Conditional Control Charts for Weibull Quantiles Under Type II Censoring |
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| Authors: | Firoozeh Haghighi Francis Pascual Philippe Castagliola |
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| Affiliation: | 1. Department of Mathematics, Statistics and Computer Sciences, University of Tehran, Tehran, Iran;2. IRCCyN UMR CNRS 6597, Nantes, France;3. Department of Mathematics, Washington State University, Pullman, WA 99164‐3113, USA;4. LUNAM Université, Université de Nantes & IRCCyN UMR CNRS 6597, Nantes, France |
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| Abstract: | In this article, we propose control charts for the quantiles of the Weibull distribution, for type II censored data, based on the distribution of a pivotal quantity conditioned on ancillary statistics. These control charts must be considered as alternatives to bootstrap type control charts. We derive an analytical form of the conditional distribution function of the monitored statistic and we use this function to propose ARL‐unbiased control limits. We further demonstrate that the proposed conditional chart have a general analytical form for the ARL that can be evaluated numerically without use of simulations and we also show that these charts perform at least as well as the bootstrap type ones. We finally apply the conditional charts to a dataset on the strength of carbon fibers to detect shifts in a specified Weibull quantile. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | average run length conditional charts statistical process control unbiased control charts Weibull quantiles |
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