Monitoring Weibull Quantiles by EWMA Charts Based on a Pivotal Quantity Conditioned on Ancillary Statistics

In this article, we study exponentially weighted moving average (EWMA) charts for monitoring Weibull quantiles (percentiles) based on a monitoring statistic conditioned on ancillary statistics when samples may be Type II censored. The monitoring statistic has a distribution form that is intractable, but analytic forms of the density and distribution functions can be derived when it is conditioned on ancillary statistics. We use these results to develop EWMA control charts and, in certain cases, evaluate their average run length without resorting to simulations. We compare the average run length performance of the EWMA charts with those of probability‐limit charts, studied by the authors, and probability‐limit charts enhanced with Western Electric alarm rules. We apply the charts to the breaking strength of carbon fibers to detect shifts in a specific Weibull quantile. Copyright © 2016 John Wiley & Sons, Ltd.