Generalised estimation of stress-strength reliability R = P ( X > Y )

This paper focuses on the point estimation of the stress-strength reliability coefficient R=P(X>Y) in the case of two distributions that their functional forms are known but depend on unknown parameters. Previous studies in this field estimated R by evaluating the exact value of the double integral and then estimating the apparent parameter using methods such as maximum likelihood estimation. Due to the large number of candidate distributions available for data modelling, many research papers addressing this issue have emerged over the past three decades. In this paper, we establish a general model for R, which is applicable to any pair of continuous statistical distributions. The estimation process led to three new estimators for R, all of which rely on the cumulative distribution function of the assumed random variables. The consistency property for each estimator is established and also their performances for finite sample sizes are investigated by conducting a limited simulation study. The numerical results demonstrated the effectiveness of the proposed method, comparing to the current estimators, the performances of the proposed estimators are very promising. Although the generality of the model may lead to some loss of efficiency, this loss is small in most cases.