New control charts for monitoring the Weibull percentiles under complete data and Type‐II censoring

In this paper, we propose 3 new control charts for monitoring the lower Weibull percentiles under complete data and Type‐II censoring. In transforming the Weibull distribution to the smallest extreme value distribution, Pascaul et al (2017) presented an exponentially weighted moving average (EWMA) control chart, hereafter referred to as EWMA‐SEV‐Q, based on a pivotal quantity conditioned on ancillary statistics. We extended their concept to construct a cumulative sum (CUSUM) control chart denoted by CUSUM‐SEV‐Q. We provide more insights of the statistical properties of the monitoring statistic. Additionally, in transforming a Weibull distribution to a standard normal distribution, we propose EWMA and CUSUM control charts, denoted as EWMA‐YP and CUSUM‐YP, respectively, based on a pivotal quantity for monitoring the Weibull percentiles with complete data. With complete data, the EWMA‐YP and CUSUM‐YP control charts perform better than the EWMA‐SEV‐Q and CUSUM‐SEV‐Q control charts in terms of average run length. In Type‐II censoring, the EWMA‐SEV‐Q chart is slightly better than the CUSUM‐SEV‐Q chart in terms of average run length. Two numerical examples are used to illustrate the applications of the proposed control charts.