Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values.

Ehsan Fayyazishishavan,Serpil Kılıç Depren,Feng Chen

doi:10.1371/journal.pone.0249028

Ehsan Fayyazishishavan, Serpil Kılıç Depren + Show 1 more

Open Access

https://doi.org/10.1371/journal.pone.0249028

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Journal: PloS one	Publication Date: Apr 2, 2021
Citations: 1	License type: CC BY 4.0

Affiliation: Yıldız Technical University

Abstract

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This paper investigates the estimation of the parameters of this distribution by using lower records values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real data set is provided to illustrate the proposed methods.

Highlights

In engineering applications, a system may be subjected to several stresses such as extreme temperature and pressure
The models which try to measure this resistance are called stress-strength models, and in the simplest terms, it can be described as an evaluation of the experienced random “stress” (Y) and the available “strength” (X) which overcomes the stress
The estimation of the reliability parameter has extensive literature. It has been studied under different assumptions over the distribution of X and Y. [1] studied the ML estimation of R under the assumption that the stress and strength variables follow a bivariate exponential distribution

Summary

Introduction

A system may be subjected to several stresses such as extreme temperature and pressure. In some recent works [5], estimated R under the assumption that the stress and strength variables are independent and follow a generalized exponential distribution. [16], based on the record data, by considering one parameter generalized exponential distribution, has been studied ML and Bayesian estimation of R. Another type of incomplete data is record values which usually appear in many real-life applications. He provided a foundation for a mathematical theory of records He defined the record values as consecutive extremes appearing in a sequence of independent identically distributed (i.i.d.) random variables.

Maximum likelihood estimation

I22I33 À

Bayesian estimation

Inference on R when λ is known

Real data analysis

Conclusion