Geometric Charts with Estimated Control Limits

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 (c) 2012 John Wiley & Sons, Ltd.