The present paper focuses on reliability analysis of a phased mission system (PMS) with time-varying dependence structure used to account for environmental disturbances over a specified number of mission cycles. Gumbel-Hougaard copula parameterized to depend on time is used for the purpose. It is assumed that the copula parameter is generated by Autoregressive Moving Average (ARMA)(1,1) process. Each component in a phase is assumed to follow Weibull life distribution. The effect of external environmental factors such as temperature and pressure on each component resulting in its degradation is modelled using generalized Eyring relationship. The performances of a PMS after each cycle are measured using reliability and mean residual life time. The method developed has been explained using a numerical example of an aircraft flight PMS wherein the PMS model with time-varying copula has been compared with that based on constant copula parameter, and also compared with that without environmental stress factors for a given number of cycles.
SomaniAKRitceyJAAuSH.Computationally-efficient phased-mission reliability analysis for systems with variable configurations. IEEE Transact Reliab1992; 41(4): 504–511.
2.
XingL.Reliability evaluation of phased-mission systems with imperfect fault coverage and common-cause failures. IEEE Transact Reliab2007; 56(1): 58–68.
3.
ZangXSunNTrivediKS.A BDD-based algorithm for reliability analysis of phased-mission systems. IEEE Transact Reliab1999; 48(1): 50–60.
4.
MuralIBondavalliAZangX, et al. Dependability modeling and evaluation of phased mission systems: a DSPN approach. In Dependable computing for critical applications7, IEEE1999: 319–337.
5.
HuangXAslettLJCoolenFP.Reliability analysis of general phased mission systems with a new survival signature. Reliab Eng Sys Saf2019; 189: 416–422.
6.
AlamMSongMHesterSL, et al. Reliability analysis of phased-mission systems: a practical approach. In RAMS’06. Annual Reliability and Maintainability Symposium, IEEE, 23, 551-558.
7.
ShresthaAXingLDaiY. Reliability analysis of multi-state phased-mission systems. In: 2009 Annual reliability and maintainability symposium, IEEE2009: 151–156, DOI: 10.1109/RAMS.2009.4914667.
8.
ShresthaAXingL.Improved modular reliability analyses of hybrid phased mission systems. Proceed Instit Mech Eng Part O J Risk Reliab2008; 222(4): 507–520. DOI: 10.1243/1748006XJRR197.
9.
LiuCKramerANeumannS.Reliability assessment of repairable phased-mission system by Monte Carlo simulation based on modular sequence-enforcing fault tree model. Eksploatacja i Niezawodność2020; 22(2): 272–281.
10.
YangXWuX.Mission reliability assessment of space TT&C system by discrete event system simulation. Qual Reliab Eng Int2014; 30(8): 1263–1273.
11.
HuYWangCXingL.Reliability analysis of k-out-of-n phased-mission systems with phase-AND requirement. In IOP Conference series: materials science and engineering, IOP Publishing, 2021: 1043(3): 032038.
12.
XingLAmariSV. Reliability of phased-mission systems. In: MisraKB(ed.), Handbook of Performability Engineering, Springer-Verlag Lindon Limited, 2008, pp. 349–368.
13.
WuDPengRXingL.Recent advances on reliability of phased mission systems. Stochastic models in reliability, network security and system safety, JHC80 2019. Communications in computer and information science, Springer, Singapore, 2019; (1102), https://doi.org/10.1007/978-981-15-0864-6_2
14.
MuraI. Stochastic modeling and analysis of phased-mission systems dependability. In: 2021 Annual reliability and maintainability symposium (RAMS), IEEE2021: 1–6.
15.
PengRZhaiQXingL, et al. Reliability of demand-based phased-mission systems subject to fault level coverage. Reliab Eng Sys Saf2014; 121: 18–25.
16.
KimKParkKS.Phased-mission system reliability under Markov environment. IEEE Transact Reliab1994; 43(2): 301–309.
17.
AmariSVWangCXingL, et al. An efficient phased-mission reliability model considering dynamic k-out-of-n subsystem redundancy. IISE Transact2018; 50(10): 868–877.
18.
ZhaiQXingLPengR, et al. Aggregated combinatorial reliability model for non-repairable parallel phased-mission systems. Reliab Eng Sys Saf2018; 176: 242–250.
19.
LiXYXiongXGuoJ, et al. Reliability assessment of non-repairable multi-state phased mission systems with backup missions. Reliab Eng Sys Saf2022; 223: 108462.
20.
SrivastavaPWSatya Rani. Copula-based approach to reliability analysis of phased-mission systems. Int J Reliab Risk Saf Theory Appl2022; 5(2): 49–62.
21.
XuDYuanJXingM. A time-varying vine copula model for dependence analysis of failure system. In: 2018 international conference on sensing, diagnostics, prognostics, and control (SDPC), IEEE2018: 437-442.
22.
ZhangJMaXZhaoY.A stress-strength time-varying correlation interference model for structural reliability analysis using copulas. IEEE Transact Reliab2017; 66(2): 351–365.
23.
WangYPhamH.Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying copulas. IEEE Transact Reliab2011; 61(1): 13–22.
24.
SunYZhangZZhangQ, et al. Multiple failure mode reliability modeling and analysis in failure crack propagation based on time-varying copula. J Mech Sci Technol2018; 32: 4637–4648.
25.
XuPWangDWangY, et al. Time-varying copula and average annual reliability-based nonstationary hazard assessment of extreme rainfall events. J Hydrol2021; 603: 126792.
26.
ZhouLHeZ. Application research on reliability modeling of multi-failure modes correlation system based on time varying copula model. In: IOP conference series: materials science and engineering, IOP Publishing2020; 964(1): 012031.
27.
YangCGuXZhaoF.Reliability analysis of degrading systems based on time-varying copula. Microelect Reliab2022; 136: 114628.
28.
NelsenRB.An introduction to copulas, 2nd edition.Springer Science + Business Media, Inc., New York2006.
29.
YangG.Life cycle reliability engineering. John Wiley & Sons, 2007.
30.
LeeCKWenMJ.A multivariate weibull disitribution. Pak J Stat Oper Res2009; (2): 55-66.
31.
NelsonWB.Accelerated testing: statistical models, test plans, and data analysis. John Wiley & Sons, New York1990.
32.
BanjevicD.Remaining useful life in theory and practice. Metrika2009; 69(2): 337–349.
33.
SrivastavaPWSatya Rani. Predictive maintenance scheme for phased mission systems. Reliab Theory Appl2024; 19(1): 675–687.
