Maximizing System Reliability of a Four Stage RAP with Two Chance Constraints Having Stochastic Reliability Components

This paper deals with the solution of the chance constrained reliability-redundancy allocation problems in imprecise environment. The reliabilities of the components are imprecise numbers and the type of the constraints are chance constraints i. e. , stochastic in nature. This paper proposes a stochastic simulation based genetic algorithm approach for solving the reliability optimization problems of the type mentioned. The impreciseness is represented in the stochastic approach. In case of stochastic approach, the reliabilities of the components are taken to be random variables having normal distribution. Then Monte Carlo simulation technique is applied to transform the chance constraints into the deterministic ones. Then Big-M penalty technique is applied to transform the problem to unconstrained one. The altered problem is then solved by the real coded genetic algorithm based on stochastic simulation. Some numerical illustrations are presented to show the performance of the proposed procedure.