Estimation of<i> R</i>_<i>3</i> = Pr(<i>Y₃ </i>> max(<i>Y₁, Y₂</i>)) for Exponential Distribution

Abstract

This paper deals with the estimation of the reliability function R3 = Pr(Y3 > max (Y1, Y2)), when the random variables Y1, Y2 and Y3 are independent exponential with respective unknown location parameters µ1, µ2 and µ3. Here we have derived several estimators of R3 which includes uniformly minimum variance unbiased estimator (UMVUE), Bayes estimator (BE) and generalized Bayes estimator(GBE). Moreover, we have compared these estimators based on their risks under different loss functions.