Reliability Validation via Success-Failure Testing: A Hidden Controversy

Article

Wasserman, G. S.   (1999, Marcel Dekker, Inc. and ASQ)   Wayne State University, Detroit, MI

Quality Engineering    Vol. 12    No. 2
QICID: 13901    December 1999    pp. 267-276
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Article Abstract

[This abstract is based on the author's abstract.] Binomial confidence limit expressions are shown in terms of the cumulative binomial distribution, which is discrete, and in equivalent representations of either the beta-distributional or F-distributional form. They are compared to similar expressions for percentiles on a rank distribution of F(t), the empirical distribution of time to failure. It is shown that expressions for the lower binomial confidence limit match exactly the corresponding expressions for the rank distribution. Expressions for the upper limit do not quite match, differing only in the degrees of freedom parameters of the F distribution. The expressions do match when r +1 is substituted for r in the upper binomial confidence limit expression. Many handbooks and textbooks recommend binomial confidence limit formulas for estimating RL, a lower confidence limit on the reliability, R(t). This limit will not be in agreement with similar expressions based on the upper tail of the rank distribution. The underlying reason for differences in the two estimation approaches is explained, along with a description of the advantages and disadvantages of using binomial confidence limits.

Keywords

Binomial distribution,Reliability,Statistics,Confidence limits


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