A Review and perspective on surveillance of Bernoulli processes

Self Cite

The geometric control chart has been shown to be more effective than p and np‐charts for monitoring the proportion of nonconforming items, especially for high‐quality Bernoulli processes. When implementing a geometric control chart, the in‐control proportion nonconforming is typically unknown and must be estimated. In this article, we used the standard deviation of the average run length (SDARL) and the standard deviation of the average number of inspected items to signal, SDARL*, to show that much larger phase I sample sizes are needed in practice than implied by previous research. The SDARL (or SDARL*) was used because practitioners would estimate the control limits based on different phase I samples. Thus, there would be practitioner‐to‐practitioner variability in the in‐control ARL (or ARL*). In addition, we recommend a Bayes estimator for the in‐control proportion nonconforming to take advantage of practitioners' knowledge and to avoid estimation problems when no nonconforming items are observed in the phase I sample. If the in‐control proportion nonconforming is low, then the required phase I sample size may be prohibitively large. In this case, we recommend an approach to identify a more informative continuous variable to monitor. Copyright © 2012 John Wiley & Sons, Ltd.

Section: Introductionmentioning

confidence: 99%

Geometric Charts with Estimated Control Limits

Zhang

Peng

Schuh

et al. 2012

Self Cite

“…Many methods have been proposed for monitoring rare event data; see Woodall and Driscoll, Szarka and Woodall, and Ali et al …”

Section: Resultsmentioning

confidence: 99%

An Evaluation of Wheeler's Method for Monitoring the Rate of Rare Events

Mao

Ginther

Woodall

2016

Self Cite

Its wide application in practice makes the monitoring of the rate of rare events a popular research topic. Recently a researcher proposed plotting the counts between events on an individuals X‐chart with an upper control limit to detect process improvement and plotting the reciprocals of the counts on an X‐chart to detect process deterioration. He also used the median as the center line and the median moving range to obtain control limits in both control charts to address the problem of the standard deviation estimate inflation caused by extreme values. In our paper, we investigated the statistical performance of the four proposed approaches using simulation. We find using the mean results in a high proportion of ineffective control limits, while using the median avoids the issue of ineffective control limits but produces an unacceptably high proportion of false alarms. Copyright © 2016 John Wiley & Sons, Ltd.

“…When they are results from Bernoulli experiments, the n p and p charts may be applied to monitor the stability of nonconforming proportion . Good review papers about attribute charts can be found in the literature as these written by Szarka and Woodall and Woodall . Some recent contributions on n p or p charts varying estimator, sampling, or decision scheme can be cited .…”

Section: Introductionmentioning

confidence: 99%

Control charts to monitor rates and proportions

Fernandes

Bourguignon

2018

In this paper, we call attention for monitoring proportions and rates when they are not results of Bernoulli experiments. To deal with this problem, usually control charts based on Beta distributions are built as this distribution is a well‐known one. However, in practice, there are other distributions to be considered as Simplex and Unit Gamma distributions. The impact of the speed to signal a shift in the average proportion in terms of out‐of‐control average run length is measured when the control limits determined under a Beta distribution is equivocally used to monitor individual rates from Simplex or Unit Gamma distributions or vice versa.