Inferences on the Competing Risk Reliability Problem for Exponential Distribution Based on Fuzzy Data

The problem of estimating the reliability parameter originated in the context of reliability where X represents the strength subjected to a stress Y. But traditionally it is assumed that the available data from the stress and strength populations are performed in exact numbers. However, some collected data might be imprecise, and are represented in the form of fuzzy numbers. In this paper, we consider the estimation of the stress-strength parameter R, when X and Y are statistically independent exponential random variables, and the obtained data from both distributions are reported in the form of fuzzy numbers. We consider the classical and Bayesian approaches. In the Bayesian setting, we obtain the estimate of R by using the approximation forms of Lindley, and Tierney & Kadane, as well as a Markov Chain Monte Carlo method under the assumption of statistically independent gamma priors. The estimation procedures are discussed in detail, and compared via Monte Carlo simulations in terms of their average values and mean squared errors.