Combination Mean Residual Life Order with Reliability Applications

TL;DR

This paper introduces a new stochastic order based on mean residual life and combination convexity, explores its properties under various reliability operations, and demonstrates its applications in reliability and survival analysis.

Contribution

It presents a novel stochastic order integrating mean residual life and convexity, with characterization properties and applications in reliability theory.

Findings

The new order is preserved under monotone transformations and mixture operations.

Characterization of the order via residual life at random times and renewal processes.

Applications demonstrate the order's usefulness in reliability and survival analysis.

Abstract

The purpose of this paper is to introduce, study and analyze a new stochastic order which lies in the framework of the mean residual life and the combination convexity orders. Several preservation properties of the new order under reliability operations of monotone transformation, mixture, weighted distributions and shock models are discussed. In addition, two characterization properties of the new order based on the concept of residual life at random time and the concept of excess lifetime in renewal processes are given. Finally, we highlight some new applications of this order in the context of reliability and survival analysis.