ROCOF of higher order for semi-Markov processes

• Published in: Applied mathematics and computation Vol. 441; p. 127719
• Main Authors: D’Amico, Guglielmo, Petroni, Filippo
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.03.2023
• Subjects: Failure; Random system; Reliability; Volatility; Random system; Reliability; Volatility; Failure
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127719

•The rate of occurrence of failure of higher order provides a measure of association of tuples of failures.•The ROCOF is represented by means of an explicit formula.•The analysis is implemented under state-duration random initial conditions of the semi-Markov system. In this paper, we study the rate of occurrence of failures (ROCOF) of higher order for continuous time semi-Markov processes (SMP). This indicator gives information on whether there are a lot of failures or only a few within a time interval. It also considers the relative positioning of tuples of failures in time. Here, we consider SMP with a mixed probability distribution for the initial law of the system taking into account the possible random starting from any state with any duration. Furthermore, under suitable assumptions on the transition rates, we determine an explicit formula for the ROCOF of higher order and we recover as particular cases previous results obtained in the literature. A numerical example demonstrates the possibility of using this index in real applications. A possible application in the field of mathematical finance is also discussed.