A New Approach to Analysis of Interval Availability

This paper gives a novel and useful representation of interval availability over a time period [0, T] for a 2-state continuous time Markov chain (2-CTMC) model. The representation is in terms of an order statistic of a binomially distributed random rank in a random sample of Poisson size from a distribution uniform on the interval [0,1]. This representation is then used to obtain the variance of interval availability for the 2-CTMC model. It is proposed to judge the fluctuations in interval availability by considering the derived coefficient of variation. Both the order statistic representation and the variance of interval availability constitute new contributions to the availability literature.