Abstract
As we all know, the theory of fuzzy sets facilitates a much better model for human cognition than traditional approaches. The developments of the fuzzy set theory was motivated largely by the need for computational framework in dealing with systems in which human judgment, behavior, and emotion play a dominate role. One of the applications in the theory of fuzzy sets is fuzzy judgment for multiple focal-factors (i.e., attributes of an object to be judged), called the fuzzy integrated judgment. Areas in which the fuzzy integrated judgment has been successfully applied are often quite fruitful and tangible. In particular, an application of the fuzzy dynamic integrated judgment for cotton allocation was explored by Zhao, Peng, and Cheng [8]. Also, some principles and approaches of model building of fuzzy dynamic integrated judgment were studied by Zhao and Cheng [7]. The total failure time of a system with several components often plays an important role in the reliability theory. In some cases, all components of a system with several identical components may be put on test until an r-th smallest failure time occurs and the total time on test is subsequently calculated. The total failure time from exponentially distributed censored data has been proved to be an adequate statistic by Nair and Cheng [2] in light of the works by Skibinsky [3] and Cheng and Mordeson [1]. The test may be repeated for many times. As a result, since the total failure time until the r-th ordered failure time is observed will be recorded for each test, several total failure times for the same system are available for use in analyzing the reliability of the system. In this proposal, an integrated use of these total failure times will be discussed by means of the approach of model building of fuzzy dynamic integrated judgment.