Reliability evaluation of generalised multi-state k-out-of-n systems based on FMCI approach

Abstract

Most studies on k-out-of-n systems are in the binary context. The k-out-of-n system has failed if and only if at least k components have failed. The generalised multi-state k-out-of-n: G and F system models are defined by Huang et al. [Huang, J., Zuo, M.J., and Wu, Y.H. (2000), ‘Generalized Multi-state k-out-of-n: G Systems’, IEEE Transactions on reliability, 49, 105–111] and Zuo and Tian [Zuo, M.J., and Tian, Z.G. (2006), ‘Performance Evaluation of Generalized Multi-state k-out-of-n Systems’, IEEE Transactions on Reliability, 55, 319–327], respectively. In this article, by using the finite Markov chain imbedding (FMCI) approach, we present a unified formula with the product of matrices for evaluating the system state distribution for generalised multi-state k-out-of-n: F systems which include the decreasing multi-state F system, the increasing multi-state F system and the non-monotonic multi-state F system. Our results can be extended to the generalised multi-state k-out-of-n: G system. Three numerical examples are presented to illustrate the results.

Keywords:

• k-out-of-n systems
• multi-state systems
• finite Markov chain imbedding approach
• system state distribution

Acknowledgement

This work was supported by the National Natural Science Foundation of China (70901008) and the Excellent Yound Scholars Research Fund of the Beijing Institute of Technology (2008Y0818).