Reliability Evaluation of Repairable Parallel-Series Multi-State System Implementing Interval Valued Universal Generating Function

Abstract

In this paper, we have studied a repairable parallel-series multi-state system. The proposed system consists of m components in series and n components in parallel in which each component has three possible states. The interval universal generating function (IUGF) is presented, and the corresponding composition operators are defined. The reliability assessment of the considered system is done with the help of the IUGF approach. It is worth mentioning that IUGF got attention from various researchers due to its straightforwardness, less complexity, and universal applications. In the present model, probabilities of different components, reliability, sensitivity, and mean time to failure are evaluated with the help of the Markov process; Laplace-Steiltjes transform method applying IUGF. A numerical example has also been taken to illustrate the proposed technique.