Fuzzy states as a basis for a theory of fuzzy reliability

Various engineering backgrounds have shown that the binary state assumption in probist (i.e., conventional) reliability theory, i.e. defining a system as fully failed or functioning, is not extensively acceptable, and thus the fuzzy state assumption should be used to replace the binary state assumption. As a result, the concept of profust reliability is introduced and a conceptual framework of profust reliability theory is developed on the basis of the fuzzy state assumption and the probability assumption. Profust reliability function, profust lifetime function and profust failure rate function and the mathematically rigorous relationships among them, lay a solid foundation for profust reliability theory. On the other hand, the concept of the virtual random lifetime builds a bridge linking profust reliability theory with probist reliability theory. In addition, in this paper, typical systems including the series system, parallel system, Markov model, mixture model and coherent system are briefly discussed within the conceptual framework of profust reliability theory.