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Abstract
We address several theoretic issues involved in the design of geometric control charts. Primary among these is the question of setting probability limits, based on notions of “unbiasedness” and “conditional power”. A nearly ARL-unbiased design is defined by setting the in-control ARL as near as possible, given the discrete nature of the geometric distribution, to the peak of the ARL curve. An optimal design criterion, based on minimizing the sum of out-of-control ARLs for upward and downward shift is also suggested. These are shown to produce improved conditional power compared with the usual design.
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