Phase II Performance of P-Charts and P'-Charts

Abstract

The p-chart has traditionally been used to monitor processes that yield binary data. The p'-chart that adjusts the p-chart control limits for between subgroup variation was proposed in 2002 in an effort to reduce the p-chart's false alarm rate in the presence of large subgroup sizes. As illustrated with an example using real pharmacy data, the p-chart and p'-chart often yield very different results and how to decide which chart is appropriate for a given situation is not clear. A simulation study was undertaken to examine the phase II performance of the p-chart and p'-chart. With large subgroup sizes or when the between subgroup variation is high, p-charts have relatively high sensitivity to detect out-of-control shifts, but exhibit a high false alarm rate when the process is in-control, while p'-charts have low sensitivity to detect out-of-control shifts but have relatively low false alarm rates. For a specific situation, Youden's index can be used to decide whether to act on p-chart or p'-chart results while considering the relative costs of false positives and false negatives.