Confidence limits for reliability and tolerance limits in the inverse Weibull distribution

Abstract

The inverse Weibull distribution has been recently proposed as a suitable model to describe mechanical degradation phenomena. In this paper the statistical properties of the maximum likelihood estimator, R̂(t), of the inverse Weibull reliability, R(t), are investigated. Tables of lower confidence limits for R(t), for confidence levels of 0·90, 0·95 and 0·98, are also provided. Tolerance limits based upon maximum likelihood estimators of the parameters are derived, and it is shown that the same tables needed for obtaining confidence intervals for the reliability allow one to estimate tolerance limits, too. A numerical example is given to clarify the use of the tables.