Preservation results for life distributions based on comparisons with asymptotic remaining life under replacements

Abstract

We investigate some preservation properties of two nonparametric classes of survival distributions and their duals, under appropriate reliability operations. The aging properties defining these nonparametric classes are based on comparing the mean life of a new unit to the mean residual life function of the asymptotic remaining survival time of the unit under repeated perfect repairs. They are motivated from a point of view that realistic notions of degradation, applicable to repairable systems, should be based on contrasting some aspect of the remaining life of a repairable unit (under a given repair strategy, such as renewals) to the life of a new unit.

Moment inequalities for HNBRUE with hypothesis testing application

“…It is important to mention that in relation (2.1) equality holds if and only if the distribution F is Exp(µ), i.e., the life distribution of the system is approaching a stable regime which is described by the exponential distribution; see e.g. Bhattacharjee et al [5]. Later we make use of such a property and build new test statistic for exponentiality.…”

“…In particular, the class H includes the classes NBU, NBUE, HNBUE, and NBRUE. Further details can be found in Bhattacharjee et al [5].…”

“…Other possible comparisons between these random variables have been studied by several authors including, e.g. Shaked and Shanthikumar [19], Müller and Stoyan [13] and Bhattacharjee et al [5]. Cheng and Lam [6] studied upper and lower bounds for the reliability function in harmonic new better than used in expectation (HNBUE) life distribution class with known first two moments.…”

Moments Inequalities for NBRUrp Distributions with Hypotheses Testing Applications

“…The past decades witnessed some aging notions based on a stochastic comparison between a random life X and its equilibrium version * which are introduced and studied by Li and Xu [19] and Bhattacharjee et al [6].…”

Properties of classes of life distribution based on the conditional variance

“…In reliability analysis, several classes of life distribution have been proposed and studied to model the lifetime of complex systems. Of the huge literature in this area, we mention only a few sources: Barlow and Proschan (1981), Bryson and Siddiqui (1969), Launer (1984) and Bhattacharjee et al (2000); see also the references therein.…”