A bi-objective dynamic model for multi-state weighted k-out-of-n system reliability

Nowadays, improving system reliability is becoming an important criterion for engineering industries. Many studies have been developed to evaluate the reliability of the systems which is the first step in system improvement. Most of these studies have been done in non-dynamic conditions in which the components have the constant reliability values during functioning periods. However, the components’ reliability level varies over time due to both failures and maintenance actions. Therefore, time dimension should be added into system reliability evaluation. In this paper, a dynamic assessment is presented for multi-state weighted k-out-of-n systems. The k-out-of-n system is a popular structure in fault-tolerant systems in which n components work in parallel form with a pre-defined k as a condition. This dynamic assessment considers the reliability variation of the components over finite and discrete time periods. It provides an opportunity to assign decision variables for each functioning period, and analyze the impact of each decision on the whole system reliability. In addition, the income generated during each period is defined as an importance weight of the components. Therefore, the present value of the system is obtained by Universal Generating Function (UGF) and engineering economics’ tools. Furthermore, an optimization model is developed to find optimal decisions based on system reliability and cost. Since the system reliability is estimated by money, the expected profit of the system can be as the objective function. As a result, the objective function can maximize system reliability and minimize system cost simultaneously. A Matlab programming is created for a numerical example to illustrate the proposed model.