Reliability redundancy allocation problems under fuzziness using genetic algorithm and dual-connection numbers

Abstract

Abstract The reliability of a system is represented as the chances of durability that a system will persist up to a stipulated period of time over some prescribed circumstances. Thus, the system reliability depends on exact determination of related parameters. However, due to some unexpected real-life situations, it is not possible to set the exact/proper parametric values of systems. Moreover, during the designing period of the systems, design parameters (viz. component reliabilities, cost, weight, and volume) are basically imprecise in nature. Considering the impreciseness of all the parameters, the reliability redundancy allocation problem (RRAP) has been unraveled by the genetic algorithm (GA) to find out the maximum reliability value of the whole system. The GA is a very popular and effective technique for solving the RRAP. In this chapter, we have applied the GA to find the optimal solution of a five-link bridge network system where all the restrictions associated to the problem are imprecise. The triangular fuzzy number (TFN) is considered to represent the impreciseness of the parameters. The well-known Big-M approach has been exploited to steer the interval constraints of the problem. Moreover, dual-connection numbers (DCNs) have been taken into consideration as they can easily handle impreciseness. Therefore, the main aim of this chapter is to explore a solution procedure for solving the RRAP of a bridge network system with imprecise parameters in which the impreciseness of parameters is described in terms of TFNs. The solution procedure is based on DCNs of fuzzy parameters and use of real coded genetic algorithm (GA). The proposed method is illustrated at the end of the chapter using a hypothetical numerical example.