JSM 2005 Online Program

Abstract #304317

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Activity Number:	457
Type:	Contributed
Date/Time:	Wednesday, August 10, 2005 : 2:00 PM to 3:50 PM
Sponsor:	Section on Physical and Engineering Sciences
Abstract - #304317
Title:	Weibull Confidence Bounds with Few or Zero Failures
Author(s):	Ulrike Genschel*+ and William Q. Meeker
Companies:	University of Dortmund and Iowa State University
Address:	Department of Statistics, Dortmund, 44221, Germany
Keywords:	confidence bounds ; Weibull distribution ; time-censored data ; low failure rates
Abstract:	Due to practical constraints, life tests of high-reliable products often yield time-censored data with few or even zero observed failures. Most procedures allow for such censored data, but depend on a sufficiently large fraction failing for reasonable distributional approximations for setting confidence intervals. The goal of our work is to evaluate confidence interval procedures for estimating the scale parameter of an exponential failure time model when the number of failures during life tests is small or even zero. In the event of zero failures, often only a lower confidence bound can be constructed for the exponential parameter. For this situation, Nelson (1985) proposed a lower confidence bound, known to be conservative, and the amount of conservatism can be extreme. We numerically compare the performance of Nelson's procedure with several alternatives. We find that a confidence bound from Bartholomew (1963) gives good coverage probabilities when there are few failures. Confidence limits for the exponential parameter may be applied to set confidence bounds for the scale parameter in Weibull failure-time models assuming that the Weibull shape parameter is known.

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