Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 403-416 |
| Number of pages | 14 |
| Journal | Quality and Reliability Engineering International |
| Volume | 34 |
| Issue number | 3 |
| DOIs | |
| State | Published - 04 2018 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:Copyright © 2017 John Wiley & Sons, Ltd.
Keywords
- CUSUM chart
- EWMA chart
- Type-II censoring
- Weibull percentiles
- complete data
- pivotal quantity