An ARL-unbiased c-chart

In statistical process control (SPC), it is usual to assume that counts have a Poisson distribution. The non‐negative, discrete, and asymmetrical character of a control statistic with such a distribution and the value of its target mean may prevent the quality control practitioner to deal with a c‐chart with a pre‐specified in‐control average run length (ARL) or the ability to control not only increases but also decreases in the mean of those counts in a timely fashion. Furthermore, the c‐charts proposed in the SPC literature tend to be ARL‐biased, in the sense that some out‐of‐control ARL values are larger than the in‐control ARL. In this paper, we explore the notions of randomized and uniformly most powerful unbiased tests to eliminate the bias of the ARL function of the c‐chart.