Skip to main content
SpringerLink
Log in

Importance analysis by logical differential calculus

  • Linear Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The physical objects or processes include many interconnected components representing a complex systems. Their reliability analysis usually considers two states interpreted as failure and operability. They are described in terms of the binary mathematical model. Importance analysis of the system elements is a traditional component of the reliability analysis. It enables one to estimate the impact of individual components on the system’s operability or failure. The present paper proposed a new approach to analysis and estimation of the system importance on the basis of the logical differential calculus.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Rainshke, K. and Ushakov, I.A., Otsenka nadezhnosti sistem s ispol’zovaniem grafov (Estimation of System Reliability with the Use of Graphs), Moscow: Radio i Svyaz’, 1988.

    Google Scholar 

  2. Marseguerra, M. and Zio, E., Monte Carlo Estimation of the Differential Importance Measure: Application to the Protection System of a Nuclear Reactor, Reliab. Eng. Syst. Safety, 2004, vol. 86, no. 1, pp. 11–24.

    Article  Google Scholar 

  3. Natvig, B., Eide, K., Gasemyr, J., et al., Simulation Based Analysis and an Application to an Offshore Oil and Gas Production System af the Natvig Measures of Component Importance in Repairable Systems, Reliab. Eng. Syst. Safety, 2009, vol. 94, no. 10, pp. 1629–1638.

    Article  Google Scholar 

  4. Fricks, R. and Trivedi, K., Importance Analysis with Markov Chains, in Proc. 49th IEEE Annual Reliability Maintainability Sympos., Tampa, USA, 2003, pp. 89–95.

  5. Chang, Y., Amari, S., and Kuo, S., Computing System Failure Frequencies and Reliability Importance Measures Using OBDD, IEEE Trans. Comput., 2004, vol. 53, no. 1, pp. 54–68.

    Article  Google Scholar 

  6. Beeson, S. and Andrews, J.D., Importance Measure for Noncoherent-System Analysis, IEEE Trans. Reliab., 2003, vol. 52, no. 3, pp. 301–310.

    Article  Google Scholar 

  7. Armstrong, M., Reliability-Importance and Dual Failure-mode Components, IEEE Trans. Reliab., 1997, vol. 46, no. 2, pp. 212–221.

    Article  Google Scholar 

  8. Birnbaum, L.W., On the Importance of Different Components in a Multicomponent System, in Multivariate Analysis II, Krishnaiah, P.R., Ed., New York: Academic, 1969, pp. 581–592.

    Google Scholar 

  9. Fussell, J.B., How to Hand-calculate System Reliability and Safety Characteristics, IEEE Trans. Reliab., 1975, vol. R-24, no. 3, pp. 169–174.

    Article  Google Scholar 

  10. Vesely, W.E., A Time Dependent Methodology for Fault Tree Evaluation, Nuclear Eng. Design, 1970, vol. 13, no. 2, pp. 337–360.

    Article  Google Scholar 

  11. Borgonovo, E., Differential, Criticality and Birnbaum Importance Measures: An Application to Basic Event, Groups and SSCs in Event Trees and Binary Decision Diagrams, Reliab. Eng. Syst. Safety, 2007, vol. 92, no. 10, pp. 1458–1467.

    Article  Google Scholar 

  12. Zaitseva, E. and Levashenko, V., Dynamic Reliability Indices for Parallel, Series and k-out-of-n Multistate System, in Proc. 52nd IEEE Annual Reliability Maintainability Sympos., Newport Beach, USA, 2006, pp. 253–259.

  13. Zio, E., Reliability Engineering: Old Problems and New Challenges, Reliab. Eng. Syst. Safety, 2009, vol. 94, no. 2, pp. 125–141.

    Article  Google Scholar 

  14. Ryabinin, I.A. and Parfenov, Yu.M., Determination of “Weight” and “Importance” of Individual Elements at Reliability Estimation of a Complex System, Izv. Akad. Nauk SSSR, Energet. Transport, 1978, no. 6, pp. 22–32.

  15. Moret, B. and Thomason, M., Boolean Difference Techniques for Time-sequence and Common-cause Analysis of Fault-trees, IEEE Trans. Reliab., 1984, vol. R-33, no. 5, pp. 399–405.

    Article  Google Scholar 

  16. Zaitseva, E.N. and Pottosin, Yu.V., Analysis of Failure Probability of Unrestorable System with the Use of the Logic-algebraic Methods, Informatika, 2007, no. 2, pp. 77–85.

  17. Schneeweiss, W., A Short Boolean Derivation of Mean Failure Frequency for Any (also Non-coherent) System, Reliab. Eng. Syst. Safety, 2009, vol. 94, no. 8, pp. 1363–1367.

    Article  Google Scholar 

  18. Bochmann, D. and Posthoff, Ch., Binäre dynamische Systeme, Berlin: Akademie, 1981. Translated under the title Dvoichnye dinamicheskie sistemy, Moscow: Energoatomizdat, 1986.

    MATH  Google Scholar 

  19. Kukharev, G.A., Shmerko, V.P., and Zaitseva, E.N., Algoritmy i sistolicheskie protsessory dlya obrabotki mnogoznachnykh dannykh (Algorithms and Systolic Processors to Process Many-valued Data), Minsk: Nauka i Tekhnika, 1990.

    Google Scholar 

  20. Kumar, S.K. and Breuer, M., Probabilistic Aspects of Boolean Switching Function via a New Transform, J. ACM, 1981, vol. 28, no. 3, pp. 502–520.

    Article  MathSciNet  MATH  Google Scholar 

  21. Levashenko, V., Moraga, K., Kholovinski, G., Yanushkevich, S., and Shmerko, V., A Test Algorithm for Multiple-Valued Logic Combinational Circuits, Autom. Remote Control, 2000, vol. 61, no. 5, pp. 844–857.

    MATH  Google Scholar 

  22. Zaitseva, E., Importance Analysis of Multi-state System by Tools of Differential Logical Calculus, in Reliability, Risk and Safety. Theory and Applications, Bris, R., Guedes, C., and Martorell, S., Eds., Singapore: London: CRC Press, 2010, pp. 1579–1584.

    Google Scholar 

  23. Ryabinin, I.A., Nadezhnost’ i bezopasnost’ strukturno-slozhnykh sistem (Reliability and Safety of the Structurally Complex Systems), St. Petersburg: Politekhnika, 2000.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Žilina, Žilina, Slovakia

    E. N. Zaitseva & V. G. Levashenko

Authors
  1. E. N. Zaitseva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. G. Levashenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © E.N. Zaitseva, V.G. Levashenko, 2013, published in Avtomatika i Telemekhanika, 2013, No. 2, pp. 6–21.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zaitseva, E.N., Levashenko, V.G. Importance analysis by logical differential calculus. Autom Remote Control 74, 171–182 (2013). https://doi.org/10.1134/S000511791302001X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000511791302001X

Keywords

Search

Navigation