Misuse of XmR quality control charts for common single parameter probability distributions

Individuals XmR control charts based on the normality assumption and a moving range estimate for a sigma typically are used if data occur infrequently or rational subgroups are not obvious. Although often are advised as a simple robust omnibus chart for any (non-normal) data, this practice is not always advisable, especially for common single parameter distributions for which exact and equally simple methods exist or for ldquophase 1rdquo start-up data of unknown stability. We investigate performance consequences when these charts are applied erroneously to binomial, Poisson, geometric, or exponential processes, using either 3-sigma or probability limits, often resulting in significantly compromised average run lengths due to over-fitting of both natural and unnatural variation via an in-fact non-existent second parameter (sigma).