Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context

Conventional reliability theory is based on the binary-state assumption and the probability assumption, namely (1) the systems are precisely defined as functioning or failed, (2) the system behavior is fully characterized in the context of probability measures. However the probability assumption is no longer reasonable in the case of small size of samples, since the term probability stems from the sample generality. In this way possibility measures should be used to characterize the sample particularity. In this paper the binary-state assumption is reserved and the possibility assumption is taken in place of the probability assumption. Thus a concept of fuzzy reliability (i.e., posbist reliability) is introduced and a theory of fuzzy reliability (i.e., posbist reliability theory) is established. Various conclusions which are contrary to statements in conventional reliability theory (i.e., probist reliability theory) are then drawn.