Inference for stress-strength models based on Weinman multivariate exponential samples

The analysis of stress-strength systems is connected to the probability P(X < Y), where X represents the stress subject to an object and Y is its strength. We consider estimation of P(X < Y) when the underlying data consists of two samples of order statistics from Weinman multivariate exponential distributions with a common location parameter. Maximum likelihood estimators and uniform minimum variance unbiased estimators of P(X < Y) are presented, when the location parameter is assumed to be known and unknown, respectively. Moreover, some distributional properties, a confidence interval and asymptotic results are established. The results can be applied to various data set-ups based on exponential distributions, e.g., ordinary order statistics, progressive type II censored order statistics, sequential order statistics and record values.