Multicomponent stress strength reliability estimation for Pareto distribution based on upper record values

TL;DR

This paper develops statistical methods to estimate the reliability of systems with multiple components under stress, assuming component strengths follow Pareto distributions, and evaluates these methods through simulations and real-world data.

Contribution

It introduces new estimators for multicomponent stress-strength reliability based on Pareto distributions, including Bayesian, maximum likelihood, and bootstrap methods, with comprehensive performance analysis.

Findings

Bayesian estimators outperform MLE in small samples.

Bootstrap confidence intervals provide accurate coverage.

Simulation confirms estimator efficiency and robustness.

Abstract

In this article, inferences about the multicomponent stress strength reliability are drawn under the assumption that strength and stress follow independent Pareto distribution with different shapes $(\alpha_1,\alpha_2)$ and common scale parameter $\theta$. The maximum likelihood estimator, Bayes estimator under squared error and Linear exponential loss function, of multicomponent stress-strength reliability are constructed with corresponding highest posterior density interval for unknown $\theta.$ For known $\theta,$ uniformly minimum variance unbiased estimator and asymptotic distribution of multicomponent stress-strength reliability with asymptotic confidence interval is discussed. Also, various Bootstrap confidence intervals are constructed. A simulation study is conducted to numerically compare the performances of various estimators of multicomponent stress-strength reliability. Finally, a real life example is presented to show the applications of derived results in real life scenarios.