If conventional system reliability analysis, the reliabilities of components of a system are treated as exact values in estimating the reliability of the system. For many systems, it is often difficult to evaluate the reliabilities of components because the environments of the system change and past data are not enough significant. Therefore, the paper propose to employ a fuzzy set defined in probability space. The fuzzy reliability is more predictive than the ordinary reliability; the latter is a limiting case of the former.
In the case that the reliabilities of components are given fuzzy sets, the problem is to calculate the membership function of the system reliability. The system reliability is a function of reliabilities of components in the system. Then the membership function of the system reliability is determined by the extension principle. The inverse function of membership function is used to obtain the fuzzy set of the system reliability.
