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An ARL-unbiased modified np-chart for autoregressive binomial counts

Morais, M. C. ; Wittenberg, P.; Cruz, C.J.

Stochastics and Quality Control, 38 (2023), 11-24

Independence between successive counts is not a sensible premise while dealing, for instance, with very high sampling rates. After assessing the impact of falsely assuming independent binomial counts in the performance of np-charts, such as the one with 3-sigma control limits, we propose a modified np-chart for monitoring first-order autoregressive counts with binomial marginals. This simple chart has an in-control average run length (ARL) larger than any out-of-control ARL, i.e., it is ARL-unbiased. Moreover, the ARL-unbiased modified np-chart triggers a signal at sample t with probability one, if the observed value of the control statistic is beyond the lower and upper control limits L and U. In addition to this, the chart emits a signal with probability gL (resp. gU) if that observed value coincides with L (resp. U ). This randomization allows us to set the control limits in such a way that the in-control ARL takes the desired value ARL0, in contrast to traditional charts with discrete control statistics. Several illustrations of the ARL-unbiased modified np-chart are provided, using the R statistical software and resorting to real and simulated data.