A heuristic method for obtaining quasi ARL‐unbiased p‐Charts

Abstract

AbstractIt is known that control charts based on equal tail probability limits are ARL biased when the distribution of the plotted statistic is skewed. This is the case for p‐Charts that serve to monitor processes on the basis of the binomial distribution. For the particular case of the standard three‐sigma Shewhart p‐Chart, which is built on the basis of the binomial to normal distribution approximation, this ARL‐biased condition is particularly severe, and it greatly affects its monitoring capability. Surprisingly, in spite of this, the standard p‐Chart is still widely used and taught. Through a literature search, it was identified that several, simple to use, improved alternative p‐Charts had been proposed over the years; however, at first instance, it was not possible to determine which of them was the best. In order to identify the alternative that excelled, an ARL performance comparison was carried out in terms of their ARL bias severity level (ARLBSL) and their In‐Control ARL (ARL0). The results showed that even the best performing alternative charts would often be ARL‐biased or have nonoptimal ARL0. To improve on the existing alternatives, the “Kmod p‐Chart” was developed; it offers easiness of use, superior ARL performance, and a simple and effective method for verifying its ARL‐bias condition.