Parametric nonlinear programming approach for a repairable system with switching failure and fuzzy parameters

This paper proposes a procedure to construct the membership functions of the system characteristics of a repairable system with two primary units, one standby unit, and one repair facility when switching to standby may fail. Failure times of primary and standby units are assumed to follow fuzzified exponential distributions, and repair times of the failed units are also assumed to have a fuzzified exponential distribution. The α-cut approach is used to extract from the fuzzy repairable system from a family of conventional crisp intervals for the desired system characteristics, determined with a set of parametric nonlinear programs using their membership functions. A numerical example is solved successfully to illustrate the practicality of the proposed approach. Because the system characteristics are governed by the membership functions, more information is provided for use by designers and practitioners. The successful extension of the parameter spaces to fuzzy environments permits the repairable system to have wider practical applications.