Non-parametric Shewhart control charts

Abstract

Consider a training sample of independent random variables having an unknown strongly unimodal distribution. This sample is used to estimate the upper control limit (UCL) of a one-sided Shewhart control chart. The resulting control chart is meant to detect possible positive shifts of the distribution. A randomized estimator of the UCL is presented, the finite sample local optimality of the corresponding control chart is proved for sufficiently large sample sizes, and first-order asymptotic optimality of the error probabilities of this chart is derived.