Some Bayes estimators for the repairable system

An impressive array of paper has been devoted to the reliability properties and the hazard rates of the order statistics along with IFR (increasing failure rate) and DFR (decreasing failure rate) property. However, studies relating to the Bayesian estimation on the repairable system along with IFR property of the failure time distribution and on the repair time distributions have received comparatively less attention. The choice of the loss function may be crucial. It has always been recognized that the most commonly used loss function, squared error loss function (SELF) is inappropriate in many situations. If the SELF is taken as a measure of inaccuracy then the resulting risk is often too sensitive to the assumptions about the behavior of the tail of the probability distribution. In addition, in some estimation problems overestimation is more serious than the underestimation, or vice-versa [7]. To deal with such cases an useful and flexible class of asymmetric loss function (LINEX loss function (LLF)) was introduced by Varian [13] for any parameter θ (when θ̂ is any estimator of the parameter θ) as