Reliability analysis of a multi-state system with identical units having two dependent components

Abstract

The performance evaluation of a system having n identical units, each of which consists of two components has been successfully discussed in binary-state reliability analysis. In this paper, we study the performance evaluation of a multi-state system based on bivariate order statistics. The multi-state system consists of n independent and identical units, each having two components. The components of each unit are assumed to be s-dependent. However, the units work s-independently with each other. The system and each component of each unit having three performance levels “0 (failure), 1 (partially working) and 2 (completely working)” are considered. The degradation of the components follows Markov Process and also Farlie-Gumbel-Morgenstern distribution is used to model the s-dependence of the components. The reliability analysis of a multi-state k-out-of-n system are evaluated under the assumptions. Some dynamic performance measures for the system such as the mean residual and mean past lifetime functions based on bivariate order statistics are also evaluated. The performance of the system is especially examined for different values of s-dependence parameter, the degradation rates and different number of units for the system. The results are supported with some numerical examples and graphical representations.

Keywords

Multi-state system order statistics reliability analysis binomial fourfold model markov degradation model

Get full access to this article

View all access options for this article.

References

Kuo

Zuo

MJ.

Optimal reliability modeling: principles and applications. New Jersey: John Wiley & Sons, 2003.

Lisnianski

Levitin

Multi-state system reliability: assessment, optimization, applications. Singapore: World Scientific Publishing Company, 2003.

Liu

Kapur

KC.

Reliability measures for dynamic multistate nonrepairable systems and their applications to system performance evaluation. IIEE Trans 2006; 38(6): 511–520.

Lisnianski

Extended block diagram method for a multi-state reliability assessment. Reliab Eng Syst Saf 2007; 92(12): 1601–1607.

Amari

Zuo

Dill

A fast and robust reliability evaluation algorithm for generalized multi-state k-out-of-n systems. IEEE Trans Reliab 2009; 58(1): 88–97.

Shrestha

Xing

Dai

Decision Diagram based methods and complexity analysis for multi-state systems. IEEE Trans Reliab 2010; 59(1):145–161.

Eryilmaz

Bozbulut

AR.

An algorithmic approach for the dynamic reliability analysis of non-repairable multi-state weighted k-out-of-n:G system. Reliab Eng Syst Saf 2014; 131: 61–65.

Eryilmaz

Lifetime of multistate k-out-of-n systems. Qual Reliab Eng Int 2014; 30(7): 1015–1022.

Eryilmaz

A reliability model for a three-state degraded system having random degradation rates. Reliab Eng Syst Saf 2016; 156: 59–63.

10.

Eryilmaz

Reliability analysis of multi-state system with three state components and its application to wind energy. Reliab Eng Syst Saf 2018; 172: 58–63.

11.

Xue

Yang

Dynamic reliability analysis of coherent multistate system. IEEE Trans Reliab 1995; 44(4): 683–688.

12.

Eryilmaz

Dynamic assessment of multi-state systems using phase-type modeling. Reliab Eng Syst Saf 2015; 140: 71–77.

13.

Liu

Zuo

, et al. Dynamic reliability assessment for multi-state systems utilizing system-level inspection data. IEEE Trans Reliab 2015; 64(4):1287–1299.

14.

Iscioglu

Dynamic performance evaluation of multi-state systems under non-homogeneous continuous time Markov process degradation using lifetimes in terms of order statistics. Proc Inst Mech Eng O J Risk Reliab 2017; 231(3): 255–264.

15.

Guess

Proschan

12 Mean residual life: theory and applications. Handb Stat 1988; 7: 215–224.

16.

Asadi

Goliforushani

On the mean residual life function of coherent systems. IEEE Trans Reliab 2008; 57(4): 574–580.

17.

Shen

Xie

Tang

LC.

On the change point of the mean residual life of series and parallel systems. Aust N Z J Stat 2010; 52(1): 109–121.

18.

Asadi

Bayramoglu

The mean residual life function of a k-out-of-n structure at the system level. IEEE Trans Reliab 2006; 55(2): 314–318.

19.

Gurler

Bairamov

Parallel and k-out-of-n:G systems with nonidentical components and their mean residual life functions. Appl Math Model 2009; 33(2): 1116–1125.

20.

Raqab

Rychlik

Bounds for the mean residual life function of a k-out-of-n system. Metrika 2011; 74(3): 361–380.

21.

Asadi

On the mean past lifetime of the components of a parallel system. J Stat Plan Inference 2006; 136(4): 1197–1206.

22.

Sadegh

MK.

Mean past and mean residual life functions of a parallel system with nonidentical components. Communications in Statistics—Theory and Methods 2008; 37(7): 1134–1145.

23.

Tavangar

Asadi

A study on the mean past lifetime of the components of (n-k+1)-out-of-n system at the system level. Metrika 2010; 72(1): 59–73.

24.

Poursaeed

Nematollahi

AR.

On the mean past and the mean residual life under double monitoring. Commun Stat Theory Methods 2008; 37(7): 1119–1133.

25.

Zhang

Yang

Ordered properties on the residual life and inactivity time of (n-k+1)-out-of-n systems under double monitoring. Stat Probab Lett 2010; 80(7–8): 711–717.

26.

Zhang

Chang

MRL and MPL Functions of Parallel Systems with INID Components under Double Monitoring. Commun Stat Simul Comput 2011; 40(9): 1514–1523.

27.

Eryilmaz

Mean residual and mean past lifetime of multi-state systems with identical components. IEEE Trans Reliab 2010; 59(4): 644–649.

28.

Bayramoglu

Reliability and mean residual life of complex systems with two dependent components per element. IEEE Trans Reliab 2013; 62(1): 276–285.

29.

Omey

Vesilo

. Local limit theorems for shock models. HUB research papers, Economics & Managament 2011/23.

30.

Ross

SM.

Stochastic processes. 2nd ed. New York: John Wiley & Sons. Inc, 1995.

31.

Aven

On performance measures for multi-state monotone systems. Reliab Eng Syst Saf 1993; 41(3): 259–266.

32.

Aven

Jensen

Stochastic models in reliability. New York: Springer Verlag, 1999.

33.

Aitken

Gonin

HT.

XI.—On Fourfold Sampling with and without replacement. Proc R Soc Edinb 1935; 55: 114–125.

34.

Johnson

Kotz

Balakrishnan

Discrete multivariate distributions. New York, NY: Wiley, 1997.

35.

Eryilmaz

Reliability analysis of systems with components having two dependent subcomponents. Commun Stat Simul Comput 2017; 46(10): 8005–8013.