Time-to-state and availability assessment of multi-state weighted k-out-of-n: G systems

Recently, various models are proposed for complex systems. The multi-state k-out-of-n system is one of the successful models. Because complex systems are often subject to aging process, the system state probability also changes with time. Therefore, we extend the traditional multi-state k-out-of-n system into a dynamic model by including the time factor. Further, based on the fact that most of the systems are in monitoring and recovery functions, the system would return back to higher states after switching to lower states. Therefore, we propose a model to find Time-To-State (TTS) data of reversible systems. For dynamic systems, we propose a framework which includes Universal Generating Function (UGF) and Markov process to model system availability. For reversible systems, a Semi-Markov process is considered and flow-graph and Moment Generating Function (MGF) are applied to derive TTS data. Our method is applied to one real-world marine transportation system.