NEW MATRIX BASED ALGORITHM FOR CALCULATION OF IMPORTANCE MEASURES
DOI:
https://doi.org/10.26906/SUNZ.2019.6.033Keywords:
Structure function, Importance measures, Logical Differential Calculus, Direct Partial Boolean DerivativesAbstract
The system reliability/availability is complex term that is evaluated based on numerous indices and measures. There are different methods for the calculation of these indices and measures. Some of the most used are importance measures. These measures allow to evaluate the influence of fixed system components or set of components to the system reliability/availability. Importance measures are used to allow for various aspects of the impact of system elements on its failure or operability. Analysis of element importance is used in the system design, diagnosis, and optimization. In this paper new algorithm for the calculation some of importance measures is developed based on the matrix procedures. This paper goal is development of new algorithm to calculate importance measures of the system based on the matrix procedures that can be transformed in the parallel procedures/algorithm. This algorithm is developed based on the application of Logical Differential Calculus of Boolean logic for importance analysis of system. The application of parallel algorithm in importance analysis allows the evaluation of system of large dimension. Importance specific of the proposed matrix procedures for calculation of importance measures is the application of structure function for the mathematical representation of investigated system. This function defined the correlation of the system components states and system reliability/ availability. The structure function in this case is defined as truth vector to be used in the matrix transformation. The truth vector of Boolean function is column of the truth table of function if the values of the variables are lexicographically orderedDownloads
References
Kuo, W., Zhu, X. Importance Measures in Reliability, Risk and Optimization, John-Wiley & Sons Publ., 2012. 440 p.
Zaitseva, E., Levashenko, V. Importance Analysis by Logical Differential Calculus. Automation and Remote Control, 2013, vol. 74, no. 2, pp. 171–182.
Levitin, G. Lisnianski, A. Multi-state System Reliability Analysis and Optimization, Handbook of Reliability Engineering, London, Berlin, NY, Springer Publ., 2003. 342 p.
Barlow, R. E., Proschan, F. Importance of system components and fault tree events. Stochastic Processes and their Applications, 1975, vol. 3, no. 2, pp. 153–173.
Kvassay, M., Levashenko, V., Zaitseva, E. Analysis of minimal cut and path sets based on direct partial Boolean derivatives. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2016, vol. 230, no. 2 pp.147–161.
Schneeweiss, W.G. A short Boolean derivation of mean failure frequency for any (also non-coherent) system, Reliability and Engineering System Safety, 2009, vol. 94, no. 8, pp. 1363–1367.
Zhang, L., Xing, L., Liu, A., Mao, K. Multivalued Decision Diagrams-Based Trust Level Analysis for Social Networks, IEEE Access, 2019, vol. 7, no. 12, pp. 180620-180629.
Zhang, S., Sun, S., Si, S., Wang, P. A decision diagram based reliability evaluation method for multiple phased-mission systems. Eksploatacja i Niezawodnosc - Maintenance and Reliability, 2017, vol. 19, no. 3, pp. 485-492.
Xin, S., Yan, C., Xingyou, Z., Chuanzhi, W. A novel multi-microgrids system reliability assessment algorithm using parallel computing. Energy Internet and Energy System Integration: Proceedings of the 2017 IEEE Conference, Beijing, China, 2017, pp. 1-6.
Quan, Z. Wang, Z.-J., Ye, T., Guo, S. Task Scheduling for Energy Consumption Constrained Parallel Applications on Heterogeneous Computing Systems. IEEE Transactions on Parallel and Distributed Systems, 2019, vol. 45, no. 12, pp. 1-8.
Kukharev, G. Shmerko, V., Zaitseva, E. Multiple-Valued Data Processing Algorithms and Systolic Processors. Minsk, Nauka and Technika Publ., 1990. 320 p.
Zaitseva, E., Levashenko, V. Reliability analysis of Multi-State System and Multiple-Valued Logic. International Journal of Quality & Reliability Management, 2017, vol. 34, no. 6, pp. 862-878.
Beeson, S., Andrews, J. D. Importance measure for non-coherent-system analysis. IEEE Transaction on Reliability, 2003, vol. 52, no. 3, pp. 301-310.
Steinbach, B., Posthoff, C. Boolean Differential Caculus. San Rafael, Morgan & Claypool Publ., 2018. 720 p.
Posthoff, C., Steinbach, B. Logic Functions and Equations: Binary Models for Computer Science. Second ed., Springer Publ., 2019. 507 p.
Moret, B. M. E., Thomason, M. G. Boolean Difference Techniques for Time-Sequence and Common-Cause Analysis of Fault-Trees. IEEE Transaction on Reliability, 1984, vol. R-33, pp. 399-405.
Birnbaum Z. W. On the Importance of Different Components in a Multicomponent System. Multivariate Analysis II. New York, Academic Press Publ., 1969, pp. 581–922.
