This paper focuses on the reliability analysis of -out-of- systems which are designed to perform a given mission consisting of several distinct phases. As the phases of the mission change, the reliability characteristics of the system and the system structure vary accordingly. The phase transition probabilities, phase durations, and component failure rates are dependent on the number of operating components. Moreover, the system is allowed to have cold, warm, or hot standby components. We propose computationally tractable methods to compute the system reliability, mean time to failure, and long-run availability for such a general system structure. We also provide a numerical analysis to show the applicability and the empirical computational complexity of the proposed methods.
YeZ SXieM.Stochastic modelling and analysis of degradation for highly reliable products. Appl Stoch Model Bus2015; 31(1): 16–32.
2.
DongQCuiLSiS.Reliability and availability analysis of stochastic degradation systems based on bivariate Wiener processes. Appl Math Model2020; 79: 414–433.
3.
ShenJElwanyACuiL.Reliability analysis for multi-component systems with degradation interaction and categorized shocks. Appl Math Model2018; 56: 487–500.
4.
DongQCuiL.A study on stochastic degradation process models under different types of failure thresholds. Reliab Eng Syst Safe2019; 181: 202–212.
5.
DuSCuiLLinC.Some reliability indexes and sojourn time distributions for a repairable degradation model. Proc IMechE, Part O: J Risk and Reliability2016; 230(3): 334–349.
6.
BaraldiPCompareMZioE.Uncertainty analysis in degradation modeling for maintenance policy assessment. Proc IMechE, Part O: J Risk and Reliability2013; 227(3): 267–278.
7.
WangH KLiY FLiuY, et al. Remaining useful life estimation under degradation and shock damage. Proc IMechE, Part O: J Risk and Reliability2015; 229(3): 200–208.
8.
ShahrakiA FYadavO PLiaoH.A review on degradation modelling and its engineering applications. Int J Performability Eng2017; 13(3): 299–314.
9.
ZhangZSiXHuC, et al. Degradation modeling-based remaining useful life estimation: A review on approaches for systems with heterogeneity. Proc IMechE, Part O: J Risk and Reliability2015; 229(4): 343–355.
10.
EsaryJZiehmsH. Reliability analysis of phased missions. In: Proceedings of the conference on reliability and fault tree analysis, Monterey, CA: SIAM, 1975, pp.213–236.
11.
ÇekyayBÖzekiciS.Mean time to failure and availability of semi-Markov missions with maximal repair. Eur J Oper Res2010; 207(3): 1442–1454.
12.
XingLAmariS V.Reliability of phased-mission systems. In: KrishnaB M (ed.) Handbook of performability engineering. London: Springer-Verlag, 2008, pp.349–368.
13.
LevitinGXingLAmariS, et al. Reliability of non-repairable phased-mission systems with propagated failures. Reliab Eng Syst Safe2013; 119: 218–228.
14.
LevitinGXingLAmariSV, et al. Reliability of nonrepairable phased-mission systems with common cause failures. IEEE T Syst, Man, Cys2013; 43 (4): 967–978.
15.
LevitinGAmariSXingL.Algorithm for reliability evaluation of non-repairable phased-mission systems consisting of gradually deteriorating multi-state elements. IEEE T Syst, Man, Cys2013; 43 (1): 63–73.
16.
SomaniA KRitceyJ AAuS H L.Computationally efficient phased-mission reliability analysis for systems with variable configurations. IEEE T Reliab1992; 41 (4): 504–511.
17.
ZangXSunHTrivediK S.A BDD-based algorithm for reliability analysis of phased-mission systems. IEEE T Reliab1999; 48 (1): 50–60.
18.
PedarASarmaV V S. Phased-mission analysis for evaluating the effectiveness of aerospace computing-systems. IEEE T Reliab1981; R-30(5): 429–437.
19.
WinokurH SGoldsteinL J.Analysis of mission-oriented systems. IEEE T Reliab1969; R-18 (4): 144–148.
20.
BrickerJ L.A unified method for analyzing mission reliability for fault tolerant computer systems. IEEE T Reliab1973; R-22 (2): 72–77.
21.
ÇekyayBÖzekiciS.Performance measures for systems with Markovian missions and aging. IEEE T Reliab2012; 61 (3): 769–778.
22.
ÇekyayBÖzekiciS.Optimal maintenance of systems with Markovian mission and deterioration. Eur J Oper Res2012; 219 (1): 123–133.
23.
ÇekyayBÖzekiciS.Optimal maintenance of semi-Markov missions. Probab Eng Inform Sc2015; 29 (1): 77–98.
24.
ÇekyayBÖzekiciS.Reliability of semi-Markov missions. Stoch Models2015; 35 (1): 63–88.
25.
XingLAmariS VWangC.Reliability of k-out-of-n systems with phased-mission requirements and imperfect fault coverage. Reliab Eng Syst Safe2012; 103: 45–50.
26.
MohammadRKalamAAmariS V.Reliability of phased mission systems with warm standby subsystems. In: 2013 Proceedings annual reliability and maintainability symposium (RAMS), Orlando, FL, 2013, pp.1–5.
27.
MohammadRKalamAAmariS V.Reliability evaluation of phased-mission systems with load-sharing components. In: 2012 Proceedings annual reliability and maintainability symposium, Reno, NV, 23–26 January 2012, pp.1–6.
28.
JiakaiCYanHWeiW.Reliability analysis and optimization of equal load-sharing k-out-of-n phased-mission systems. Eksploat Niezawodn2015; 17: 250–259.
29.
LevitinGXingLDaiY.Minimum mission cost cold-standby sequencing in non-repairable multi-phase systems. IEEE T Reliab2014; 63: 251–258.
30.
AmariS VXingL.Reliability analysis of k-out-of-n systems with phased-mission requirements. Int J Performability Eng2011; 7 (6): 604-609.
31.
AmariS V.A practical method for reliability analysis of phased-mission systems. In: 2011Proceedings-annual reliability and maintainability symposium, Lake Buena Vista, FL, 24–27 January 2011, pp.1–6.
32.
AmariS VWangCXingL, et al. An efficient phased-mission reliability model considering dynamic -out-of- subsystem redundancy. IISE Trans2018; 50(10): 868–877.
33.
EruguzA STanTvan HoutumG J.Optimizing usage and maintenance decisions for -out-of- systems of moving assets. Nav Res Log2017; 64 (5): 418–434.
34.
ZhangNFouladiradMBarrosA.Reliability-based measures and prognostic analysis of a K-out-of-N system in a random environment. Eur J Oper Res2019; 272 (3): 1120–1131.
35.
AmariS VJacobDDillG.Probability of failure per flight computations for aircraft systems. In: 2013 Proceedings annual reliability and maintainability symposium (RAMS), Orlando, FL, 2013, pp.1–6.
TingaTJanssenR.The interplay between deployment and optimal maintenance intervals for complex multi-component systems. Proc IMechE, Part O: J Risk and Reliab2013; 227 (3): 227–240.
38.
WangDTrivediK S.Reliability analysis of phased-mission system with independent component repairs. IEEE T Reliab2007; 56 (3): 540–551.
39.
ShresthaAXingLDaiY.Reliability analysis of multistate phased-mission systems with unordered and ordered states. IEEE T Syst Man Cy A2011; 41 (4): 625–636.
40.
LevitinGXingLDaiY.Optimal work distribution and backup frequency for two non-identical work sharing elements. Reliab Eng Syst Safe2018; 170: 127–136.
41.
NeutsM.Matrix-geometric solutions in stochastic models, an algorithmic approach. New York: Dover Publications, 1994.
42.
MolerCvan LoanC.Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev2003; 45 (1): 3-49.
43.
ÇınlarE.Introduction to stochastic processes. New Jersey: Prentice-Hall, 1975.
