Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

Abstract

We consider a suitable replacement model for random lifetimes, in which at a fixed time an item is replaced by another one having the same age but different lifetime distribution. We focus first on stochastic comparisons between the involved random lifetimes, in order to assess conditions leading to an improvement of the system. Attention is also given to the relative ratio of improvement, which is proposed as a suitable index finalized to measure the goodness of the replacement procedure. Finally, we provide various results on the dynamic differential entropy of the lifetime of the improved system.

Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy

“…It is worth pointing out that the latter relation is in agreement with the result provided in Proposition 2 of [3].…”

“…Less attention has been devoted to the cases when the uncertainty is related to the previous status of the system. Within such framework, in this paper we continued the study of a replacement model considered in [3]. In the previous paper, the replacement is planned in advance, the replaced item possessing a different failure distribution and having the same age of the replaced item.…”

“…In these instances, it is necessary to study the reliability measures of interest under the condition of truncated or doubly truncated random variables. In this contribution, we refer to a previous investigation centered on a stochastic model dealing with the replacement of items occurring at deterministic arbitrary instants (see Di Crescenzo and Di Gironimo [3]). We aim to generalize this model, by assuming that a given item is replaced by another item at a fixed instant, in such a way that their lifetimes have the same age but possess different distributions.…”

A Dynamic Failure Time Degradation-Based Model

“…Therefore, the methods developed in order for degradation data analysis are becoming typical tools over the last decades. The analysis of degradation data is possible after setting the definition of lifetime (see, e.g, Di Crescenzo and Di Gironimo [15], Guo and Lee [16], Lee et al [17], and Liu et al [18]).…”

Stochastic Order for a Multivariate Uniform Distributions Family

“…Wang et al [18] showed that the system performance is better (worse) with the stronger component heterogeneity in the parallel (series) system under the usual stochastic order and the (reversed) hazard rate order under the conditions of interdependency and independency. Also, Di Crescenzo et al [19] gave results for stochastic comparisons of random lifetimes in a replacement model.…”