Dependability analysis of semi-Markov systems

This paper presents a dependability analysis (Availability-Reliability-Maintainability, Mean times) for semi-Markov systems with finite state space, by a new method, based on algebraic calculus within a convolution algebra. This method permits us to obtain, by simple matrix calculus, closed form solutions of transition probabilities and dependability measures. It is a quite general method that does not need the semi-Markov kernel to be absolutely continuous. Thus we obtain, as an example, the classical availability formulae modelled by an alternating renewal process, by a simple algebraic calculus without probabilistic argument. A detailed application of the method is given.