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

Year 2021, Volume: 13 Issue: 2, 74 - 87, 01.07.2021

Gülce Cüran Fatih Kızılaslan

Abstract

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.

Keywords

Stress-strength reliability, parallel system, cold standby redundancy

References

• 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 eectiveness 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 eectiveness 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.