Numerical Method for Reliability Analysis of Phased-Mission System Using Markov Chains

Abstract

This article presents a numerical method for solving continuous time Markov chain (CTMC) model for reliability evaluation of phased-mission system. The method generates infinitesimal matrix based on the statistical independence of subsystem failure and repair process. The infinitesimal generator matrix is stored by the use of sparse matrix-compressed storage schemes, and the transient solution of the CTMC model is obtained by using three methods including the uniformization method, forward Euler method, and Runge-Kutta method, which take advantage of the sparseness of the infinitesimal generator matrix. An example PMS is used to compare the preconditioning methods for sparse matrix and numerical methods. Experiment results show that compressed row storage scheme (CRS) saves more storage than other storage formats, and uniformization method combined with CRS achieves the best efficiency and accuracy.

Keywords:

• Continuous time Markov chains
• Numerical method
• Phased-mission system
• PMS
• Reliability analysis

Mathematics Subject Classification:

• Primary 60J22
• Secondary 90B25

Acknowledgment

This work is supported by the National Natural Science Foundation of China with Grant No. 71071159.