Some new aspects of the transient analysis of discrete-parameter Markov models with an application to the evaluation of repair events in power transmission

In Markov reliability modelling, a partitioned state space is used to describe the behaviour of a system each state of which is associated with the system either being functional or under repair. Such a system alternates between working and repair periods indefinitely. Recent research results on the distribution of the sequences of the lengths of working and repair periods afford the reliability analyst a set of system characteristics which can be used in addition to the traditional ones (reliability, point availability, etc.) to describe the system’s transient behaviour. This paper presents a concise derivation of closed-form expressions for the probability mass function and the factorial moments of the total cumulative ‘time’ spent in a subset of the state space by an irreducible or absorbing discrete-parameter Markov chain during the first n time instances. This result is then applied to analyse the sequence of repair events categorized as ‘minor’ and ‘major’ of a Markov model of a power transmission system. The numerical implementation using the Macintosh version of MatLab is also discussed.