Uncertainty analysis in reliability modeling

In reliability analysis of computer systems, models such as fault trees, Markov chains, and stochastic Petri nets (SPN) are built to evaluate or predict the reliability of the system. In general, the parameters in these models are usually obtained from field data, or by the data from systems with similar functionality, or even by guessing. In this paper, we address the parameter uncertainty problem. First, we review and classify three ways to describe the parameter uncertainty in the model: reliability bounds, confidence intervals, and probability distributions. Second, by utilizing the second-order approximation and the normal approximation, we propose an analytic method to derive the confidence interval of the system reliability from the confidence intervals of parameters in the transient solution of Markov models. Then, we study the Monte Carlo simulation method to derive the uncertainty in the system reliability, and use it to validate our proposed analytic method. Our effort makes the reliability prediction more realistic compared with the result without the uncertainty analysis.