Inference about reliability parameter with gamma strength and stress

The statistical inference about the reliability parameter R involving independent gamma stress and strength is considered. Assuming the two shape parameters are known arbitrary real numbers, the UMVUE of R is obtained. The performances of the UMVUE and the MLE are compared numerically based on extensive Monte Carlo simulation. Simulation studies indicate that the performance of the two estimators are about the same. The MLE is preferred due to its computational simplicity.