| Summary: | 碩士 === 國立臺灣科技大學 === 工業管理系 === 105 === In this paper, we propose three 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 (ARL). In Type-II censoring, the EWMA-SEV-Q chart is slightly better than the CUSUM-SEV-Q chart in terms of ARL. Two numerical examples are used to illustrate the applications of the proposed control charts.
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