Int J Performability Eng ›› 2022, Vol. 18 ›› Issue (5): 329-337.

### Variance-Based Sensitivity Analysis for Markov Models using Moment Approximation

Jiahao Zhanga,*, Junjun Zhengb, Hiroyuki Okamuraa, and Tadashi Dohia

1. aGraduate School of Advanced Science Engineering, Hiroshima University, Higashihiroshima, 7398527, Japan;
bDepartment of Information Science and Engineering, Ritsumeikan University, Kusatsu, 5258577, Japan
• Submitted on  ;  Revised on  ; Accepted on
• Contact: * E-mail address: jzheng@fc.ritsumei.ac.jp
• About author:Jiahao Zhang is a doctoral student with the Graduate School of Advanced Science and Engineering, Hiroshima University, Japan. His research interests in dependable computing and uncertainty propagation.
Junjun Zheng is an Assistant Professor with the Department of Information Science and Engineering, Ritsumeikan University, Japan. His research interests include performance evaluation and dependable computing.
Hiroyuki Okamura is a Professor with the Graduate School of Advanced Science and Engineering, Hiroshima University, Japan. His research interests include performance evaluation, dependable computing, and applied statistics.
Tadashi Dohi is a Professor with the Graduate School of Advanced Science and Engineering, Hiroshima University, Japan. His research interests include reliability engineering, software reliability, and dependable computing.

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.