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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-σ 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 probabilityγL{\gamma_{L}}(resp.γU{\gamma_{U}}) 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 valueARL0{\operatorname{ARL}_{0}}, in contrast to  traditional  charts with discrete control statistics. Several illustrations of the ARL-unbiased modified  np -chart are provided, using the statistical software R and resorting to real and simulated data.

An ARL-Unbiased Modified np -Chart for Autoregressive Binomial Counts