Improving reliability design of multi-state k-out-of-n systems by fuzzy programming

In a multi-state system, both the system and its components are allowed to experience more than two possible states, e.g. completely working, partially working or partially failed, and completely failed. In this paper reliability evaluation and reliability optimization of k-out-of-n systems are studied for the case where the components and the system have multiple performance levels. A recursive algorithm is used for reliability evaluation of multi-state k-out-of-n systems with independent components. Then a fuzzy model is presented for minimization total cost subject to reliability constraint. In the fuzzy model a fuzzy constraint is used for reliability that may we use different weights to constraint and objective function, and as a consequence the amount of importance of each objective function and reliability constraint can consider. Finally a numerical example is given.