Abstract
The concept of mean residual life plays an important role in reliability and life testing. In this paper, we introduce and study a new stochastic order called proportional mean residual life order. Several characterizations and preservation properties of the new order under some reliability operations are discussed. As a consequence, a new class of life distributions is introduced on the basis of the anti-star-shaped property of the mean residual life function. We study some reliability properties and some characterizations of this class and provide some examples of interest in reliability.
Highlights
Stochastic orders have shown that they are very useful in applied probability, statistics, reliability, operation research, economics, and other related fields
A new class of lifetime distributions, namely, anti-star-shaped mean residual life (ASMRL) class of life distribution, which is closely related to the concept of the proportional mean residual life (PMRL) order, is introduced and studied
There exist plenty of scenarios where a statistical comparison of reliability measures is required in both reliability engineering and biomedical fields
Summary
Stochastic orders have shown that they are very useful in applied probability, statistics, reliability, operation research, economics, and other related fields. The MRL function is an important characteristic in various fields such as reliability engineering, survival analysis, and actuarial studies. It has been extensively studied in the literature especially for binary systems, that is, when there are only two possible states for the system as either working or failed. The purpose of this paper is to propose a new stochastic order called proportional mean residual life (PMRL) order which extends the MRL order to a more general setting. A new class of lifetime distributions, namely, anti-star-shaped mean residual life (ASMRL) class of life distribution, which is closely related to the concept of the PMRL order, is introduced and studied.
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