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.

Mission Reliability Assessment of Space TT&C System by Discrete Event System Simulation

“…First, an effective algorithm is required to compute state probability vector of each phase Markov model; then, a states mapping mechanism is needed to obtain initial states probability vector of each phase (except the first one). The uniformization method 19 is used to solve the state probability vector and the states mapping rules are adapted from 20 to handle the mapping problems between consecutive phase state spaces.…”

Reliability analysis of large phased-mission systems with repairable components based on success-state sampling

“…One common strategy [23][24][25][26][27] is to apply truncation to BDD (or fault tree) to slow down the exponential growth of time cost or space cost. Another strategy [28,29] focuses on the shrinkage of the Markovian methods through the compression storage of large sparse matrices. However, Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ress some experimental works [30][31][32][33] show that the fixed truncation limit may result in the significant error in results.…”

Mission reliability modeling and evaluation of multi-mission phased mission system based on an extended object-oriented Petri net

“…Combinational method is one of the most effective analytical methods in analyzing non-repairable PMS which are mainly based on binary decision diagrams (BDD) algorithm, but has to combine with state-based approaches to deal with repairable PMS [7,13]. State-based approaches could consider each possible state of the repairable systems [9]. However, they may suffer state space explosion problems when there are large number of components.…”