The present paper obtains Bayes estimators for the probability p(Y<X) when X and Y are two independent but not identically distributed the Burr-type X random variables and an asymmetric loss functions are used. An approximation based on the Laplace approximation method (Tierney and Kadane(1986)) is used for obtaining the Bayes estimators of P(Y<X). In order to compare the Bayes estimators with respect to squared error loss(SEL), linex loss and squarex loss functions respectively and MLE of the system reliability, Monte Carlo simulations are used.