Gompertz Fréchet stress-strength Reliability Estimation

Sarah A Jabr,Nada S Karam

doi:10.24996/ijs.2021.62.12.27

Abstract

In this paper, the reliability of the stress-strength model is derived for probability P(Y<X) of a component having its strength X exposed to one independent stress Y, when X and Y are following Gompertz Fréchet distribution with unknown shape parameters and known parameters . Different methods were used to estimate reliability R and Gompertz Fréchet distribution parameters, which are maximum likelihood, least square, weighted least square, regression, and ranked set sampling. Also, a comparison of these estimators was made by a simulation study based on mean square error (MSE) criteria. The comparison confirms that the performance of the maximum likelihood estimator is better than that of the other estimators.

Highlights

1-Introduction The reliability of stress-strength was used by Church and Harris in 1970
The word stress-strength refers to a part of a system that has a random strength component X subjected to a random stress Y to determine reliability [2]
mean square error (MSE) was used to compare the performance of estimators, as the value of MSE

Summary

Introduction

The reliability of stress-strength was used by Church and Harris in 1970. It is defined as, where X represents the strength random variable and Y represents the stress random variable [1]. The reliability of stress-strength was used by Church and Harris in 1970. Where X represents the strength random variable and Y represents the stress random variable [1]. The word stress-strength refers to a part of a system that has a random strength component X subjected to a random stress Y to determine reliability [2]. Some attempts have been made to define modern types of distributions, extend renewed families, and at the same time, provide higher resilience in forming data in practice. Many families employing more than one parameters to generate modern distributions have been suggested in the statistical literature. The cumulative distribution function CDF of the Gompertz-G family is defined as [4]:

Objectives

Methods

Conclusion