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.
Acknowledgements
Most of this research was done under the NWO grant Semiparametrics in Statistical Process Control for the first author.