Point estimation of the stress–strength reliability parameter for parallel system with independent and non-identical components

ABSTRACT

In this article, the estimation problem of the multicomponent stress–strength reliability parameter is considered where the stress and the strength systems have arbitrary fixed numbers of independent and non-identical parallel components. It is assumed that the distribution functions of the stress and the strength components satisfy the proportional reversed hazard rate model. The study is done in more details when the baseline distributions are exponential. Maximum likelihood and uniformly minimum variance unbiased estimators are obtained and compared. Also, Bayes and empirical Bayes estimators are discussed and Monte Carlo simulations are carried out to compare their performances.

KEYWORDS:

• Maximum likelihood estimator
• Prior distribution
• Stress–strength reliability
• Uniformly minimum variance unbiased estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62N05
• Secondary 62F10

Acknowledgment

The authors are grateful to three anonymous referees for making many helpful comments and suggestions on an earlier version of this article.

Funding

This research was supported by a grant from Ferdowsi University of Mashhad; No. 2/43047.