Ordering Results between Two Extreme Order Statistics with Heterogeneous Linear Failure Rate Distributed Components

TL;DR

This paper investigates stochastic comparisons of series and parallel systems with components having heterogeneous linear failure rate distributions, providing theoretical results, numerical illustrations, and real-world applications.

Contribution

It establishes new stochastic comparison results for systems with heterogeneous linear failure rate components, expanding reliability analysis methods.

Findings

Stochastic orders between system lifetimes are characterized.

Numerical examples illustrate the theoretical comparisons.

Real-world application demonstrates practical relevance.

Abstract

Stochastic comparisons of series and parallel systems are important in many areas of engineering, operations research and reliability analysis. These comparisons allow for the evaluation of the performance and reliability of systems under different conditions, and can inform decisions related to system design, probabilities of failure, maintenance and operation. In this paper, we investigate the stochastic comparisons of the series and parallel systems under the assumption that the component lifetimes have independent heterogeneous linear failure rate distributions. The comparisons are established based on the various stochastic orders including magnitude, transform and variability orders. Several numerical examples and counterexamples are constructed to illustrate the theoretical outcomes of this paper. Finally, we summarized our findings with a real-world application and possible future scopes of the present study.