Dynamic reliability evaluation for a multi-state component under stress-strength model

Volume 10, Issue 2, pp 377--385 http://dx.doi.org/10.22436/jnsa.010.02.04

Publication Date: February 20, 2017 Submission Date: November 23, 2016

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2493 Downloads
• 4936 Views

Authors

Sinan Çalık - Department of Statistics, Faculty of Science, Fırat University, 23119 Elazığ, Turkey.

Abstract

For many technical systems, stress-strength models are of special importance. Stress-strength models can be described as an assessment of the reliability of the component in terms of \(X\) and \(Y\) random variables where \(X\) is the random ”stress” experienced by the component and \(Y\) is the random ”strength” of the component available to overcome the stress. The reliability of the component is the probability that component is strong enough to overcome the stress applied on it. Traditionally, both the strength of the component and the applied stress are considered to be both time-independent random variables. But in most of real life systems, the status of a stress and strength random variables clearly change dynamically with time. Also, in many important systems, it is very necessary to estimate the reliability of the component without waiting to observe the component failure. In this paper we study multi-state component where component is subjected to two stresses. In particular, inspired by the idea of Kullback-Leibler divergence, we aim to propose a new method to compute the dynamic reliability of the component under stress-strength model. The advantage of the proposed method is that Kullback-Leibler divergence is equal to zero when the component strength is equal to applied stress. In addition, the formed function can include both stresses when two stresses exist at the same time. Also, the proposed method provides a simple way and good alternative to compute the reliability of the component in case of at least one of the stress or strengths quantities depend on time.

Share and Cite

Keywords

• Kullback-Leibler divergence
• dynamic reliability
• stress-strength model
• multi-state component
• gamma distribution.

MSC

•  62N05
•  62F10

References

• [1] C. Bauckhage, Computing the Kullback-Leibler divergence between two Generalized Gamma distributions, ArXiv, 2014 (2014 ), 7 pages.
  • Google Scholar


• [2] R. D. Brunelle, K. C. Kapur , Review and classification of reliability measures for multistate and continuum models, IIE Trans., 31 (1999), 1171–1180.
  • View Article
  • Google Scholar


• [3] S. Chandra, D. B. Owen, On estimating the reliability of a component subject to several different stresses (strengths), Naval Res. Logist. Quart., 22 (1975), 31–39.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] E. Chiodo, D. Fabiani, G. Mazzanti, Bayes inference for reliability of HV insulation systems in the presence of switching voltage surges using a Weibull stress-strength model, IEEE Power Tech. Conf. Proc., Bologna, 3 (2003),
  • View Article
  • Google Scholar


• [5] E. Chiodo, G. Mazzanti, Bayesian reliability estimation based on a Weibull stress-strength model for aged power system components subjected to voltage surges, IEEE Trans. Dielectr. Electr. Insul., 13 (2006), 146–159.
  • View Article
  • Google Scholar


• [6] R. Dahlhaus, On the Kullback-Leibler information divergence of locally stationary processes, Stochastic Process. Appl., 62 (1996), 139–168.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] M. N. Do, Fast approximation of Kullback-Leibler distance for dependence trees and hidden Markov models, IEEE Signal Process. Lett., 10 (2003), 115–118.
  • View Article
  • Google Scholar


• [8] N. Ebrahimi, Multistate reliability models, Naval Res. Logist. Quart., 31 (1984), 671–680.
  • View Article
  • Google Scholar


• [9] S. Eryılmaz , Mean residual and mean past lifetime of multi-state systems with identical components, IEEE Trans. Rel., 59 (2010), 644–649.
  • View Article
  • Google Scholar


• [10] S. Eryılmaz, On stress-strength reliability with a time-dependent strength, J. Qual. Reliab. Eng., 2013 (2013 ), 6 pages.
  • View Article
  • Google Scholar


• [11] S. Eryılmaz, F. İşçioğlu, Reliability evaluation for a multi-state system under stress-strength setup, Comm. Statist. Theory Methods, 40 (2011), 547–558.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] G. Gökdere, M. Gürcan, Erlang Strength Model for Exponential Effects, Open Phys., 13 (2015), 395–399.
  • Google Scholar


• [13] G. Gökdere, M. Gürcan, Laplace-Stieltjes transform of the system mean lifetime via geometric process model, Open Math., 14 (2016), 384–392.
  • View Article
  • Google Scholar
  • MATH


• [14] G. Gökdere, M. Gürcan, New Reliability Score for Component Strength Using Kullback-Leibler Divergence, Eksploatacja i Niezawodnosc.-Maintenance and Reliability, 18 (2016), 367–372.
  • View Article
  • Google Scholar


• [15] I. S. Gradshteyn, I. M. Ryzhik, Table of integrals, series, and products, Translated from the Russian, Sixth edition, Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger, Academic Press, Inc., San Diego, CA (2000)
  • MathSciNet


• [16] L. Guo, M.-M. Zhang, A Time-varying repairable system with repairman vacation and warning device, J. Nonlinear Sci. Appl., 9 (2016), 316–331.
  • MathSciNet
  • Google Scholar
  • MATH


• [17] J. C. Hudson, K. C. Kapur, Reliability analysis for multistate systems with multistate components, IIE Trans., 15 (1983), 127–135.
  • View Article
  • Google Scholar


• [18] F. K. Hwang, Y.-C. Yao, Multistate consecutively-connected systems, IEEE Trans. Rel., 38 (1989), 472–474.
  • View Article
  • Google Scholar
  • MATH


• [19] A. Kossow, W. Preuss, Reliability of linear consecutively-connected systems with multistate components, IEEE Trans. Rel., 44 (1995), 518–522.
  • View Article
  • Google Scholar


• [20] S. Kotz, Y. Lumelskii, M. Pensky, The stress-strength model and its generalizations: theory and applications, World Scientific Publishing Co. Inc., Singapore (2003)
  • Google Scholar
  • MATH


• [21] S. Kullback, R. A. Leibler, On information and sufficiency, Ann. Math. Statistics, 22 (1951), 79–86.
  • MathSciNet


• [22] W. Kuo, M. J. Zuo, Optimal reliability modeling: principles and applications, John Wiley & Sons, New York, New York (2003)
  • Google Scholar


• [23] Y. K. Lee, B. U. Park, Estimation of Kullback-Leibler divergence by local likelihood, Ann. Inst. Statist. Math., 58 (2006), 327–340.
  • View Article
  • MathSciNet
  • Google Scholar


• [24] A. Lisnionski, G. Levitin, Multi-state system reliability: assessment, optimization and applications, Series on Guality, Reliability and Engineering Statistics, World Scientific Publishing Co. Inc., Singapore (2003)
  • MATH


• [25] Z. Rached, F. Alajaji, L. L. Campbell, The Kullback-Leibler divergence rate between Markov sources, IEEE Trans. Inf. Theory, 50 (2004), 917–921.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [26] G. Yari, A. Mirhabibi, A. Saghafi, Estimation of the Weibull parameters by Kullback-Leibler divergence of survival functions, Appl. Math. Inf. Sci., 7 (2013), 187–192.
  • View Article
  • MathSciNet
  • Google Scholar


• [27] X. Zhang, L. Guo, A new kind of repairable system with repairman vacations, J. Nonlinear Sci. Appl., 8 (2015), 324–333.
  • MathSciNet
  • Google Scholar