Sensitivity and Uncertainty Analysis of Markov Reward Models

Markov-reward models are often used to analyze the reliability and performability of computer systems. One difficult problem therein is the quantification of the model parameters. If they are available, e.g., from measurement data collected by manufacturers, they are: (a) generally regarded as confidential; and (b) difficult to access. This paper addresses two ways of dealing with uncertain parameters: (1) sensitivity analysis, and (2) Monte Carlo uncertainty analysis. Sensitivity analysis is relatively fast and cheap but it correctly describes only the local behavior of the model outcome uncertainty as a result of the model parameter uncertainties. When the uncertain parameters are dependent, sensitivity analysis is difficult. The authors extend the classical sensitivity analysis so that the results conform better to those of the Monte Carlo uncertainty analysis. Monte Carlo uncertainty analysis provides a global view. Since it can include parameter dependencies, it is more accurate than sensitivity analysis. By two examples they demonstrate both approaches and illustrate the effects uncertainty and dependence can have.