Exact parametric tolerance limits or confidence limits on reliability are not available for the gamma distribution, and it is, difficult to determine approximate methods which are accurate for all parameter values. The precision lost by using the distribution-free tolerance-limit method based on the first order statistic, compared to using an approximate gamma tolerance limit method is studied. The robustness of the approximate gamma tolerance limit when the true model is Weibull and the robustness of a Weibull tolerance limit when the true model is gamma are also studied. The efficiency of the distribution-free method ranges from about 0.60 to 0.90 in the range of values studied. Neither the Weibull nor gamma method is very robust for the alternate model, but the Weibull tolerance limit is conservative for the gamma model for parameter values commonly encountered in life testing problems and may be preferable to the distribution-free method in this case. © 1989 IEEE


Mathematics and Statistics


Air Force Office of Scientific Research, Grant AFOSR 84-0 164

Keywords and Phrases

Confidence limit; Gamma distribution; Percentile; Weibull distribution

International Standard Serial Number (ISSN)

1558-1721; 0018-9529

Document Type

Article - Journal

Document Version


File Type





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Publication Date

01 Jan 1989