Techniques, and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - Faculté des Sciences et des Techniques

Subjects
021103 operations research, General Computer Science, Markov chain, Computer science, Parametric Probability Distribution, 0211 other engineering and technologies, General Engineering, Exponentially weighted moving average, Nonparametric statistics, 02 engineering and technology, [STAT]Statistics [stat], Chart, 0202 electrical engineering, electronic engineering, information engineering, Range (statistics), 020201 artificial intelligence & image processing, Control chart, EWMA chart, Algorithm, Statistic, ComputingMilieux_MISCELLANEOUS, Count data
Abstract

The AEWMA (Adaptive Exponentially Weighted Moving Average) chart is a scheme that combines the Shewhart and the classical EWMA charts in a smooth way. In this paper, a new nonparametric AEWMA-type chart for count data, based on the sign statistic (denoted as the CAEWMA SN chart), is proposed without requiring any parametric probability distribution for the underlying process. The most valuable characteristics of this work are: (i) it combines the advantages of a nonparametric control chart with the best overall shift detection properties of an AEWMA-type chart, (ii) only positive integer-valued weights are used for the monitoring of count data, and the plotted statistic is also an integer and (iii) an appropriate discrete-time Markov chain technique is provided to compute the exact run length properties of the proposed chart without any expensive simulation or unreliable approximation. Detailed guidelines and recommendations for selecting the chart’s parameters are provided with two illustrative examples. An extensive comparative study demonstrates the superiority of the CAEWMA SN chart over a number of existing control charts, including a discrete EWMA-type sign chart, two classical continuous EWMA-type charts and a GWMA-type sign chart, for detecting a wide range of location shifts.

Published
2019
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37. The adaptive EWMA median chart for known and estimated parameters

Author

Philippe Castagliola, Anan Tang, Jinsheng Sun, Xuelong Hu, Nanjing University of Science and Technology [Nanjing], Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - Faculté des Sciences et des Techniques, 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 - Faculté des Sciences et des Techniques, Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Nanjing University of Science and Technology (NJUST), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST)

Subjects
Statistics and Probability, 021103 operations research, Applied Mathematics, 0211 other engineering and technologies, Exponentially weighted moving average, 02 engineering and technology, 01 natural sciences, [STAT]Statistics [stat], 010104 statistics & probability, Chart, Modeling and Simulation, Statistics, EWMA chart, 0101 mathematics, Statistics, Probability and Uncertainty, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

The Adaptive Exponentially Weighted Moving Average (AEWMA) chart is known to combine the Shewhart and the classical EWMA schemes in a smooth way. Its performance has been investigated under the ass...

Published
2019

38. Conditional design of the CUSUM median chart for the process position when process parameters are unknown

Author

Xuelong Hu, Anan Tang, Philippe Castagliola, Nanjing University of Posts and Telecommunications [Nanjing], Nanjing university of posts and telecommunications, Systèmes Logistiques et de Production (SLP ), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - Faculté des Sciences et des Techniques, 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 - Faculté des Sciences et des Techniques, Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Nanjing University of Science and Technology [Nanjing], Nanjing University of Posts and Telecommunications [Nanjing] (NJUPT), 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), Nanjing University of Science and Technology (NJUST), and Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST)

Subjects
Statistics and Probability, 021103 operations research, Applied Mathematics, 0211 other engineering and technologies, Process (computing), CUSUM, 02 engineering and technology, 01 natural sciences, [STAT]Statistics [stat], 010104 statistics & probability, Chart, Position (vector), Modeling and Simulation, Statistics, Control chart, 0101 mathematics, Statistics, Probability and Uncertainty, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

In practice, different practitioners will use different Phase I samples to estimate the process parameters, which will lead to different Phase II control chart's performance. Researches ref...

Published
2019
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