SPC Q Charts for a Binomial Parameter p : Short or Long Runs

Approximately normalized control charts, called Q charts, are proposed for charting a binomial random variable. Transformations are given for the two cases when the parameter p is known before charting is begun and when it is not known before charting is begun. These charts permit real-time charting essentially from the beginning of sampling and are especially useful for the case when p is not known in advance. These charts are all plotted in a standard normal scale and permit a flexible chart management program. For the case when p is assumed known, we present a table to compare the closeness of the control probabilities for these Q charts with those of the approximating normal distribution, and with those achieved by either classical 3-sigma p charts or with charts based on a standardized arcsin transformation chart. These results show that Q charts give better approximations than the classical p charts to the nominal normal probabilities, and are comparable with, but differ from, the arcsin charts.