On the Interval Estimation of Stress–Strength Reliability for Exponentiated Scale Family of Distributions

Abstract

The stress-strength reliability R D P.X 1 < X 2 / where X 1 and X 2 represent the stress applied and strength of an equipment, respectively, plays a crucial role in setting warranty periods while launching new brands of a product. The paper addresses the issue of estimating R when X 1 and X 2 belong to the exponentiated scale family, which includes the popular EED that has proven to be an excellent model for lifetime distributions. The cases of known/unknown and equal/unequal scale parameters are handled separately. For known scale parameter, a generalized pivot quantity for the shape parameter and R are developed. The interval estimates of R based on the proposed generalized pivot quantity exhibited uniformly best performance. For an unknown scale parameter, a maximum scale invariant likelihood estimator of the shape and an allied estimator of the scale are introduced. The parametric bootstrap interval estimates of R based on a proposed maximum scale invariant likelihood estimator of the shape parameter exhibited best performance among others. An application in setting warranty periods is illustrated based on two real data sets.