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The problem of detecting a shift of a percentile of a strength distribution in a quality control setting is considered. Shewhart-type charts for lower percentiles are developed based on small samples. Lower and upper control limits for “percentile charts” for Weibull (extreme-value) and lognormal (normal) distributions which were obtained by Monte Carlo simulations are presented. Average run lengths of the Weibull percentile charts and the relationships between them and X̄ and R charts for Weibull data are also investigated. An application to the breaking stress of carbon fibers is presented to illustrate the methods.
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Padgett et al. (1990) studied this question.
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