Reliability estimation in Rayleigh distribution based on fuzzy lifetime data

Some work has been done in the past on the estimation of reliability characteristics of Rayleigh distribution based on complete and censored samples. But, traditionally it is assumed that the available data are performed in exact numbers. However, in real world situations, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. In this paper, we present a Bayesian approach to estimate the parameter and reliability function of Rayleigh distribution from fuzzy lifetime data. Based on fuzzy data, the Bayes estimates can not be obtained in explicit forms; therefore, we provide two approximations, namely Lindley’s approximation and Tierney and Kadane’s approximation as well as a Markov Chain Monte Carlo method to compute the Bayes estimates of the parameter and reliability function. Their performance is then assessed through Monte Carlo simulations. Finally, one real data set is analyzed for illustrative purposes.