Stress-strength Reliability for Equi-correlated Multivariate Normal and its estimation

In this article it is mainly focused on discussion about estimation of stress-strength reliability under equi-correlated multivariate setup. It is seen in some situations that the components of a system are equi-correlated. Generally, the form of the equi-correlation structure within the components of a system is known for a given situation, however parameters that are involved in the equi-correlation structure always unknown. In this article, we propose a procedure to compute and estimate the stress-strength reliability R= Pr(𝒂'𝒙 > 𝒃'𝒚) when 𝒙 and 𝒚 are distributed non-independently equicorrelated multivariate normal distribution, where 𝒂 and 𝒃 are two known vectors. Here we have proposed the method of moments estimator to estimate these unknown parameters. Actually, we want to find out overall strength is larger than overall stress. In order to do that we take 𝒂'𝒙 and 𝒃'𝒚 as their representatives e.g. principal components of the respective vectors do the job approximately. An asymptotic distribution used to obtain confidence intervals for the stress-strength reliability. The performance of these intervals checked through the simulation study. Finally, we provide a real data analysis.