Probabilistic Approach in Mathematical Programming Model to Solve Redundancy Allocation Problems in a Series-Parallel System with All Unit Discount Policy

Abstract

Nowadays, designing and implementing systems with premier features and higher reliability is deemed to be a basic principle for the engineers and users. Because regarding this point can result in the proper use of a system during its lifetime. Reliability refers to a measure of quality versus time factor that is computed by a probability of working without any failure in a given time and under some specific conditions. Since a system consists of many items, which withstand several stress factors, manufacturers commonly employ different solution approaches to increase the reliability. One of the main strategies in this regard is to consider some additional items in parallel to original ones. This is also called redundancy allocation. Different items have different reliability, cost, weight, and importance level. So, making decision on assigning redundant would be of interest under limited budget and volume or weight in system development. Some redundant item is not turned on until the main item works correctly. Hence, a switch and sensors would be considered to monitor the status of the main item and to decide when the redundant must start working. This type is called standby item. In today's competitive world, offering a system with lower total expense, given that its high reliability is maintained, can make the company popular with the customers. Although in recent years, research on optimization have been presented with all unit discount for components of a system, this paper not only addresses the active redundancy strategy, but also it discusses a combination of components with active or cold redundancy strategy. It uses a system that generates the all unit discount to the sum of the components with the two strategies mentioned. Additionally, in order to make the problem more realistic to the real world, failure rate and cost parameters were considered uncertain. To solve two models with the aims of maximizing the reliability and minimizing the cost, chance constrained approach was employed for the constraints of cost and reliability. The proposed model was solved with accurate method using GAMS software. With regard to the model's proper treatment of changes in effective factors proposed in the model, it is concluded that this model is exploitable for optimizing stability in mass production industries where applying the global discount policy leads to some benefits.