Communications - Scientific Letters of the University of Zilina 2014, 16(1):114-120 | DOI: 10.26552/com.C.2014.1.114-120

Reliability Analysis of Noncoherent Systems by Logical Differential Calculus and Binary Decision Diagrams

Jozef Kostolny1, Miroslav Kvassay1, Stefan Kovalik1
1 Department of Informatics, Faculty of Management Science and Informatics, University of Zilina, Slovakia

Reliability is the important characteristic of systems. Most of the systems consist of more than one component. Moreover, modern systems are very complex and they include a lot of components. Therefore, effective methods have to be developed for analysis of these systems. The techniques that have been already considered for this purpose are the Binary Decision Diagrams and the Logical Differential Calculus. However, these methods have been considered only for the coherent systems. In this paper, their use in the reliability analysis of the noncoherent systems is considered.

Keywords: noncoherent system, binary decision diagram, direct partial logic derivative, importance analysis, strucutral importance measure

Published: February 28, 2014  Show citation

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Kostolny, J., Kvassay, M., & Kovalik, S. (2014). Reliability Analysis of Noncoherent Systems by Logical Differential Calculus and Binary Decision Diagrams. Communications - Scientific Letters of the University of Zilina, 16(1), 114-120. doi: 10.26552/com.C.2014.1.114-120
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    References

    1. ZIO, E.: Reliability Engineering: Old Problems and New Challenges, Reliability Engineering & System Safety, vol. 94, No. 2, pp. 125-141, 2009. Go to original source...
    2. CHANG, Y., AMARI, S.: Computing System Failure Frequencies and Reliability Importance Measures using OBDD, IEEE Transactions on Computers, vol. 53, No. 1, pp. 54-68, 2004. Go to original source...
    3. BRYANT, R. E.: Graph-Based Algorithms for Boolean Function Manipulation, IEEE Transactions on Computers, vol. C-35, No. 8, pp. 677-691, 1986. Go to original source...
    4. KOSTOLNY, J., KVASSAY, M., KOVALIK, S.: Analysis of System Reliability by Logical Differential Calculus and Decision Diagrams, Intern. Conference on Digital Technologies (DT), 2013, pp. 170-175. Go to original source...
    5. ZAITSEVA E. N., LEVASHENKO, V. G.: Importance Analysis by Logical Differential Calculus, Automation and Remote Control, vol. 74, No. 2, pp. 171-182, 2013. Go to original source...
    6. KUO, W., ZHU, X.: Importance Measures in Reliability, Risk, and Optimization. Chichester, John Wiley & Sons, Ltd, 2012. Go to original source...
    7. UPADHYAYA, S. J., PHAM, H.: Analvsis of Noncoherent Systems and an Architecture for the Computation of the System Reliability, IEEE Transactions on Computers, vol. 42, No. 4, pp. 484-493, 1993. Go to original source...
    8. INAGAKI, T., HENLEY, E. J.: Probabilistic Evaluation of Prime Implicants and Top-events for Non-coherent Systems, IEEE Transactions on Reliability, vol. 3, No. 5, pp. 361-367, 1980. Go to original source...
    9. JACKSON, P. S.: On the s-importance of Elements and Prime Implicants of Non-coherent Systems, IEEE Transactions on Reliability, vol. R-32, No. 1, pp. 21-25, 1983. Go to original source...
    10. ANDREWS, J. D., BEESON, S.: Birnbaum's Measure of Component Importance for Noncoherent Systems, IEEE Transactions on Reliability, vol. 52, No. 2, pp. 213-219, 2003. Go to original source...
    11. BEESON, S., ANDREWS, J. D.: Importance Measures for Non-coherent-system Analysis, IEEE Transactions on Reliability, vol. 52, No. 3, pp. 301-310, 2003. Go to original source...
    12. KUO, W., ZHU, X.: Relations and Generalizations of Importance Measures in Reliability, IEEE Transactions on Reliability, vol. 61, No. 3, pp. 659-674, 2012. Go to original source...
    13. AKERS, S. B., Jr.: On a Theory of Boolean Functions, J. of the Society for Industrial and Applied Mathematics, vol. 7, No. 4, p. 487, 1959. Go to original source...
    14. ARMSTRONG, M. J.: Reliability-importance and Dual failure-mode Components, IEEE Transactions on Reliability, vol. 46, No. 2, pp. 212-221, 1997. Go to original source...
    15. ZAITSEVA, E., LEVASHENKO, V.: Multiple-Valued Logic Mathematical Approaches for Multi-state System Reliability Analysis, J. of Applied Logic, vol. 11, No. 3, pp. 350-362, 2013. Go to original source...

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