On the Interval Estimation of Stress–Strength Reliability for Exponentiated Scale Family of Distributions. (1st February 2017)

• Record Type: Journal Article
• Authors: Patil, K.P.; Kulkarni, H.V.
• Is Part Of: Quality and reliability engineering international. Volume 33:Number 7(2017:Nov.)
• Page Start: 1447
• Page End: 1453
• Publication Date: 2017-02-01
• Subjects: exponentiated exponential distribution -- generalized pivot quantity -- maximal scale invariant likelihood estimator -- warranty period; Reliability (Engineering) -- Periodicals; Quality control -- Periodicals; High technology -- Periodicals; 620.00452
• DOI: 10.1002/qre.2117
• Languages: English
• ISSNs: 0748-8017

Abstract

Abstract : The stress–strength reliability R = 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. Copyright © 2017 John Wiley & Sons, Ltd.