Research on analysis of replacement time in standby systems has focused on systems with binary-state standby components. However, when the standby components are multi-state, the replacement time depends on the state of the standby component when it is activated for replacement. This article considers the impacts of state-dependent random replacement times on 1-out-of-N systems consisting of multi-state standby components. Numerical algorithms for evaluating the multi-state standby system’s instantaneous availability, expected availability over system mission time and the expected mission completion time are proposed. A Markov state transition model is used to describe the component behaviour in standby mode. The time-to-failure of the operating component and the replacement time of the standby component can obey arbitrary types of distributions. Illustrative examples are provided to demonstrate the proposed numerical algorithms. The effects of the number of standby components, different replacement time distributions and activation sequences are also discussed.
ElerathJGPechtM. A highly accurate method for assessing reliability of redundant arrays of inexpensive disks (raid). IEEE T Comput2009; 58(3): 289–299.
2.
HsiehCCHsiehYC. Reliability and cost optimization in distributed computing systems. Comput Oper Res2003; 30(8): 1103–1119.
3.
WangNYAvizienisAA. A unified reliability model for fault-tolerant computers. IEEE T Comput1980; C-29(11): 1002–1011.
4.
JohnsonBWJulichPM. Fault tolerant computer system for the A129 helicopter. IEEE T Aero Elec Sys1985; 21(2): 220–229.
5.
SinakiG. Ultra-reliable fault-tolerant inertial reference unit for spacecraft. Adv Astronaut Sci1994; 86: 239–248.
6.
PedarASarmaVVS. Phased-mission analysis for evaluating the effectiveness of aerospace computing-systems. IEEE T Reliab1981; R-30(5): 429–437.
7.
PhamHPhanHKAmariSV. A general model for evaluating the reliability of telecommunications systems. Commun Reliab Maintainab Support Int J1995; 2: 4–13.
8.
ANSI /IEEE 446-1995: IEEE recommended practice for emergency and standby power systems for industrial and commercial applications.
9.
AmariSVPhamHMisraRB. Reliability characteristics of k-out-of-n warm standby systems. IEEE T Reliab2012; 61: 1007–1018.
10.
ZhangTXieMHorigomeM. Availability and reliability of k-out-of-(M+N): G warm standby systems. Reliab Eng Syst Safe2006; 91(4): 381–387.
11.
ZhangTHorigomeM. Availability of 3-out-of-4: G warm standby system. IEICE T Fund Electr2000; E83A(5): 857–862.
12.
Ruiz-CastroJEFernández-VillodreG. A complex discrete warm standby system with loss of units. Eur J Oper Res2012; 218(2): 456–469.
13.
RaoMSNaikanVNA. Reliability analysis of repairable systems using system dynamics modeling and simulation. J Ind Eng Int2014; 10: 69.
14.
KeJSuZWangKet al. Simulation inferences for an availability system with general repair distribution and imperfect fault coverage. Simul Model Pract Th2010; 18(3): 338–347
15.
MoghaddassRZuoMJPandeyM. Optimal design and maintenance of a repairable multi-state system with standby components. J Stat Plan Infer2012; 142(8): 2409–2420
16.
AzaronAKatagiriHKatoKet al. Reliability evaluation of multi-component cold-standby redundant systems. Appl Math Comput2006; 173(1): 137–149.
17.
KeJCHuangHILinCH. A redundant repairable system with imperfect coverage and fuzzy parameters. Appl Math Model2008; 32(12): 2839–2850.
18.
LevitinG. The Universal generating function in reliability analysis and optimization. London: Springer-Verlag, 2005.
19.
DingYSinghCGoelLet al. Short-term and medium-term reliability evaluation for power systems with high penetration of wind power. IEEE T Sustain Energ2014; 5(3): 896–906.
20.
EbrahimipourVSheikhalishahiMShojaBMet al. A Universal generating function approach for redundancy optimization for hot-standby multi-state series parallel k-out-of-n systems. In: UKSim European symposium on computer modeling and simulation, Pisa, 17–19 November 2010, pp.235–239. New York: IEEE.
21.
ZhaiQPengRXingLet al. Reliability of demand-based warm standby systems subject to fault level coverage. Appl Stoch Model Bus2015; 31(3): 380–393.
22.
ZhaiQPengRXingLet al. Bdd-based reliability evaluation of k-out-of-(n + k) warm standby systems subject to fault-level coverage. Proc IMechE, Part O: J Risk and Reliability2013; 227(5): 540–548.
23.
XingLTannousOBechta DuganJ. Reliability analysis of nonrepairable cold-standby systems using sequential binary decision diagrams. IEEE T Syst Man Cy A2012; 42(3): 715–726.
24.
ZhaiQXingLPengRet al. Multi-valued decision diagram-based reliability analysis of k -out-of-n cold standby systems subject to scheduled backups. IEEE T Reliab2015; 64(4): 1310–1324.
25.
AmariSVXingLShresthaAet al. Performability analysis of multistate computing systems using multivalued decision diagrams. IEEE T Comput2010; 59(10): 1419–1433.
26.
LevitinGXingLDaiY. Optimal backup distribution in 1-out-of-N cold standby systems. IEEE T Syst Man Cy-S2015; 45(4): 636–646.
27.
LevitinGXingLDaiY. Optimal sequencing of warm standby components. Comput Ind Eng2013; 65: 570–576.
28.
LevitinGXingLDaiY. Heterogeneous 1-out-of-N warm standby systems with dynamic uneven backups. IEEE T Reliab2015; 64(4): 1325–1339.
29.
LevitinGXingLDaiY. Reliability of non-coherent warm standby systems with reworking. IEEE T Reliab2015; 64(1): 444–453.
30.
GeorgievANikolovNPapanchevT. Maintenance process efficiency when conduct reliability-centered maintenance of complex electronic systems. In: 19th international symposium on electrical apparatus and technologies, Bourgas, 29 May–1 June 2016, pp.1–4. New York: IEEE.
31.
Standard: IEC 60706–5. Guide on maintainability of equipment-part 5: section 4: diagnostic testing.
32.
LevitinGXingLDaiY. Non-homogeneous 1-out-of-N warm standby systems with random replacement times. IEEE T Reliab2015; 64(2): 819–828.
33.
ChenYJinJHuangZ. A simulation algorithm of operational availability and maintenance cost for multi-mode system. In: Proceedings of 2011 9th international conference on reliability, maintainability and safety, Guiyang, China, 12–15 June 2011, pp.789–792. New York: IEEE.
34.
CuiYShiJWangZ. Multi-state adaptive bit false alarm reduction under degradation process. IEEE T Instrum Meas2015; 64(3): 671–682.
35.
LevitinGXingLJohnsonBWet al. Mission reliability, cost and time for cold standby computing systems with periodic backup. IEEE T Comput2015; 64(4): 1043–1057.
36.
LevitinGXingL. Reliability performance of multi-state systems (special issue). Reliab Eng Syst Safe2017; 166: 1–180.
37.
LiuYZuoMJLiYFet al. Dynamic reliability assessment for multi-state systems utilizing system-level inspection data. IEEE T Reliab2015; 64(4): 1287–1299.
38.
George -WilliamsHPatelliE. A hybrid load flow and event driven simulation approach to multi-state system reliability evaluation. Reliab Eng Syst Safe2016; 152: 351–367.
39.
DuSZengZCuiLet al. Reliability analysis of Markov history-dependent repairable systems with neglected failures. Reliab Eng Syst Safe2017; 159: 134–142.
40.
JafaryBFiondellaL. A universal generating function-based multi-state system performance model subject to correlated failures. Reliab Eng Syst Safe2016; 152: 16–27.
41.
JiaHDingYPengRet al. Reliability evaluation for demand-based warm standby systems considering degradation process. IEEE Trans Reliab2017; 66: 795–805.
42.
LevitinGJiaHDingYet al. Reliability of multi-state systems with free access to repairable standby elements. Reliab Eng Syst Safe2017; 167: 192–197.
43.
KuoWZuoMJ. Optimal reliability modeling: principles and application. Hoboken, NJ: John Wiley & Sons, 2003.
44.
AbdallahHMarieRSericolaB. Point and expected interval availability analysis with stationarity detection. Comput Oper Res1999; 26(3): 211–218.
45.
LiLLiYLuMet al. Quantification and comparison of insulator pollution characteristics based on normality of relative contamination values. IEEE T Dielect El In 2016; 23(2): 965–973.
46.
LiJSimaWSunCet al. Use of leakage currents of insulators to determine the stage characteristics of the flashover process and contamination level prediction. IEEE T Dielect El In 2010; 17(2): 490–501.
47.
WuCGaoYWangJet al. Cleaning effect of rainfall on salt in pollution layer of silicone rubber insulators. In: IEEE conference on electrical insulation and dielectric phenomena, Des Moines, IA, 19–22 October 2014, pp.275–278. New York: IEEE.
48.
NelsonWB. Accelerated testing: statistical models, test plans, and data analyses. John Wiley & Sons: New York, 1990.
49.
WeibullW. A statistical distribution function of wide applicability. J Appl Mech1951; 18(2): 293–297.
