A Recent Developments in the computation of the ROCOF of multi-state system and its application

This paper reviews several theoretical works on the computation of the Rate of Occurrence of Failure (ROCOF) for general multi-state random systems, focusing on recent generalizations. The discussion begins by defining the ROCOF for a Markov process and discussing the main results achieved in the literature, then moves towards the richer framework represented by semi-Markov systems. The paper discusses complications that arise when extending the ROCOF to higher orders so that a measure of the association of failures in time can be obtained. The work then analyzes possible modifications in terms of a conditional version of the ROCOF, which is of special interest in applications. The findings are illustrated by a numerical example from reliability, and the broad applicability is demonstrated by a discussion of different applications in other doma