A Bayesian approach to estimate the reliability P (X > Y) utilizing an initial guess

This paper presents a Bayesian approach to estimate the probability that one random variable exceeds another based on two independent Weibull-distributed random variables. The proposed methodology utilizes an initial guess of the reliability through an informative prior, which constitutes the cornerstone of the model. A Monte Carlo simulation study is conducted to compare the performance of the new estimators with both the MaximumLikelihood Estimation (MLE) and the Shrinkage estimators. The comparison is conducted with respect to the Mean Squared Error (MSE) for different values of the scale and shape parameters of the Weibull distribution using small, moderate, and large sample sizes. The proposed method outperforms the two aforementioned alternative methods.