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

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.

[1]  Sivan Toledo,et al.  Improving the memory-system performance of sparse-matrix vector multiplication , 1997, IBM J. Res. Dev..

[2]  Liudong Xing,et al.  Reliability Analysis of Multistate Phased-Mission Systems With Unordered and Ordered States , 2011, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[3]  Kishor S. Trivedi,et al.  Reliability Analysis of Phased-Mission System With Independent Component Repairs , 2007, IEEE Transactions on Reliability.

[4]  P. Sadayappan,et al.  On improving the performance of sparse matrix-vector multiplication , 1997, Proceedings Fourth International Conference on High-Performance Computing.

[5]  W. Stewart,et al.  A numerical study of large sparse matrix exponentials arising in Markov chains 1 1 This work has ben , 1999 .

[6]  Joanne Bechta Dugan.  Automated analysis of phased-mission reliability , 1991 .

[7]  James A. Ritcey,et al.  Computationally-efficient phased-mission reliability analysis for systems with variable configurations , 1992 .

[8]  Yuchang Mo,et al.  New Insights Into the BDD-Based Reliability Analysis of Phased-Mission Systems , 2009, IEEE Transactions on Reliability.

[9]  Liudong Xing,et al.  Reliability Evaluation of Phased-Mission Systems With Imperfect Fault Coverage and Common-Cause Failures , 2007, IEEE Transactions on Reliability.

[10]  Yuchang Mo.  Variable Ordering to Improve BDD Analysis of Phased-Mission Systems With Multimode Failures , 2009, IEEE Transactions on Reliability.

[11]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[12]  Mansoor Alam,et al.  Quantitative Reliability Evaluation of Repairable Phased-Mission Systems Using Markov Approach , 1986, IEEE Transactions on Reliability.

[13]  Sarah J. Dunnett,et al.  Phased mission modelling of systems with maintenance-free operating periods using simulated Petri nets , 2008, Reliab. Eng. Syst. Saf..

[14]  Liudong Xing,et al.  Analysis of generalized phased-mission system reliability, performance, and sensitivity , 2002, IEEE Trans. Reliab..

[15]  James Daniel. Esary,et al.  Reliability analysis of phased missions. , 1975 .

[16]  Cleve B. Moler,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later , 1978, SIAM Rev..

[17]  Hassan S. Bakouch,et al.  Probability, Markov chains, queues, and simulation , 2011 .

[18]  Sheldon M. Ross,et al.  Introduction to probability models , 1975 .

[19]  Kishor S. Trivedi,et al.  A BDD-based algorithm for reliability analysis of phased-mission systems , 1999 .

[20]  Liudong Xing,et al.  Reliability Analysis of Phased-Mission Systems with , 2001 .

[21]  Sean Reed,et al.  Improved Efficiency in the Analysis of Phased Mission Systems With Multiple Failure Mode Components , 2011, IEEE Transactions on Reliability.

[22]  Antoine Rauzy,et al.  An experimental study on iterative methods to compute transient solutions of large Markov models , 2004, Reliab. Eng. Syst. Saf..

[23]  Daniel P. Siewiorek,et al.  Mission reliability analysis of fault-tolerant multiple-phased systems , 2008, Reliab. Eng. Syst. Saf..

[24]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[25]  Xiaoyue Wu,et al.  Runge-Kutta algorithm of reliability model based on Markov chain for TT&C system , 2011, The Proceedings of 2011 9th International Conference on Reliability, Maintainability and Safety.

[26]  A. Usman,et al.  Review of Storage Techniques for Sparse Matrices , 2005, 2005 Pakistan Section Multitopic Conference.