Dependability Modelling and Sensitivity Analysis of Scheduled Maintenance Systems

  • Andrea Bondavalli
  • Ivan Mura
  • Kishor S. Trivedi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1667)


In this paper we present a new modelling approach for dependability evaluation and sensitivity analysis of Scheduled Maintenance Systems, based on a Deterministic and Stochastic Petri Net approach. The DSPN approach offers significant advantages in terms of easiness and clearness of modelling with respect to the existing Markov chain based tools, drastically limiting the amount of user-assistance needed to define the model. At the same time, these improved modelling capabilities do not result in additional computational costs. Indeed, the evaluation of the DSPN model of SMS is supported by an efficient and fully automatable analytical solution technique for the time-dependent marking occupation probabilities. Moreover, the existence of such explicit analytical solution allows to obtain the sensitivity functions of the dependability measures with respect to the variation of the parameter values. These sensitivity functions can be conveniently employed to analytically evaluate the effects that parameter variations have on the measures of interest.


Sensitivity Function Markov Chain Modelling Reachability Graph Explicit Analytical Solution Complete Check 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Allmaier and S. Dalibor, “PANDA-Petri net analysis and design assistant,” in Proc. Performance TOOLS’97, Saint Malo, France, 1997.Google Scholar
  2. 2.
    C. Beounes, M. Aguera, J. Arlat, C. Bourdeau, J.-E. Doucet, K. Kanoun, J.-C. Laprie, S. Metge, J. Moreira de Souza, D. Powell and P. Spiesser, “SURF-2: a program for dependability evaluation of complex hardware and software systems,” in Proc. IEEE FTCS’23, Fault-Tolerant Computing Symposium, Toulouse, France, 1993, pp. 668–673.Google Scholar
  3. 3.
    J. T. Blake, A. Reibman and K. S. Trivedi, “Sensitivity analysis of reliability and performability measures for multiprocessor systems,” Duke University, Durham NC, USA 1987.Google Scholar
  4. 4.
    A. Bondavalli, I. Mura and M. Nelli, “Analytical Modelling and Evaluation of Phased-Mission Systems for Space Applications,” in Proc. IEEE High Assurance System Engineering Workshop (HASE’97), Bethesda Maryland, USA, 1997, pp. 85–91.Google Scholar
  5. 5.
    H. Choi, V.G. Kulkarni and K.S. Trivedi, “Transient analysis of deterministic and stochastic Petri nets.,” in Proc. 14th International Conference on Application and Theory of Petri Nets, Chicago Illinois, USA, 1993, pp. 166–185.Google Scholar
  6. 6.
    H. Choi, V. Mainkar and K. S. Trivedi, “Sensitivity analysis of deterministic and stochastic petri nets,” in Proc. MASCOTS’93, 1993, pp. 271–276.Google Scholar
  7. 7.
    G. Ciardo, J. Muppala and K.S. Trivedi, “SPNP: stochastic petri net package.,” in Proc. International Conference on Petri Nets and Performance Models, Kyoto, Japan, 1989.Google Scholar
  8. 8.
    J. B. Dugan, “Automated Analysis of Phased-Mission Reliability,” IEEE Transaction on Reliability, Vol. 40, pp. 45–52, 1991.zbMATHCrossRefGoogle Scholar
  9. 9.
    P. M. Frank, “Introduction to System Sensitivity Theory,” New York, Academic Press, 1978.zbMATHGoogle Scholar
  10. 10.
    P. Heidelberger and A. Goyal, “Sensitivity analysis of continuous time Markov chains using uniformization,” in Proc. 2-nd International Workshop on Applied Mathematics and Performance/Reliability models of Computer/Communication systems, Rome, Italy, 1987.Google Scholar
  11. 11.
    C. Lindemann, “Performance modeling using DSPNexpress,” in Proc. Tool Descriptions of PNPM’97, Saint-Malo, France, 1997.Google Scholar
  12. 12.
    C. Lindemann, “Performance modeling using deterministic and stochastic petri nets,” John Wiley & Sons, 1998.Google Scholar
  13. 13.
    J.F. Meyer, D.G. Furchgott and L.T. Wu, “Performability Evaluation of the SIFT Computer,” in Proc. IEEE FTCS’79 Fault-Tolerant Computing Symposium, June20-22, Madison, Wisconsin, USA, 1979, pp. 43–50.Google Scholar
  14. 14.
    J. K. Muppala and K. S. Trivedi, “GSPN models: sensitivity analysis and applications,” in Proc. 28-th ACM Southeast Region Conference, 1990.Google Scholar
  15. 15.
    I. Mura, A. Bondavalli, X. Zang and K. S. Trivedi, “Dependability Modeling and Evaluation of Phased Mission Systems: a DSPN Approach,” in Proc. DCCA-99, San Jose, CA, USA, 1999.Google Scholar
  16. 16.
    W. H. Sanders, W. D. Obal II, M. A. Qureshi and F. K. Widjanarko, “The UltraSAN modeling environment,” Performance Evaluation, Vol. 21, pp. 1995.Google Scholar
  17. 17.
    M. Smotherman and K. Zemoudeh, “A Non-Homogeneous Markov Model for Phased-Mission Reliability Analysis,” IEEE Transactions on Reliability, Vol. 38, pp. 585–590, 1989.zbMATHCrossRefGoogle Scholar
  18. 18.
    A. K. Somani, J. A. Ritcey and S. H. L. Au, “Computationally-Efficent Phased-Mission Reliability Analysis for Systems with Variable Configurations,” IEEE Transactions on Reliability, Vol. 41, pp. 504–511, 1992.CrossRefGoogle Scholar
  19. 19.
    A. K. Somani and K. S. Trivedi, “Phased-Mission Systems Using Boolean Algebraic Methods,” Performance Evaluation Review, Vol. pp. 98–107, 1994.Google Scholar
  20. 20.
    D. W. Twigg, A. V. Ramesh, U. R. Sandadi, A. Ananda and T. Sharma, “Reliability computation of systems that operate in multiple phases and multiple missions,” Boeing Commercial Airplane GroupGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Andrea Bondavalli
    • 1
  • Ivan Mura
    • 1
  • Kishor S. Trivedi
    • 2
  1. 1.CNUCE/CNRPisaItaly
  2. 2.CACC, Dept. of ECEDuke UniversityDurhamUSA

Personalised recommendations