A Binomial GLR Control Chart for Monitoring a Proportion

Huang, Wandi; Reynolds, Marion R.; Wang, Qianqian

doi:10.1080/00224065.2012.11917895

Cited by 28 publications

(26 citation statements)

References 20 publications

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“…The SSANOS values in Table 3 show clearly that the MGLR chart has better performance than the set of two-sided Bernoulli CUSUM charts. In fact, the MGLR chart in column [11] is uniformly better than the CUSUM charts in columns [4] to [6]. We conclude that the MGLR chart is clearly the preferred choice when the components of p 0 are of approximately the same magnitude.…”

Section: Performance Comparison Of the Mglr Chart And The Set Of Twmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

“…Some work on using a GLR chart to monitor a process proportion has been done in the past, but this work has focused on monitoring when there are two categories. For more details, see Huang et al 11 and Wang and Reynolds. 12 In past work on the GLR chart, it is usually assumed that the in-control parameters are well estimated from Phase I. Hawkins et al 13 proposed a change-point control chart to monitor a normal process mean where Phase I estimation is not required.…”

Section: Introductionmentioning

confidence: 99%

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A GLR control chart for monitoring a multinomial process

Lee

Peng²,

Wang

et al. 2017

Quality & Reliability Eng

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The problem of detecting changes in the parameter p in a Bernoulli process with two possible categories for each observation has been extensively investigated in the SPC literature, but there is much less work on detecting changes in the vector parameter p in a multinomial process where there are more than two categories. A few papers have considered the case in which the direction of the change in p is known, but there is almost no work for the important case in which the direction of the change is unknown and individual observations are obtained. This paper proposes a multinomial generalized likelihood ratio (MGLR) control chart based on a likelihood ratio statistic for monitoring p when individual observations are obtained and the direction and size of the change in p are unknown. A set of 2‐sided Bernoulli cumulative sum (CUSUM) charts is proposed as a reasonable competitor of the MGLR chart. It is shown that the MGLR chart has better overall performance than the set of 2‐sided Bernoulli CUSUM charts over a wide range of unknown shifts. Equations are presented for obtaining the control limit of the MGLR chart when there are three or four components in p.

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Section: Performance Comparison Of the Mglr Chart And The Set Of Twmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A GLR control chart for monitoring a multinomial process

Lee

Peng²,

Wang

et al. 2017

Quality & Reliability Eng

Self Cite

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“…Early work was reviewed by Xie et al and Topalidou and Psarakis . Recent developments for monitoring binomial data include Xie et al, Huang et al, Huang et al, and Wang and Reynolds . As to the monitoring of multinomial data, one can refer to the probability tree method with h − 1 stages for h categories developed by Duran and Albin and cumulative sum (CUSUM) chart based on likelihood ratio test suggested by Ryan et al To follow up, Weiß and Yashchin made more recent contributions to monitoring multinomial data.…”

Section: Introductionmentioning

confidence: 99%

Latent change‐point detection in ordinal categorical data

Wang

Ding

2018

Quality & Reliability Eng

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Statistical process control (SPC) techniques have been widely used for online surveillance and offline diagnosis in many applications. Because of cost constraint or technical difficulty, it is quite common that the quality of products or service is measured by ordinal factors with ordered attribute levels such as excellent, acceptable, and unacceptable. This article studies phase I analysis of such ordinal categorical processes to identify change points. By assuming that attribute levels are determined by a latent continuous variable, this work suggests a modified log‐linear model to characterize ordinal information among the attribute levels. Then a change‐point detection method is proposed on the basis of the generalized likelihood ratio test (GLRT). Simulation results prove the method's strong detection power, high diagnostic accuracy, and robustness under various distributions of the latent variable.

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“…GLR charts have some advantages that the size of the parameter change does not need to be specified and these charts have been shown to be very effective in a wide variety of settings in SPC applications. Recent investigations of this chart include Hawkins et al (2003), Runger and Testik (2003), Capizzi and Masarotto (2008), Zou et al (2009), Reynolds and Lou (2010), Huang et al (2012Huang et al ( , 2013, Xu et al (2012Xu et al ( , 2013, Wang and Reynolds (2013), and Reynolds et al (2013).…”

Section: Introductionmentioning

confidence: 99%

GLR Charts for Simultaneously Monitoring a Sustained Shift and a Linear Drift in the Process Mean

Choi¹,

Lee²

2014

Communications for Statistical Applications and Methods

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This paper considers the problem of monitoring the mean of a normally distributed process variable when the objective is to effectively detect both a sustained shift and a linear drift. The design and application of a generalized likelihood ratio (GLR) chart for simultaneously monitoring a sustained shift and a linear drift are evaluated. The GLR chart has the advantage that when we design this chart, we do not need to specify the size of the parameter change. The performance of the GLR chart is compared with that of other control charts, such as the standard cumulative sum (CUSUM) charts and the cumulative score (CUSCORE) charts. And we compare the proposed GLR chart with the GLR charts designed for monitoring only a sustained shift and for monitoring only a linear drift. Finally, we also compare the proposed GLR chart with the chart combinations. We show that the proposed GLR chart has better overall performance for a wide range of shift sizes and drift rates relative to other control charts, when a special cause produces a sustained shift and/or a linear drift in the process mean.

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A Binomial GLR Control Chart for Monitoring a Proportion

Cited by 28 publications

References 20 publications

A GLR control chart for monitoring a multinomial process

A GLR control chart for monitoring a multinomial process

Latent change‐point detection in ordinal categorical data

GLR Charts for Simultaneously Monitoring a Sustained Shift and a Linear Drift in the Process Mean

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