Araştırma Makalesi
BibTex RIS Kaynak Göster

Estimation of stress-strength reliability of a parallel system with cold standby redundancy at component level

Yıl 2021, Cilt: 13 Sayı: 2, 74 - 87, 01.07.2021

Öz

In this paper, we consider the estimation problem of stress-strength reliability of a parallel system with cold standby redundancy. The reliability of the system is estimated when both strength and stress variables follow the exponential distribution and associated approximate confidence interval is constructed. Two different maximum likelihood and Bayes estimates are obtained. Lindley's approximation method has been utilized for Bayesian calculations. A real-life data set is analysed for illustrative purposes of the findings.

Kaynakça

  • Akgul, F.G. (2019). Reliability estimation in multicomponent stress-strength model for Topp-Leone distribution. Journal of Statistical Computation and Simulation, 89(15), 2914-2929.
  • Birnbaum, Z. (1956). On a use of the Mann-Whitney statistic. The Regents of the University of California, Vol. 1. Washington: Univ. of Calif. Press, 13-17.
  • Birnbaum, Z.W. and McCarty, B.C. (1958). A distribution-free upper con dence bounds for Pr(Y <X) based on independent samples of X and Y . The Annals of Mathematical Statistics, 29(2), 558-562.
  • Boland, P.J. and El-Neweihi, E. (1995). Component redundancy vs system redundancy in the hazard rate ordering. IEEE Transactions on Reliability, 44(4), 614-619.
  • Chen, J., Zhang, Y., Zhao P. and Zhou S. (2018). Allocation strategies of standby redundancies in series/parallel system. Communications in Statistics-Theory and Methods, 47(3), 708-724.
  • Church, J.D. and Harris, B. (1970). The estimation of reliability from stress-strength relationships. Tech- nometrics, 12(1), 49-54.
  • Dey, S., Mazucheli, J. and Anis, M.Z. (2017). Estimation of reliability of multicomponent stress-strength for a Kumaraswamy distribution. Communications in Statistics -Theory and Methods, 46(4), 1560-1572.
  • Eryilmaz, S. (2008). Multivariate stress-strength reliability model and its evaluation for coherent structures. Journal of Multivariate Analysis, 99(9), 1878-1887.
  • Eryilmaz, S. and Tank, F. (2012). On reliability analysis of a two-dependent-unit series system with a standby unit. Applied Mathematics and Computation, 218(15), 7792-7797.
  • Eryilmaz, S. (2017). The e ectiveness of adding cold standby redundancy to a coherent system at system and component levels. Reliability Engineering and System Safety, 165, 331-335.
  • Hasselman, B. (2018). Package `nleqslv', Version 3.3.2, https://cran.r-project.org/web/packages/nleqslv.
  • Kızılaslan, F. (2018). Classical and Bayesian estimation of reliability in a multicomponent stress-strength model based on a general class of inverse exponentiated distributions. Statistical Papers, 59(3), 1161-1192.
  • Kotz, S., Lumelskii, Y. and Pensky M. (2003). The Stres-Strength Model and its Generalizations. Singapore: World Scienti c Press.
  • Lindley, D.V. (1980). Approximate Bayes method. Trabajos de Estadistica, 3, 281-288.
  • Liu, Y., Shi, Y., Bai, X. and Zhan P. (2018). Reliability estimation of a N-M-cold-standby redundancy system in a multicomponent stress-strength model with generalized half-logistic distribution. Physica A, 490, 231-249.
  • Nelson, W.B.(1972). Graphical analysis of accelerated life test data with the inverse power law model. IEEE Transactions on Reliability, 21(1), 2-11.
  • Nojosa, R. and Rathie, P.N. (2020). Stress-strength reliability models involving generalized gamma and Weibull distributions. International Journal of Quality & Reliability Management, 37(4), 538-551.
  • Pakdaman, Z. and Ahmadi, J. (2013). Stress-strength reliability for P(Xr:n1 <Yk:n2 ) in the exponential case. Istatistik: Journal of the Turkish Statistical Association, 6(3), 92-102.
  • R Core Team. (2020). R: A language and environment for statistical computing. Vienna, Austria; R Foundation for Statistical Computing.
  • Rao, C.R. (1965). Linear Statistical Inference and Its Applications. Wiley, New York.
  • Roy, A. and Gupta N. (2020). Reliability function of k-out-of-n system equipped with two cold standby components. Communications in Statistics - Theory and Methods, DOI: 10.1080/03610926.2020.1737122
  • Roy, A. and Gupta, N. (2020). Reliability of a coherent system equipped with two cold standby components. Metrika, 83(6), 677-697.
  • Shen, K. and Xie, M. (1991). The e ectiveness of adding standby redundancy at system and component levels. IEEE Transactions on Reliability, 40(1), 53-55.
  • Siju, K.C. and Kumar, M. (2017). Estimation of stress-strength reliability of a parallel system with active, warm and cold standby components. Journal of Industrial and Production Engineering, 34(8), 590-610.
  • Tuncel, A. (2017). Residual lifetime of a system with a cold standby unit. Istatistik Journal of The Turkish Statistical Association, 10(1), 24-32.
  • Yan, R., Lu, B. and Li, X. (2019). On Redundancy allocation to series and parallel systems of two components. Communications in Statistics - Theory and Methods, 48(18), 4690-4701.
  • Zhao, P., Zhang, Y. and Li, L. (2015). Redundancy allocation at component level versus system level. European Journal of Operational Research, 241(2), 402-411.
Yıl 2021, Cilt: 13 Sayı: 2, 74 - 87, 01.07.2021

Öz

Kaynakça

  • Akgul, F.G. (2019). Reliability estimation in multicomponent stress-strength model for Topp-Leone distribution. Journal of Statistical Computation and Simulation, 89(15), 2914-2929.
  • Birnbaum, Z. (1956). On a use of the Mann-Whitney statistic. The Regents of the University of California, Vol. 1. Washington: Univ. of Calif. Press, 13-17.
  • Birnbaum, Z.W. and McCarty, B.C. (1958). A distribution-free upper con dence bounds for Pr(Y <X) based on independent samples of X and Y . The Annals of Mathematical Statistics, 29(2), 558-562.
  • Boland, P.J. and El-Neweihi, E. (1995). Component redundancy vs system redundancy in the hazard rate ordering. IEEE Transactions on Reliability, 44(4), 614-619.
  • Chen, J., Zhang, Y., Zhao P. and Zhou S. (2018). Allocation strategies of standby redundancies in series/parallel system. Communications in Statistics-Theory and Methods, 47(3), 708-724.
  • Church, J.D. and Harris, B. (1970). The estimation of reliability from stress-strength relationships. Tech- nometrics, 12(1), 49-54.
  • Dey, S., Mazucheli, J. and Anis, M.Z. (2017). Estimation of reliability of multicomponent stress-strength for a Kumaraswamy distribution. Communications in Statistics -Theory and Methods, 46(4), 1560-1572.
  • Eryilmaz, S. (2008). Multivariate stress-strength reliability model and its evaluation for coherent structures. Journal of Multivariate Analysis, 99(9), 1878-1887.
  • Eryilmaz, S. and Tank, F. (2012). On reliability analysis of a two-dependent-unit series system with a standby unit. Applied Mathematics and Computation, 218(15), 7792-7797.
  • Eryilmaz, S. (2017). The e ectiveness of adding cold standby redundancy to a coherent system at system and component levels. Reliability Engineering and System Safety, 165, 331-335.
  • Hasselman, B. (2018). Package `nleqslv', Version 3.3.2, https://cran.r-project.org/web/packages/nleqslv.
  • Kızılaslan, F. (2018). Classical and Bayesian estimation of reliability in a multicomponent stress-strength model based on a general class of inverse exponentiated distributions. Statistical Papers, 59(3), 1161-1192.
  • Kotz, S., Lumelskii, Y. and Pensky M. (2003). The Stres-Strength Model and its Generalizations. Singapore: World Scienti c Press.
  • Lindley, D.V. (1980). Approximate Bayes method. Trabajos de Estadistica, 3, 281-288.
  • Liu, Y., Shi, Y., Bai, X. and Zhan P. (2018). Reliability estimation of a N-M-cold-standby redundancy system in a multicomponent stress-strength model with generalized half-logistic distribution. Physica A, 490, 231-249.
  • Nelson, W.B.(1972). Graphical analysis of accelerated life test data with the inverse power law model. IEEE Transactions on Reliability, 21(1), 2-11.
  • Nojosa, R. and Rathie, P.N. (2020). Stress-strength reliability models involving generalized gamma and Weibull distributions. International Journal of Quality & Reliability Management, 37(4), 538-551.
  • Pakdaman, Z. and Ahmadi, J. (2013). Stress-strength reliability for P(Xr:n1 <Yk:n2 ) in the exponential case. Istatistik: Journal of the Turkish Statistical Association, 6(3), 92-102.
  • R Core Team. (2020). R: A language and environment for statistical computing. Vienna, Austria; R Foundation for Statistical Computing.
  • Rao, C.R. (1965). Linear Statistical Inference and Its Applications. Wiley, New York.
  • Roy, A. and Gupta N. (2020). Reliability function of k-out-of-n system equipped with two cold standby components. Communications in Statistics - Theory and Methods, DOI: 10.1080/03610926.2020.1737122
  • Roy, A. and Gupta, N. (2020). Reliability of a coherent system equipped with two cold standby components. Metrika, 83(6), 677-697.
  • Shen, K. and Xie, M. (1991). The e ectiveness of adding standby redundancy at system and component levels. IEEE Transactions on Reliability, 40(1), 53-55.
  • Siju, K.C. and Kumar, M. (2017). Estimation of stress-strength reliability of a parallel system with active, warm and cold standby components. Journal of Industrial and Production Engineering, 34(8), 590-610.
  • Tuncel, A. (2017). Residual lifetime of a system with a cold standby unit. Istatistik Journal of The Turkish Statistical Association, 10(1), 24-32.
  • Yan, R., Lu, B. and Li, X. (2019). On Redundancy allocation to series and parallel systems of two components. Communications in Statistics - Theory and Methods, 48(18), 4690-4701.
  • Zhao, P., Zhang, Y. and Li, L. (2015). Redundancy allocation at component level versus system level. European Journal of Operational Research, 241(2), 402-411.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Gülce Cüran Bu kişi benim

Fatih Kızılaslan 0000-0001-6457-0967

Yayımlanma Tarihi 1 Temmuz 2021
Kabul Tarihi 14 Eylül 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 13 Sayı: 2

Kaynak Göster

APA Cüran, G., & Kızılaslan, F. (2021). Estimation of stress-strength reliability of a parallel system with cold standby redundancy at component level. Istatistik Journal of The Turkish Statistical Association, 13(2), 74-87.
AMA Cüran G, Kızılaslan F. Estimation of stress-strength reliability of a parallel system with cold standby redundancy at component level. IJTSA. Temmuz 2021;13(2):74-87.
Chicago Cüran, Gülce, ve Fatih Kızılaslan. “Estimation of Stress-Strength Reliability of a Parallel System With Cold Standby Redundancy at Component Level”. Istatistik Journal of The Turkish Statistical Association 13, sy. 2 (Temmuz 2021): 74-87.
EndNote Cüran G, Kızılaslan F (01 Temmuz 2021) Estimation of stress-strength reliability of a parallel system with cold standby redundancy at component level. Istatistik Journal of The Turkish Statistical Association 13 2 74–87.
IEEE G. Cüran ve F. Kızılaslan, “Estimation of stress-strength reliability of a parallel system with cold standby redundancy at component level”, IJTSA, c. 13, sy. 2, ss. 74–87, 2021.
ISNAD Cüran, Gülce - Kızılaslan, Fatih. “Estimation of Stress-Strength Reliability of a Parallel System With Cold Standby Redundancy at Component Level”. Istatistik Journal of The Turkish Statistical Association 13/2 (Temmuz 2021), 74-87.
JAMA Cüran G, Kızılaslan F. Estimation of stress-strength reliability of a parallel system with cold standby redundancy at component level. IJTSA. 2021;13:74–87.
MLA Cüran, Gülce ve Fatih Kızılaslan. “Estimation of Stress-Strength Reliability of a Parallel System With Cold Standby Redundancy at Component Level”. Istatistik Journal of The Turkish Statistical Association, c. 13, sy. 2, 2021, ss. 74-87.
Vancouver Cüran G, Kızılaslan F. Estimation of stress-strength reliability of a parallel system with cold standby redundancy at component level. IJTSA. 2021;13(2):74-87.