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
W. K. Shiue and L. J. Bain, "Robustness & Precision Of Parametric & Distribution-Free Tolerance Limits For Two Lifetime Distributions," IEEE Transactions on Reliability, vol. 38, no. 2, pp. 224 - 228, Institute of Electrical and Electronics Engineers, Jan 1989.
The definitive version is available at https://doi.org/10.1109/24.31111
Mathematics and Statistics
Keywords and Phrases
Confidence limit; Gamma distribution; Percentile; Weibull distribution
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 1989