Reliability-based measures for a system with an uncertain parameter environment

This article proposes a procedure to construct membership functions of the system characteristics of a repairable system with one primary machine, one standby machine and an unreliable service station. Failure and repair times of both the operating and standby machines are assumed to follow fuzzified exponential distributions. In addition, the failure and repair times of the service station also follow fuzzified exponential distributions. The alpha-cut approach is used to extract a family of conventional crisp intervals for the desired system characteristics from the fuzzy repairable system, determined with a set of parametric nonlinear programs using their membership functions. A numerical example successfully illustrates the practicality of the proposed approach. Because 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.