Shewhart-Type Charts for Percentiles of Strength Distributions

Abstract

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.

• Average Run Length
• Control Limits
• Lognormal Distribution
• Shewhart Control Charts
• Weibull Distribution

Additional information

Notes on contributors

W. J. Padgett

Dr. Padgett is a Professor and Chairman of the Department of Statistics.

John D. Spurrier

Dr. Spurrier is a Professor in the Department of Statistics.