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

Fu Kwun Wang*, Berihun Bizuneh, Xiao Bin Cheng

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

16 Scopus citations

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 languageEnglish
Pages (from-to)403-416
Number of pages14
JournalQuality and Reliability Engineering International
Volume34
Issue number3
DOIs
StatePublished - 04 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
Copyright © 2017 John Wiley & Sons, Ltd.

Keywords

  • CUSUM chart
  • EWMA chart
  • Type-II censoring
  • Weibull percentiles
  • complete data
  • pivotal quantity

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