Optimal redundancy allocation for the problem with chance constraints in fuzzy and intuitionistic fuzzy environments using soft computing technique

In some reliability optimization problem the constraints relations have probabilistic nature. These constraints are called the chance constraints and are difficult to handle up to some extent. The aim of this paper is to solve the reliabilityredundancy allocation problem involving chance constraints in precise and imprecise environments. The component reliabilities of the system are imprecise numbers and further the constraints are stochastic type i.e., chance constraints. The genetic algorithm incorporated with stochastic simulation approach is implemented to optimize the system reliability. We introduced the fuzzy and intuitionistic fuzzy numbers to consider the impreciseness. In particular, component reliabilities are assumed to be triangular fuzzy numbers and triangular intuitionistic fuzzy numbers in two different environments. The simulation technique known as Monte Carlo Simulation is used to find the deterministic constraints from the stochastic ones. To transform the constrained optimization problem into unconstrained one we make use of the effective BigM penalty approach. The problems are coded with real coded genetic algorithm. We have taken up some numerical examples to show the performance of the proposed method and the sensitivities of the GA parameters are also presented graphically.