Two-unit repairable systems with common-cause shock failures and fuzzy parameters: parametric programming approach

This article, proposes a procedure to construct the membership functions of the system characteristics of a two-unit repairable system in series and parallel, which is subject to individual failures and common-cause shock failures. Time to individual failure and common-cause shock failure of the operating units are assumed to follow fuzzified exponential distributions. In addition, time to repair of the failed units also follow fuzzified exponential distributions. The alpha-cut approach is used to extract from the fuzzy repairable system 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. Since 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.