A Probability Bound Estimation Method in Markov Reliability Analysis

In many practical systems, the uncertainty of component failure/repair rates results in uncertainty of system failure probability. Concerning a repairable system, uncertainty is evaluated as a probability bound in the Markov process. In practical analysis, the Laplace transform has the advantage of relatively less computing time than that of a numerical method, eg, Runge Kutta. This paper proposes an algorithm for evaluating this uncertainty using the Laplace transform method. This algorithm assumes the Johnson SB distribution for system-failure próbability. Then, the mean and the variance of system-failure probability are obtained using Newton´s method and an integral form for calculating parametric differentiation. Finally, the probability bounds are obtained by applying the conventional moment-matching method. A tutorial example is presented at the end of this paper.