Abstract: Sensitivity analysis plays a critical role in quantifying uncertainty in the design of computer systems. In particular, a variance-based global sensitivity analysis is often used to rank the importance of input factors based on their contribution to the variance of the output measure of interest. The variance-based sensitivity analysis is sampling-based and therefore usually applies simulation methods such as Monte Carlo simulation. That means the traditional methods for variance-based sensitivity analysis based on simulation do not need the analytic structure of the model to be analyzed. However, the simulation usually needs a huge number of realizations to obtain stable results, which incurs an undesired high computational cost. In this paper, we present an analytic approach to compute the variance-based sensitivity based on moment approximation. More specifically, we formulate the output measure of continuous-time Markov chains (CTMCs) and investigate the relationship between input parameters and output measure through variance-based sensitivity analysis. The numerical results showing the main effects of model parameters in both parallel and series system configurations indicate that a component's effect on the uncertainty in system reliability depends largely on the system structure.

Key words: variance-based sensitivity analysis, continuous-time Markov chain, moment-based approximation, main effect