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On the Reliability of Repairable Systems: Methods and Applications

  • Conference paper
Progress in Industrial Mathematics at ECMI 2004

Part of the book series: Mathematics in Industry ((TECMI,volume 8))

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Summary

Failures in repairable systems are often described by means of renewal or non-homogeneous Poisson processes, depending upon the repair policy. In the former case repairs bring the system reliability back to its initial value, whereas in the latter they restore the same reliability the system had just before the failure. We focus on the latter process, illustrating some properties and applications, mainly in a Bayesian framework.

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References

  1. H.E. Ascher and H. Feingold. Repairable Systems Reliability. Marcel Dekker, New York, 1984.

    MATH  Google Scholar 

  2. S. Bar-Lev, I. Lavi, and B. Reiser. Bayesian inference for the Power Law process. Ann. Inst. Statist. Math., 44:623–639, 1992.

    Article  MATH  Google Scholar 

  3. J.O. Berger. Statistical Decision Theory and Bayesian Analysis, 2nd ed. Springer Verlag, New York, 1985.

    MATH  Google Scholar 

  4. E. Cagno, F. Caron, M. Mancini, and Ruggeri F. On the use of a robust methodology for the assessment of the probability of failure in an urban gas pipe network. In S. Lydersen, G.K. Hansen, and Sandtorv H.A., editors, Safety and Reliability, vol. 2, pages 913–919. Balkema, Rotterdam, 1998.

    Google Scholar 

  5. E. Cagno, F. Caron, M. Mancini, and Ruggeri F. Robust Bayesian Analysis, chapter Sensitivity of replacement priorities for gas pipeline maintenance, pages 335–350. Springer Verlag, New York, 2000.

    Google Scholar 

  6. E. Cagno, F. Caron, M. Mancini, and F. Ruggeri. Using AHP in determining the prior distributions on gas pipeline failure in a robust Bayesian approach. Reliability Engineering and System Safety, 67(3):275–284, 2000.

    Article  Google Scholar 

  7. R. Calabria, M. Guida, and G. Pulcini. Bayesian estimation of prediction intervals for a Power Law process. Comm. Statist. Theory Methods, 19:3023–3035, 1990.

    MathSciNet  Google Scholar 

  8. R. Calabria, M. Guida, and G. Pulcini. Reliability analysis of repairable systems from in-service failure count data. Applied Stochastic Models and Data Analysis, 10:141–151, 1994.

    MATH  Google Scholar 

  9. D. Cavallo. Nuovi modelli bayesiani nell’analisi dell’affidabilità dei sistemi riparabili. B.Sc. Thesis, University of Milano, Milano, 1999.

    Google Scholar 

  10. D. Cavallo and F. Ruggeri. Bayesian models for failures in a gas network. In E. Zio, M. Demichela, and N. Piccinini, editors, Safety and Reliability-ESREL 2001, pages 1963–1970, 2001.

    Google Scholar 

  11. D.R. Cox and P.A. Lewis. Statistical Analysis of Series of Events. Methuen, London, 1966.

    MATH  Google Scholar 

  12. L.H. Crow. Reliability and Biometry, chapter Reliability analysis for complex repairable systems, pages 379–410. SIAM, Philadelphia, 1974.

    Google Scholar 

  13. L.H. Crow. Confidence interval procedures for the Weibull process with applications to reliability growth. Technometrics, 24:67–72, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Engelhardt and L.J. Bain. Prediction intervals for the Weibull process. Technometrics, 240:167–169, 1978.

    Article  Google Scholar 

  15. M. Fumagalli. Valutazione bayesiana della probabilità di corrosione di tubazioni interrate di acciaio di una rete per la distribuzione di gas in ambito metropolitano. B.Sc. Thesis, Politecnico di Milano, Milano, 1999.

    Google Scholar 

  16. P. Green. Reversible jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrika, 82:711–732, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  17. M. Guida, R. Calabria, and G. Pulcini. Bayes inference for a nonhomogeneous Poisson process with power intensity law. IEEE Transactions on Reliability, 38:603–609, 1989.

    Article  MATH  Google Scholar 

  18. J.F.C. Kingman. Poisson Processes. Oxford University Press, Oxford, 1993.

    MATH  Google Scholar 

  19. J. Kyparisis and N. Singpurwalla. Bayesian inference for the Weibull process with applications to assessing software reliability growth and predicting software failures. In L. Billard, editor, Proceedings of the 16th Computer Science and Statistics Symposium on the Interface, pages 57–64. North-Holland, Amsterdam, 1985.

    Google Scholar 

  20. A.Y. Lo. Bayesian nonparametric statistical inference for Poisson point processes. Z. Wahrsch. Verw. Gebiete, 59:55–66, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  21. L. Masini. Un approccio bayesiano gerarchico nell’analisi dell’affidabilità dei sistemi riparabili. B.Sc. Thesis, University of Milano, Milano, 1998.

    Google Scholar 

  22. C. Mazzali and F. Ruggeri. Bayesian analysis of failure count data from repairable systems. Technical Report 98.19, CNR-IAMI, Milano, 1998.

    Google Scholar 

  23. J.D. Musa and K. Okumoto. A logarithmic Poisson execution time model for software reliability measurements. In Proceedings of the Seventh International Conference on Software Engineering, pages 230–238, 1984.

    Google Scholar 

  24. L. Olivi, R. Rotondi, and F. Ruggeri. Measures of dissimilarities for contrasting information sources in data fusion. In V. Colombari, editor, Reliability Data Collection and Use in Risk and Availability Assessment, pages 671–681. Springer Verlag, Berlin, 1989.

    Google Scholar 

  25. A. Pievatolo and F. Ruggeri. Bayesian reliability analysis of complex repairable systems. Appl. Stoch. Models Bus. Ind., 20:253–264, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  26. A. Pievatolo, F. Ruggeri, and R. Argiento. Bayesian analysis and prediction of failures in underground trains. Quality Reliability Engineering International, 19:327–336, 2003.

    Article  Google Scholar 

  27. S.E. Rigdon and Basu A.P. The Power Law process: a model for the reliability of repairable systems. Journal of Quality Technology, 10:251–260, 1989.

    Google Scholar 

  28. S.E. Rigdon and Basu A.P. Statistical Methods for the Reliability of Repairable Systems. Wiley, New York, 2000.

    MATH  Google Scholar 

  29. D. Rios Insua and F. Ruggeri, editors. Robust Bayesian Analysis. Springer Verlag, New York, 2000.

    MATH  Google Scholar 

  30. F. Ruggeri. Posterior ranges of functions of parameters under priors with specified quantiles. Comm. Statist. Theory Methods, 19:127–144, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  31. F. Ruggeri. Sensitivity issues in the Bayesian analysis of the reliability of repairable systems. In Second International Conference on Mathematical Methods in Reliability, pages 916–919. Université Victor Segalen, Bordeaux, 2000.

    Google Scholar 

  32. F. Ruggeri and S. Sivaganesan. On modeling change points in non-homogeneous Poisson processes. Tentatively accepted by Stat. Inference Stoch. Process., 2005.

    Google Scholar 

  33. T.L. Saaty. The Analytic Hierarchy Process. McGraw-Hill, New York, 1980.

    MATH  Google Scholar 

  34. E. Saccuman. Modelli che incorporano covariate nell’analisi bayesiana dell’affidabilità di sistemi riparabili. B.Sc. Thesis, University of Milano, Milano, 1998.

    Google Scholar 

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Author information

Authors and Affiliations

  1. CNR — IMATI, Via Bassini 15, 20133, Milano, Italy

    F. Ruggeri

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  1. F. Ruggeri
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Postbus 513, 5600 MB, Eindhoven, The Netherlands

    A. Di Bucchianico , R.M.M. Mattheij  & M.A. Peletier ,  & 

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Ruggeri, F. (2006). On the Reliability of Repairable Systems: Methods and Applications. In: Di Bucchianico, A., Mattheij, R., Peletier, M. (eds) Progress in Industrial Mathematics at ECMI 2004. Mathematics in Industry, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28073-1_81

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