Realiability for KTH Order Statistics

Abstract

In the area of stress-strength models, there has been a large amount of work regarding the estimation of the reliability R = P{X₁ < X₂} when X₁ and X₂ are independent random variables belonging to the same univariate family of distributions. In this paper, we calculate P(Y_k < Y_k+1), where Y_k = X_k,n + X_k−3,n; X_n,n ≤…≤ X₁,n and X_k,n are the kth order statistics and variables (X_k,n)_k=1,n are independent and identically distributed (i.i.d) with the common distribution Gamma.