The problem of estimating the parameter of Exponential distribution on the basis of type II censoring scheme is considered when the available data are in the form of fuzzy numbers. The Bayes estimate of the unknown parameter is obtained by using the approximation forms of Lindley (1980) and Tierney and Kadane (1986) under the assumption of gamma prior. The highest posterior density (HPD) estimate of the parameter of interest is found. A Monte Carlo simulation is used to compare the performances of the different methods. A real data set is investigated to illustrate the applicability of the proposed methods.

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Statistical analysis of lifetime distributions under Type-II censoring scheme is based on precise lifetime data. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. This paper deals with the estimation of exponential mean parameter under Type-II censoring scheme when the lifetime observations are fuzzy and are assumed to be related to underlying crisp realization of a random sample. Maximum likelihood estimate of the unknown parameter is obtained by using EM algorithm. In addition, a new numerical method for parameter estimation is provided. Using the parametric bootstrap method, the construction of confidence intervals for the mean parameter is discussed. Monte Carlo simulations are performed to investigate performance of the different methods. Finally, an illustrative example is also included.