| In a conventional system, the data are always collected or regarded as exact real numbers. However, in the real world, there are instances where the data cannot always appear as exact numbers. For example, the water level of the river, the temperature or the lifetime of each component (system) cannot be recorded exactly in some unexpected situations. That is to say, we need to develop techniques to handle imprecise data. The appropriate tool is the fuzzy sets theory which is the essential tool in this research.; In order to model the imprecisely functioning probability of each component, we need to develop the fuzzy-valued probability measures. Under this setting, we can derive the Pivotal Decomposition as in the conventional case. Furthermore, we are going to estimate the survival probability, failure rate and system reliability under fuzzy environment. In this consideration, if we attempt to use the probability distribution to describe the imprecise data, then the parameters of the distributions should be assumed as fuzzy parameters. Thus it is natural that we need to create techniques for estimating the fuzzy parameters. In order to make the problem more realistic, we are going to take the Bayesian point of view, which means that we shall come up with the fuzzy Bayes estimators.; There are a lot of literatures concerned with the Bayesian reliability analysis. Since the fuzzy Bayes estimators can be created as described above, we thus can focus on the Bayesian reliability analysis under fuzzy environment. |
