Preservation of some stochastic orders by distortion functions with application to coherent systems with exchangeable components

TL;DR

This paper investigates how certain stochastic orders are preserved by distortion functions and applies these findings to analyze the reliability of coherent systems with exchangeable components.

Contribution

It provides new results on the preservation of multiple stochastic orders by distortion functions and applies them to the reliability analysis of coherent systems.

Findings

Preservation of excess wealth order by distortion functions

Preservation of total time on test transform order

Application to coherent systems with exchangeable components

Abstract

The preservation of stochastic orders by distortion functions has become a topic of increasing interest in the reliability analysis of coherent systems. The reason of this interest is that the reliability function of a coherent system with identically distributed components can be represented as a distortion function of the common reliability function of the components. In this framework, we study the preservation of the excess wealth order, the total time on test transform order, the decreasing mean residual live order, and the quantile mean inactivity time order by distortion functions. The results are applied to study the preservation of these stochastic orders under the formation of coherent systems with exchangeable components.