An Exact Asymptotically Efficient Confidence Bound for Reliability in the Case of the Weibull Distribution*

Article

Johns, M.V. Jr.; Lieberman, G.J.   (1966, ASQC and the American Statistical Association)   Stanford University

Technometrics    Vol. 8    No. 1
QICID: 7923    February 1966    pp. 135-175
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Article Abstract

* - This work was supported in part by the Army, Navy, Air Force and NASA under contract Nonr-225(53)(NR-042-002) with the Office of Naval Research.This paper presents a simple method for obtaining exact lower confidence bounds for reliabilities (tail probabilities) for items whose life times follow a Weibull distribution where both the "shape" and "scale" parameters are unknown. These confidence bounds are obtained both for the censored and non-censored cases and are asymptotically efficient. They are exact even for small sample sizes in that they attain the desired confidence level precisely. The case of an additional unknown "location" or "shift" parameter is also discussed in the large sample case. Tables are given of exact and asymptotic lower confidence bounds for the reliability for sample sizes of 10, 15, 20, 30, 50 and 100 for various censoring fractions.


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