Optimizing reliability-redundancy problem with active and cold-standby strategy with triangular fuzzy number approach

application of Reliability can be seen in many industrial, communication, In the early stages of system design, many system features such as reliability, weight, cost, and etc are associated with uncertainty due to various reasons such as lifespan, operational conditions, etc. Since the use of the probabilistic approach in solving reliability problems has limitations and can only be used in quantitative analysis of information and in many cases does not produce useful and sufficient results for experts, therefore the use of the approach Fuzzy is much more efficient for solving reliability optimization problems. One of the ways to optimize the reliability is to allocate redundancy. When using redundant components in a subsystem, how the redundant components are used is particular importance. In reliability-redundancy allocation problems, the reliability of components is not known in advance and is considered as a decision variable. In the current research, the reliability-redundancy allocation problem has been investigated with two active and cold-standby redundancy strategies and the triangular fuzzy number approach has been used in using the parameters of probability functions and reliability calculation in two model problems and an industrial system. Genetic algorithm has been used to solve the problem. In the implementation of the genetic algorithm, the the random, tournament and roulette wheel methods has been used to select parents and different types of mutation and crossover operators have been used to produce children. The results are more efficient than the results obtained from solving the deterministic model.