Estimation of failure probability from a bivariate normal stress-strength distribution

Probability (P) of equipment failure consequent upon stress exceeding built-in strength has been estimated assuming a bivariate normal stress-strength distribution. The UMVUE of P when parameters other than the means are known has been derived. An alternative estimator based on maximum likelihood estimates has been proposed in the case when all the five parameters are unknown. Asymptotic variances of both these estimators have been worked out. Some relevant numerical computations have also been reported.