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- Title
Bayes-conditional Control Charts for Weibull Quantiles under Type II Censoring.
- Authors
Haghighi, Firoozeh
- Abstract
In this paper, we develop a Bayesian approach for monitoring Weibull quantiles under Type II censoring when prior information is negligible relative to the data. The posterior median of quantiles is considered as the monitored statistic. A method based on the relationship between Bayesian and conditional limits under an appropriate prior distribution is proposed to obtain the posterior median of quantiles in closed form. A pivotal quantity based on the monitored statistic is proposed, and its distribution is conditionally derived. Then, the Bayes-conditional control limits are proposed. For the proposed charts, the probability of out-of-control can be derived without use of simulation. The performance of the Bayes-conditional charts is compared with the bootstrap charts through the simulation methods. The results show that to monitor the first quantiles, the lower-sided Bayes-conditional charts perform better than bootstrap charts in detecting a downward shift caused by decreasing in the shape parameter. Finally, an illustrative example is provided. Copyright © 2016 John Wiley & Sons, Ltd.
- Subjects
BAYESIAN analysis; WEIBULL distribution; QUANTILES; CENSORING (Statistics); RUN-length encoding; STATISTICAL process control; QUALITY control charts
- Publication
Quality & Reliability Engineering International, 2017, Vol 33, Issue 5, p959
- ISSN
0748-8017
- Publication type
Article
- DOI
10.1002/qre.2072