Abstract: Conventional reliability theory is based on the probability assumption and the binary-state assumption. However these two fundamental assumptions have been shown unacceptable in many cases and thus the possibility assumption and the fuzzy-state assumption may be taken. Consequently, fuzzy reliability theory is based on the probability assumption and the fuzzy-state assumption, or on the possibility asssumption and the binary-state assumption, or on the posssibility assumption and the fuzzy-state assumption. In this view, fuzzy reliability theory manifests three distinct forms: profust reliability theory, posbist reliability theory, and posfust reliability theory. In this paper the basic concepts are formulated in the profust and posbist reliability theories and a simple fuzzy software reliability model is introduced. Finally, we take a look at the future trends in research activities on fuzzy reliability.

Key words: fuzzy reliability, profust reliability, posbist reliability, fuzzy software reliability model