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This introductory paper explains basic probability concepts and summarizes in a fatigue context the state of the art for analyses of life data using one-sided lower statistical tolerance limits. Types I and II censoring are considered for both the two-parameter log-normal and Weibull distributions, and the corresponding approximate and exact one-sided lower tolerance limit calculations are illustrated and discussed. In addition, Antle's likelihood ratio test for discriminating between these two-parameter life distributions is summarized. The classic one-sided lower nonparametric tolerance limit analysis and a small sample modification by Little are discussed and illustrated in a fatigue context. Overall, this paper is intended to provide background and perspective for subsequent papers.
tolerance limits, one-sided lower tolerance limits, two-parameter lognormal distribution, two-parameter Weibull distribution, statistical analysis, fatigue life, fatigue
Professor, University of Michigan-Dearborn, Mich.