Monitoring the Weibull Shape Parameter by Control Charts for the Sample Range of Type II Censored Data
Version of Record online: 10 AUG 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Quality and Reliability Engineering International
Volume 28, Issue 2, pages 233–246, March 2012
How to Cite
Pascual, F. and Li, S. (2012), Monitoring the Weibull Shape Parameter by Control Charts for the Sample Range of Type II Censored Data. Qual. Reliab. Engng. Int., 28: 233–246. doi: 10.1002/qre.1239
- Issue online: 20 FEB 2012
- Version of Record online: 10 AUG 2011
- Manuscript Accepted: 12 JUN 2011
- Manuscript Received: 19 MAY 2011
- average run length;
- statistical process control;
- unbiased control charts
In this paper, we propose control charts to monitor the Weibull shape parameter β under type II (failure) censoring. This chart scheme is based on the sample ranges of smallest extreme value distributions derived from Weibull processes. We suggest one-sided (high-side or low-side) and two-sided charts, which are unbiased with respect to the average run length (ARL). The control limits for all types of charts depend on the sample size, the number of failures c under type II censoring, the desired stable-process ARL, and the stable-process value of β. This article also considers sample size requirements for phase I in retrospective charts. We investigate the effect of c on the out-of-control ARL. We discuss a simple approach to choosing c by cost minimization. The proposed schemes are then applied to data on the breaking strengths of carbon fibers. Copyright © 2011 John Wiley & Sons, Ltd.