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Abstract
This article proposes to use the theory and methods of fuzzy sets to model the reliability of a component or system experiencing continuous stochastic performance degradation. The performance characteristic variable, which indicates the continuous performance levels of degradable systems, is used to fuzzify the states of a component or system. The concept of an engineering or technological performance variable is understood by both customers and system designers and can be used to represent different degrees of success. Thus, the imprecision in the meaning of success/failure is quantified through the fuzzy success/failure membership function, which is defined over the performance characteristic variable. The proposed fuzzy reliability measures provide an alternative to model the continuous state behavior for a component or system as it evolves from a binary state to a multi-state and finally to a fuzzy state. The dynamic behavior of fuzzy reliability is investigated using the concept of a fuzzy random variable under appropriate stochastic performance degradation processes. This article also develops some reliability performance metrics that are able to capture the cumulative experiences of customers with the system. In addition, the perception and utility from the customers are utilized to develop customer-centric reliability performance measures.