Poisson DEWMA Control Chart

Zhang, Lingyun; Govindaraju, K.; Lai, C. D.

doi:10.1081/sac-120023889

Cited by 45 publications

(28 citation statements)

References 3 publications

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“…The reader should bear in mind that the PEWMA chart introduced by Borror et al, and the ones proposed by Gan, Zhang et al, Sheu and Chiu, and Rakitzis et al are all ARL‐biased.…”

Section: An Arl‐unbiased Pewma Chartmentioning

confidence: 99%

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Improving the ARL profile and the accuracy of its calculation for Poisson EWMA charts

Morais

Knoth

2020

Quality & Reliability Eng

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The Poisson exponentially weighted moving average (PEWMA) chart was proposed in 1998 by Borror, Champ, and Rigdon to monitor the mean of counts of nonconformities. This chart regrettably fails to have an in‐control average run length (ARL) larger than any out‐of‐control ARL, ie, the PEWMA chart is ARL‐biased. Moreover, due to the discrete character of its control statistic the PEWMA chart and the resulting subtleties of its ARL calculation, it is difficult to set the control limits in such way that the in‐control ARL takes a desired value, say ARL0. In this paper, we establish an improved Markov chain technique to approximate the ARL of EWMA for count output; propose two ARL‐unbiased counterparts of the PEWMA chart; and use the R statistical software to provide illustrations of these charts with a decidedly superior ARL profile and an in‐control ARL equal to ARL0. We also compare the ARL performance of the proposed charts with the one of a few competing control charts for the mean of independent and identically distributed (i.i.d.) Poisson counts.

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“…The reader should bear in mind that the PEWMA chart introduced by Borror et al, and the ones proposed by Gan, Zhang et al, Sheu and Chiu, and Rakitzis et al are all ARL‐biased.…”

Section: An Arl‐unbiased Pewma Chartmentioning

confidence: 99%

“…Take for example the modified EWMA control statistics leading to the ceil, round, and floor EWMA charts proposed by Gan . This paper has prompted several other works addressing EWMA charts for Poisson counts such as Borror et al, Zhang et al, Sheu and Chiu, and Rakitzis et al…”

Section: Introductionmentioning

confidence: 99%

Improving the ARL profile and the accuracy of its calculation for Poisson EWMA charts

Morais

Knoth

2020

Quality & Reliability Eng

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“…E-mail: au1319@mail.au.edu.tw I Downloaded by [University of Sussex Library] at 11:38 06 June 2016 offers sufficient flexibility to detect a certain type of shift. Zhang et al [20] introduced a Poisson double EWMA (PDEWMA) chart and showed that this chart is more sensitive to downward process shifts than the PEWMA chart. Khoo [6] presented a Poisson moving average control chart that provides a better alternative to the c chart.…”

Section: Introductionmentioning

confidence: 99%

On the Steady-State Performance of the Poisson Double GWMA Control Chart

Chiu

2015

Quality Technology & Quantitative Management

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______________________________________________________________________Abstract: This article presents a control chart called "Poisson double GWMA" (PDGWMA) chart for monitoring Poisson-distributed processes. Using simulation, the steady-state average run length (SSARL) of PDGWMA chart is evaluated and compared with those of other control charts including Poisson EWMA, Poisson GWMA and Poisson double EWMA (PDEWMA). It is shown that this chart is always more sensitive than other control charts in detecting an out-of-control signal. The PDGWMA chart is a generalized model for which the PDEWMA chart is a special case and also is an effective control chart in situations where the quality deterioration (upward shift) and the quality improvement (downward shift) can be detected agilely, which is important to a modern advanced system.

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“…Shamma et al and Shamma and Shamma introduced a double EWMA (DEWMA) chart for normally distributed data. Zhang et al used the DEWMA chart for monitoring Poisson data (PDEWMA), and Riaz and Abbasi proposed a nonparametric DEWMA (NPDEWMA) chart for monitoring the location parameter that has an unknown distributional behavior. Other works about DEWMA charts are in previous studies …”

Section: Introductionmentioning

confidence: 99%

A double exponentially weighted moving average control chart for monitoring COM‐Poisson attributes

Alevizakos

Koukouvinos

2019

Quality & Reliability Eng

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The Conway‐Maxwell‐Poisson (COM‐Poisson) distribution is a two‐parameter generalization of the Poisson distribution, which can be used for overdispersed or underdispersed count data and also contains the geometric and Bernoulli distributions as special cases. This article presents a double exponentially weighted moving average control chart with steady‐state control limits to monitor COM‐Poisson attributes (regarded as CMP‐DEWMA chart). The performance of the proposed control chart has been evaluated in terms of the average, the median, and the standard deviation of the run‐length distribution. The CMP‐DEWMA control chart is studied not only to detect shifts in each parameter individually but also in both parameters simultaneously. The design parameters of the proposed chart are provided, and through a simulation study, it is shown that the CMP‐DEWMA chart is more effective than the EWMA chart at detecting downward shifts of the process mean. Finally, a real data set is presented to demonstrate the application of the proposed chart.

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Poisson DEWMA Control Chart

Cited by 45 publications

References 3 publications

Improving the ARL profile and the accuracy of its calculation for Poisson EWMA charts

Improving the ARL profile and the accuracy of its calculation for Poisson EWMA charts

On the Steady-State Performance of the Poisson Double GWMA Control Chart

A double exponentially weighted moving average control chart for monitoring COM‐Poisson attributes

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