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ARL-unbiased geometric and CCC_G control charts

Morais, M. C.

Sequential Analysis, 36 (2017), 513-527

In order to control increases and decreases in a parameter in a timely fashion, a chart should be set in such way that the ARL curve attains a maximum in the in-control situation.
This paper proposes not only a geometric (or cumulative count of conforming, CCC) chart, but also a CCC chart under group inspection (CCCG) for which all out-of-control ARL values are smaller than the in-control ARL, thus, provides an improvement on the designs described in Zhang et al. (2004) and Zhang, Xie et al. (2012). Moreover, by exploring the notions of uniformly most powerful unbiased tests with randomization probabilities, we are able not only to eliminate the bias of the ARL function of the geometric charts, but also to bring their in-control ARL exactly to a pre-specified value.
Instructive examples are provided to illustrate the efficiency of the proposed charts.