Monitoring the conforming fraction of high-quality processes using a control chart p under a small sample size and an alternative estimator

Abstract

In this paper, we propose to change the traditional monitored statistic in a control chart p, by changing the sampling proportion \({\hat{p}}\) to a new statistics denoted as \({\tilde{p}}\). We aim to minimize problems in designing the control chart p for high quality processes when only a small sample size is available. The idea of the new statistics is simple, as it involves taking two independent samples of a Bernoulli population. From each sample, the sampling proportion is calculated, and the new statistic to monitor is the weighted mean of the sampling proportion of each sample employed to weight the overall sampling proportion. We note that the control chart p that employs the new \({\tilde{p}}\) statistic provides more in-control values of average run length closer to the usual fixed value of 370 than the traditional statistic, that is, the sampling proportion. Numerical examples illustrate the new proposal.