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 (UMPU) to eliminate the bias of the ARL function of the c-chart.