Availability and reliability of a parallel system under imperfect repair and replacement: analysis and cost optimization

In present paper, analysis of a parallel system with independent and identical units is introduced where the life and repair times follow general distribution. It is supposed that the repair rate of each component can be either perfect or imperfect and after the component is imperfectly repaired, it can be replaced by another new one. Markov models are used to construct the mathematical model of the system. Analysis of the availability and reliability functions of the model is discussed when the failure, repair, imperfect repair and replacement rates are general and as a special case the exponential distribution is discussed. Optimization problem is introduced in each case in order to minimize the cost of each component of the system. Algorithms based on Lagrange multiplier, penalty function methods are used to solve the introduced optimization problems in each case. Different applications are given to show how the optimization techniques can be applied.