Table of Contents
Journal of Quality and Reliability Engineering
Volume 2014, Article ID 192072, 8 pages
http://dx.doi.org/10.1155/2014/192072
Research Article

Interval Estimation of Stress-Strength Reliability Based on Lower Record Values from Inverse Rayleigh Distribution

Department of Statistics, Islamic Azad University, Maku Branch, Maku, Iran

Received 27 July 2014; Revised 24 October 2014; Accepted 29 October 2014; Published 16 November 2014

Academic Editor: Adiel Teixeira de Almeida

Copyright © 2014 Bahman Tarvirdizade and Hossein Kazemzadeh Garehchobogh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the estimation of stress-strength reliability based on lower record values when and are independently but not identically inverse Rayleigh distributed random variables. The maximum likelihood, Bayes, and empirical Bayes estimators of are obtained and their properties are studied. Confidence intervals, exact and approximate, as well as the Bayesian credible sets for are obtained. A real example is presented in order to illustrate the inferences discussed in the previous sections. A simulation study is conducted to investigate and compare the performance of the intervals presented in this paper and some bootstrap intervals.