M arkov Renewal Processes in Reliability Modeling

Abstract Renewal theory is one of the most useful tools used in reliability modeling and analysis. The stochastic structure of most models involve an embedded renewal process where the state of the system regenerates itself over these renewal times. This allows one to analyze various issues related to reliability, availability, maintenance, and repair using renewal theory. In this setting, we aim to explore this idea further by considering Markov renewal models. However, we propose to use a Markov renewal process to model a mission‐based system where the device is designed to perform a random sequence of phases or stages of the mission with random durations. The mission process is modeled as a Markov renewal process and different reliability measures are analyzed using Markov renewal theory. First, it is assumed that the system is replaced with a brand‐new one (maximal repair model) at the beginning of each stage. Under this hypothesis, the probability of survival until a predetermined time (system reliability) and the probability of completing a predetermined number of phases of the mission (mission reliability) are determined. Then, we consider cases without replacement (no repair model) and use intrinsic aging concepts to analyze mission reliability of a series system.