Fuzzy estimator of the total failure time of censored data

The total failure time of a system consisting of several components from a k-parameter exponential family often plays an important role in the reliability theory. All components of a system with several identical components may be put in test until an r-th smallest failure time occurs and the total failure time is subsequently calculated. The total failure time from exponentially distributed censored data has been proved to be a prediction sufficient statistic by Nair and Cheng in 2001 in light of the works by Skibinsky in 1967, Torgersen in 1977, and Cheng and Mordeson in 1985. Sometimes, the test may be repeated several times in order to assess the reliability of the system. In this proposal, a fuzzy estimator for the total failure time was discussed. This estimator provides more information in total failure time than just a point estimate, or just a single confidence estimate.