Electrical insulation components reliability assessment and practical Bayesian estimation under a Log-Logistic model

  • Authors

    • E Chiodo University of Naples Federico II
    • L P. Di Noia University of Naples Federico II Napoli Federico II
    • F Mottola University of Naples Parthenope
    2018-06-23
    https://doi.org/10.14419/ijet.v7i3.11494
  • Bayesian Statistics, Electrical Insulation, Log-Logistic Distribution, Stress-Strength Models, Weibull Distribution

  • This paper deals with the “physical reliability models†assessment and estimation for electrical insulation components. It is well known that the reliability model identification and estimation of most of the modern power system components, such as insulation components, may be better achieved, instead that using limited lifetime data, by the knowledge of the degradation mechanisms. Such mechanisms, which are responsible for component aging and failure, are indeed well established in the field of electrical insulation: this is also the case of the so called “Stress-Strength†models. In particular, the “Log-logistic†model, deduced by a suitable Weibull stress-strength probabilistic model, has found valid applications to the reliability assessment of the insulation components. In the framework of the estimation of such reliability model, a new Bayesian approach, based upon the “Odds Ratioâ€Â of the Log-logistic model is developed in this paper, based upon the properties that such information, being proportional to the reliability function, is available to the engineer on the basis of past data; moreover, being proportional to the Weibull scale parameter, allows to exploit known features of its conjugate prior Inverse Gamma distribution. Numerical examples and the results of extensive Monte Carlo simulations demonstrate the feasibility and efficiency of the proposed procedure.

     

     

  • References

    1. [1] G. Mazzanti, "Life and reliability models for high voltage DC extruded cables", in IEEE Electrical Insulation Magazine, vol. 33, no. 4, pp. 42-52, July-August 2017.

      [2] F. Salameh, A. Picot, M. Chabert and P. Maussion, "Parametric and Nonparametric Models for Lifespan Modeling of Insulation Systems in Electrical Machines," IEEE Transactions on Industry Applications, vol. 53, no. 3, pp. 3119-3128, May-June 2017.

      [3] E. Chiodo, D. Lauria, F. Mottola, and C. Pisani, "Lifetime characterization via lognormal distribution of transformers in smart grids: Design optimization," Applied Energy, vol. 177, 2016, pp. 127-135, Sept. 2016.

      [4] D.G. Chen, Y. Lio, H.K.T Ng, and T. Tsai, “Statistical Modeling for Degradation Dataâ€, Springer Nature Singapore, 2017

      [5] E. Chiodo, and G. Mazzanti, “Mathematical and Physical Properties of Reliability Models in View of their Application to Modern Power System Componentsâ€, invited chapter of the book: "Innovations in Power Systems Reliability", edited by G.J. Anders and A. Vaccaro, Springer-Verlag, London 2011.

      [6] E. Chiodo, and G. Mazzanti, "Bayesian Reliability Estimation Based on a Weibull Stress-Strength Model for Aged Power System Components Subjected to Voltage Surges", IEEE Transactions on Dielectrics and Electrical Insulation, vol.13, n. 1, 2006, pp. 146-159

      [7] M. Cacciari, G. Mazzanti and G. C. Montanari, “Electric Strength Measurements and Weibull Statistics on Thin EPR Films", IEEE Trans. Dielectr. Electr. Insul., Vol. 1, pp. 153-159, 1994.

      [8] C. Katz, B. Fryszczyn, A. M. Regan, W. A. Banker and B. S. Bernstein, “Field Monitoring of Parameters and Testing of EP and TR-XLPE Distribution Cablesâ€, IEEE Trans. Pow. Del., Vol. 14, pp. 679-684, 1999.

      [9] R. A. Hartlein, V. S. Harper and H. W. Ng, “Effects of Voltage Impulses on Extruded Dielectric Cable Lifeâ€, IEEE Trans. Pow. Del., Vol. 4, pp. 829-841, 1989.

      [10] H. Faremo and E. Ildstadt, “Diagnosis and Restoration of Water Tree Aged XLPE Cable Materialsâ€, Proc. 1996 IEEE ISEI, pp. 596-599, Montreal, Canada,June 16-19, 1996.

      [11] S. A. Boggs, “Mechanisms for Degradation of TR-XLPE Impulse Strength during Service Agingâ€, IEEE Trans. Pow. Del., Vol. 17, pp. 308-312, 2002.

      [12] International Electrical Commission Standard IEC 60-1, High Voltage Test Techniques – Part 1: General Definitions and Test Requirements, 1st edition 1989.

      [13] F. H. Kreuger, Industrial High Voltage, Delft University Press, Delft, The Netherlands, 1992.

      [14] A. Greenwood, Electrical Transients in Power Systems, 2nd edition, J. Wiley & sons, New York, 1991.

      [15] P. Erto and M. Giorgio, "Assessing High Reliability via Bayesian Approach and Accelerated Tests," Reliability Engineering and Systems Safety, Vol. 76, pp. 301-310, 2002.

      [16] J. R. Van Dorp, and T. A. Mazzuchi, "A general Bayes exponential inference model for accelerated life testing," Journal of Statistical Planning and Inference, vol. 119, Issue 1, 2004, pp. 55-74.

      [17] G. Mazzanti, “Analysis of the Effects of Load Cycling and Thermal Transients on Polymer-insulated HVAC Cable Lifeâ€, Proc. 2004 IEEE ICSD, pp. 456-461, Toulose (France), July 2004.

      [18] I.A. Ushakov and R.A. Harrison, Handbook of Reliability Engineering, J. Wiley & sons, New York, 1994.

      [19] R. A. Johnson, “Stress-Strength Models for Reliabilityâ€, in: Krishnaiah P.R., Rao C. R. (ed.) Handbook of Statistics, Vol. 7: “Quality Control and Reliabilityâ€, North Holland, Amsterdam, 1988.

      [20] S. Kotz, Y. Lumelskii and M. Pensky, The Stress-Strength Model and Its Generalizations: Theory and Applications, Imperial College Press, London, UK, 2003, distributed by World Scientific Publishing.

      [21] H. Hirose, "Mixture model of the power law," in IEEE Transactions on Reliability, vol. 46, no. 1, pp. 146-153, Mar 1997.

      [22] H. Hirose, “Lifetime Assessment by Intermittent Inspection under the Mixture Weibull Power Law Model with Application to XLPE Cablesâ€, Lifetime Data Analysis, Vol. 3, pp.179-189, 1997.

      [23] N. L. Johnson, S. Kotz and N. Balakrishnan, Continuous Univariate Distributions, 2nd Ed., J. Wiley & sons, New York, Vol. 1 and 2, 1994.

      [24] J. F. Lawless, Statistical Models and Methods for Lifetime Data, J. Wiley, New York, 1982.

      [25] D.A. Follmann and M.S. Goldberg, “Distinguishing Heterogeneity from Decreasing Hazard Rateâ€, Technometrics, Vol. 30, pp. 389-396, 1988.

      [26] J. Mi, "A new explanation of decreasing failure rate of a mixture of exponentials," in IEEE Transactions on Reliability, vol. 47, no. 4, pp. 460-462, Dec 1998.

      [27] V. K. Rohatgi and A. K. Saleh, An Introduction to Probability and Statistics, 2nd ed., J. Wiley, 2000.

      [28] H. F. Martz and R. A. Waller, Bayesian Reliability Analysis, Krieger Publishing, Malabar, 1991.

      [29] W. Q. Mekker and L. A. Escobar, Statistical Methods for Reliability Data, J. Wiley, New York, 1998.

      [30] S. J. Press, Subjective and Objective Bayesian Statistics: Principles, Models, and Applications, 2nd ed., J. Wiley, 2002.

      [31] E. Chiodo, D. Lauria, and F. Mottola, “On-Line Bayes Estimation of Rotational Inertia for Power Systems with High Penetration of Renewables. Part I: Theoretical Methodology,†accepted for the Proceedings of International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), Amalfi Coast, Italy, June 20-22, 2018.

  • Downloads

  • How to Cite

    Chiodo, E., P. Di Noia, L., & Mottola, F. (2018). Electrical insulation components reliability assessment and practical Bayesian estimation under a Log-Logistic model. International Journal of Engineering & Technology, 7(3), 1072-1082. https://doi.org/10.14419/ijet.v7i3.11494