Geodesic
Dynamic reliability evaluation for a multi-state component under stress-strength model
Çalık, Sinan1
1 Department of Statistics, Faculty of Science, Fırat University, 23119 Elazığ, Turkey
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 2, p. 377-385.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.02.04
Classification : 62N05, 62F10
Keywords: Kullback-Leibler divergence, dynamic reliability, stress-strength model, multi-state component, gamma distribution.

Çalık, Sinan 1

1 Department of Statistics, Faculty of Science, Fırat University, 23119 Elazığ, Turkey 
@article{JNSA_2017_10_2_a3,
     author = {\c{C}al{\i}k, Sinan},
     title = {Dynamic reliability evaluation for a multi-state component under stress-strength model},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {377-385},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2017},
     doi = {10.22436/jnsa.010.02.04},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.02.04/}
}
TY  - JOUR
AU  - Çalık, Sinan
TI  - Dynamic reliability evaluation for a multi-state component under stress-strength model
JO  - Journal of nonlinear sciences and its applications
PY  - 2017
SP  - 377
EP  - 385
VL  - 10
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.02.04/
DO  - 10.22436/jnsa.010.02.04
LA  - en
ID  - JNSA_2017_10_2_a3
ER  - 
%0 Journal Article
%A Çalık, Sinan
%T Dynamic reliability evaluation for a multi-state component under stress-strength model
%J Journal of nonlinear sciences and its applications
%D 2017
%P 377-385
%V 10
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.02.04/
%R 10.22436/jnsa.010.02.04
%G en
%F JNSA_2017_10_2_a3
Çalık, Sinan. Dynamic reliability evaluation for a multi-state component under stress-strength model. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 2, p. 377-385. doi : 10.22436/jnsa.010.02.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.02.04/

[1] Bauckhage, C. Computing the Kullback-Leibler divergence between two Generalized Gamma distributions, ArXiv, Volume 2014 (2014 ), pp. 1-7

[2] Brunelle, R. D.; K. C. Kapur Review and classification of reliability measures for multistate and continuum models, IIE Trans., Volume 31 (1999), pp. 1171-1180 | DOI

[3] Chandra, S.; Owen, D. B. On estimating the reliability of a component subject to several different stresses (strengths), Naval Res. Logist. Quart., Volume 22 (1975), pp. 31-39 | DOI | Zbl

[4] Chiodo, E.; Fabiani, D.; Mazzanti, G. 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, Volume 3 (2003) | DOI

[5] Chiodo, E.; Mazzanti, G. Bayesian reliability estimation based on a Weibull stress-strength model for aged power system components subjected to voltage surges, IEEE Trans. Dielectr. Electr. Insul., Volume 13 (2006), pp. 146-159 | DOI

[6] Dahlhaus, R. On the Kullback-Leibler information divergence of locally stationary processes, Stochastic Process. Appl., Volume 62 (1996), pp. 139-168 | DOI | Zbl

[7] Do, M. N. Fast approximation of Kullback-Leibler distance for dependence trees and hidden Markov models, IEEE Signal Process. Lett., Volume 10 (2003), pp. 115-118 | DOI

[8] Ebrahimi, N. Multistate reliability models, Naval Res. Logist. Quart., Volume 31 (1984), pp. 671-680 | DOI

[9] S. Eryılmaz Mean residual and mean past lifetime of multi-state systems with identical components, IEEE Trans. Rel., Volume 59 (2010), pp. 644-649 | DOI

[10] Eryılmaz, S. On stress-strength reliability with a time-dependent strength, J. Qual. Reliab. Eng., Volume 2013 (2013 ), pp. 1-6

[11] Eryılmaz, S.; İşçioğlu, F. Reliability evaluation for a multi-state system under stress-strength setup, Comm. Statist. Theory Methods, Volume 40 (2011), pp. 547-558 | DOI | Zbl

[12] Gökdere, G.; Gürcan, M. Erlang Strength Model for Exponential Effects, Open Phys., Volume 13 (2015), pp. 395-399

[13] Gökdere, G.; Gürcan, M. Laplace-Stieltjes transform of the system mean lifetime via geometric process model, Open Math., Volume 14 (2016), pp. 384-392 | DOI | Zbl

[14] Gökdere, G.; Gürcan, M. New Reliability Score for Component Strength Using Kullback-Leibler Divergence, Eksploatacja i Niezawodnosc.-Maintenance and Reliability, Volume 18 (2016), pp. 367-372

[15] Gradshteyn, I. S.; Ryzhik, I. M. 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

[16] Guo, L.; Zhang, M.-M. A Time-varying repairable system with repairman vacation and warning device, J. Nonlinear Sci. Appl., Volume 9 (2016), pp. 316-331 | Zbl

[17] Hudson, J. C.; Kapur, K. C. Reliability analysis for multistate systems with multistate components, IIE Trans., Volume 15 (1983), pp. 127-135 | DOI

[18] Hwang, F. K.; Yao, Y.-C. Multistate consecutively-connected systems, IEEE Trans. Rel., Volume 38 (1989), pp. 472-474 | Zbl | DOI

[19] Kossow, A.; Preuss, W. Reliability of linear consecutively-connected systems with multistate components, IEEE Trans. Rel., Volume 44 (1995), pp. 518-522 | DOI

[20] Kotz, S.; Lumelskii, Y.; Pensky, M. The stress-strength model and its generalizations: theory and applications, World Scientific Publishing Co. Inc., Singapore, 2003 | Zbl

[21] Kullback, S.; Leibler, R. A. On information and sufficiency, Ann. Math. Statistics, Volume 22 (1951), pp. 79-86

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

[23] Lee, Y. K.; Park, B. U. Estimation of Kullback-Leibler divergence by local likelihood, Ann. Inst. Statist. Math., Volume 58 (2006), pp. 327-340 | DOI

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

[25] Rached, Z.; Alajaji, F.; Campbell, L. L. The Kullback-Leibler divergence rate between Markov sources, IEEE Trans. Inf. Theory, Volume 50 (2004), pp. 917-921 | Zbl | DOI

[26] Yari, G.; Mirhabibi, A.; Saghafi, A. Estimation of the Weibull parameters by Kullback-Leibler divergence of survival functions, Appl. Math. Inf. Sci., Volume 7 (2013), pp. 187-192 | DOI

[27] Zhang, X.; Guo, L. A new kind of repairable system with repairman vacations, J. Nonlinear Sci. Appl., Volume 8 (2015), pp. 324-333

Cité par Sources :