Prognostics and health management has drawn increasing attention and gained deepening recognition and widening applications during the past decades. Due to offering guidance for sequential managements involving inspection schedule, maintenance, replacement, and spare parts ordering, remaining useful life estimation has been termed as the kernel technology of prognostics and health management and is the focus of this research in the field of reliability. Heterogeneity is widespread in the inner states of a system and its related working environments. This article provides a review on approaches for degradation modeling and remaining useful life estimation, with an emphasis on the heterogeneity in the systems. Approaches for three kinds of heterogeneity, including the unit-to-unit variability, the variability in time-varying operating conditions, and the diversity of tasks and workloads of a system during its lifetime, are summarized consecutively, and the corresponding methods are provided. Merits and drawbacks are summed up, respectively, following each approach. In addition, several possible future research directions are provided at the end of this article.
SandbornPPechtM. Introduction to special section on electronic systems prognostics and health management. Microelectron Reliab2007; 47(12): 1847–1848.
2.
DolevE. Introduction to the special section on prognostics and health management. IEEE T Reliab2009; 58(2): 262–263.
3.
LauDFongB. Special issue on prognostics and health management. Microelectron Reliab2011; 51(2): 253–254.
4.
WangW. Special section on prognostics and systems health management (PHM), extended papers from the PHM Macau 2010 conference. IEEE T Reliab2011; 60(1): 2.
5.
SmithGSchroederJNavarroS. Development of a prognostics and health management capability for the Joint Strike Fighter. In: IEEE AUTOTESTCON proceedings, Anaheim, CA, 22–25 September 1997, pp.676–682. New York: IEEE.
6.
Department of Defense (DoD). Performance based logistics (Chapter 5.3, DoD 5000.2 policy document). Washington, DC: Defense Acquisition Guidebook, 2004.
7.
PechtM. Prognostics and health management of electronics. Hoboken, NJ: John Wiley & Sons, Ltd, 2008.
8.
SunBZengSKangR. Benefits and challenges of system prognostics. IEEE T Reliab2012; 61(2): 323–335.
9.
GoebelKSahaBSaxenaA. Prognostics in battery health management. IEEE Instru Meas Mag2008; 11(4): 33–40.
10.
GebraeelNLawleyMRongL. Residual-life distributions from component degradation signals: a Bayesian approach. IIE Trans2005; 37(6): 543–557.
11.
JardineKLinDBanjevicD. A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mech Syst Signal Pr2006; 20(7): 1483–1510.
12.
SiXSWangWHuCH. Remaining useful life estimation—a review on the statistical data driven approaches. Eur J Oper Res2011; 213(1): 1–14.
13.
YeZSXieM. Stochastic modelling and analysis of degradation for highly reliable products. Appl Stoch Model Bus2015; 31: 16–32.
14.
LuCMeekerW. Using degradation measures to estimate a time-to-failure distribution. Technometrics1993; 35(2): 161–174.
15.
GebraeelN. Sensory-updated residual life distributions for components with exponential degradation patterns. IEEE T Autom Sci Eng2006; 3(4): 382–393.
16.
GebraeelNPanJ. Prognostic degradation models for computing and updating residual life distributions in a time-varying environment. IEEE T Reliab2008; 57(4): 539–550.
17.
GebraeelNElwayAPanJ. Residual life predictions in the absence of prior degradation knowledge. IEEE T Reliab2009; 58(1): 106–117.
18.
SonJZhouQZhouS. Evaluation and comparison of mixed effects model based prognosis for hard failure. 2013; 62(2): 379–794.
19.
SukJBPaulHK. A nonlinear random-coefficients model for degradation testing. Technometrics2004; 46(4): 460–469.
WeaverBP. Methods for planning repeated measures degradation tests. Graduate Theses and Dissertations, Paper 11967, 2011, http://lib.dr.iastate.edu/etd/11967.
22.
WangWChristerA. Towards a general condition based maintenance model for a stochastic dynamic system. J Oper Res Soc2000; 51(4): 145–155.
23.
LawlessJCrowderM. Covariates and random effects in a gamma process model with application to degradation and failure. Lifetime Data Anal2004; 10(2): 213–227.
24.
YeZSXieMTangLC. Efficient semiparametric estimation of gamma processes for deteriorating products. Technometrics2014; 56(4): 504–513.
25.
PengWWLiYFYangYJ. Inverse Gaussian process models for degradation analysis: a Bayesian perspective. Reliab Eng Syst Safe2014; 130(1): 175–189.
WangXXuD. An inverse Gaussian process model for degradation data. Technometrics2010; 52(2): 188–197.
28.
YeZSChenN. The inverse Gaussian process as a degradation model. Technometrics2014; 56(3): 302–311.
29.
WangX. Wiener processes with random effects for degradation data. J Multivariate Anal2010; 101(1): 340–351.
30.
SiXSWangWChenMY. A degradation path-dependent approach for remaining useful life estimation with an exact and closed-form solution. Eur J Oper Res2013; 226(1): 53–66.
31.
PengCYTsengST. Mis-specification analysis of linear degradation models. IEEE T Reliab2009; 58(3): 444–455.
32.
SiXSWangWHuCH. Remaining useful life estimation based on a nonlinear diffusion degradation process. IEEE T Reliab2012; 61(1): 50–67.
33.
WangZQWangWHuCH. An additive Wiener process-based prognostic model for hybrid deteriorating systems. IEEE T Reliab2014; 63(1): 208–222.
34.
SiXSZhouDH. A generalized result for degradation model-based reliability estimation. IEEE T Autom Sci Eng2013; 11(2): 632–637.
35.
HuangX. Diagnosis of random-effect model mis-specification in generalized linear mixed models for binary response. Biometrics2009; 65(1): 361–368.
36.
McCullochCENeuhausJM. Mis-specifying the shape of a random effects distribution: why getting it wrong may not matter. Stat Sci2011; 26(3): 388–402.
37.
AlonsoALitiereSMolenberghsG. A family of tests to detect misspecifications in the random effects structure of generalized linear mixed models. Comput Stat Data An2008; 52(1): 4474–4486.
38.
AgrestiaABrianCOhman-StricklandcP. Examples in which misspecification of a random effects distribution reduces efficiency, and possible remedies. Comput Stat Data An2004; 47(1): 639–653.
39.
SarmaVKunhikrishnanKRamchandK. A decision theory model for health monitoring of aero engines. J Aircraft1979; 16(3): 222–224.
40.
ChristerAWangWSharpJ. A state space condition monitoring model for furnace erosion prediction and replacement. Eur J Oper Res1997; 101(1): 1–14.
41.
BatzelTSwansonD. Prognostic health management of aircraft power generators. IEEE T Aero Elec Sys2009; 45(2): 473–482.
42.
XuZJiYZhouD. Real-time reliability prediction for a dynamic system based on the hidden degradation process identification. IEEE T Reliab2008; 57(2): 230–242.
43.
LuoJPattipatiKQiaoL. Model-based prognostic techniques applied to a suspension system. IEEE T Syst Man Cy A2008; 38(5): 1156–1168.
44.
TangLDeCastroJKacprzynskiG. Filtering and prediction techniques for model-based prognosis and uncertainty management. IEEE prognostics and health management conference, Macao, 12–14 January 2010. New York: IEEE.
45.
OrchardMVachtsevanosG. A particle-filtering approach for on-line fault diagnosis and failure prognosis. T I Meas Control2009; 31(3–4): 221–246.
46.
PhelpsEWillettPKirubarajanT. Predicting time to failure using the IMM and excitable tests. IEEE T Syst Man Cy A2007; 37(5): 630–642.
47.
WangWHussinB. Plant residual time modelling based on observed variables in oil samples. J Oper Res Soc2009; 60(6): 789–796.
48.
WangWMatthewCXuWJ. A model for residual life prediction based on Brownian motion with an adaptive drift. Microelectron Reliab2011; 51(1): 285–293.
49.
SiXSWangWHuCH. A Wiener process based degradation model with a recursive filter algorithm for remaining useful life estimation. Mech Syst Signal Pr2013; 35(1–2): 219–237.
50.
SiXSHuCHWangW. An adaptive and nonlinear drift based Wiener process for remaining useful life estimation. In: Prognostics and system health management conference, Shenzhen, 24–25 May 2011. New York: IEEE.
51.
SiXSWangWHuCH. Estimating remaining useful life with three-source variability in degradation modeling. IEEE T Reliab2014; 63(1): 167–190.
52.
WangW. A two-stage prognosis model in condition based maintenance. Eur J Oper Res2007; 182(1): 1177–1187.
53.
FengJSunQJinTD. Storage life prediction for a high-performance capacitor using multi-phase Wiener degradation models. Commun Stat Simul Comput2012; 41(8): 1317–1335.
54.
LiWPhamH. Reliability modeling of multi-state degraded system with multi competing failures and random shocks. IEEE T Reliab2005; 54(2): 297–303.
55.
BunksDMcCarthyDAl-AniT. Condition-based maintenance of machines using hidden Markov models. Mech Syst Signal Pr2000; 14(4): 597–612.
56.
DongMHeD. Hidden semi-Markov model-based methodology for multi-sensor equipment health diagnosis and prognosis. Eur J Oper Res2007; 178(3): 858–878.
57.
DongMHeD. A segmental hidden semi-Markov model (HSMM)-based diagnostics and prognostics framework and methodology. Mech Syst Signal Pr2007; 21(5): 2248–2266.
58.
DongM. A novel approach to equipment health management based on autoregressive hidden semi-Markov model (AR-HSMM). Sci China Ser F2008; 51(9): 1291–1304.
59.
GiorgioMGuidaMPulciniG. An age- and state-dependent Markov model for degradation processes. IIE Trans2011; 43(9): 621–632.
60.
GiorgioMGuidaMPulciniG. A parametric Markov chain to model age- and state-dependent wear processes. In: PietroMPiercesareS (eds) Complex data modelling and computationally intensive statistical methods. Milan: Springer, 2010, pp.85–98.
61.
GorjianNMaLMittintyM. A review on reliability models with covariates. In: Proceedings of the 4th world congress on engineering asset management, Marriott Athens Ledra Hotel, Athens, 28–30 September 2009, pp.385–397. London: Springer-Verlag.
62.
SunYMaLMathewJ. Mechanical systems hazard estimation using condition monitoring. Mech Syst Signal Pr2006; 20(5): 1189–1201.
63.
VlokPJWnekMZygmuntM. Utilizing statistical residual life estimates of bearings to quantify the influence of preventive maintenance actions. Mech Syst Signal Pr2004; 18(1): 833–847.
64.
YeZSHongYXieM. How do heterogeneities in operating environments affect field failure predictions and test planning?Ann Appl Stat2013; 7: 2249–2271.
65.
BanjevicDJardineA. Calculation of reliability function and remaining useful life for a Markov failure time process. IMA J Manag Math2006; 17(2): 115–130.
66.
ElsayedE. Mean residual life and optimal operating conditions for industrial furnace tubes. In: BlischkeWRMurthyDNP (eds) Case studies in reliability and maintenance. Hoboken, NJ: John Wiley & Sons, Inc., 2003, pp.497–515.
67.
ZhaoXFouladiradMBérenguerC. Condition-based inspection/replacement policies for nonmonotonous deteriorating systems with environmental covariates. Reliab Eng Syst Safe2010; 95(8): 921–934.
68.
GhasemiAYacoutSOualiM. Evaluating the reliability function and the mean residual life for equipment with unobservable states. IEEE T Reliab2010; 59(1): 45–54.
69.
LuXFLiuM. Hazard rate function in dynamic environment. Reliab Eng Syst Safe2014; 130(1): 50–60.
70.
PafieeKFengQMCoitDW. Reliability modeling for dependent competing failure process with changing degradation rare. IIE Trans2014; 46(1): 483–496.
71.
NakagawaT. Shock and damage models in reliability theory. London: Springer, 2007.
72.
LiuYHuangHZPhamH. Reliability evaluation of systems with degradation and random shocks. In: Proceedings of the annual reliability and maintainability symposium, (RAMS 2008), Las Vegas, Nevada USA, 28–31 January 2008, pp. 328–333. New York: IEEE
73.
KlutkeGAYangY. The availability of inspected systems subject to shocks and graceful degradation. IEEE T Reliab2002; 51(3): 371–374.
74.
WangZLDuLHuangHZ. Reliability modeling for dependent competitive failure processes. In: Proceedings of the annual reliability and maintainability symposium, Las Vegas, NV, 28–31 January 2008, pp.278–282. New York: IEEE.
75.
WangZHuangHZLiY. An approach to reliability assessment under degradation and shock process. IEEE T Reliab2011; 60(4): 852–863.
76.
ChaJWLeeEY. An extended stochastic failure model for a system subject to random shocks. Oper Res Lett2010; 38(1): 468–473.
77.
MuratKMaillartLM. Structured replacement policies for a Markov-modulated shock model. Oper Res Lett2009; 38(1): 280–284.
78.
DeliaMCRafaelPOSegoviaMC. Survival probabilities for shock and wear models governed by phase-type distributions. Qual Technol Quant Manag2007; 4(1): 85–94.
79.
JavierROMauricioSSRahaAT. Reliability analysis of shock-based deterioration using phase-type distributions. Probabilist Eng Mech2014; 38(1): 88–101.
80.
HuangWAskinRG. A generalized SSI reliability model considering stochastic loading and strength aging degradation. IEEE T Reliab2004; 53(1): 77–82.
81.
LiWPhamH. An inspection-maintenance model for systems with multiple competing processes. IEEE T Reliab2005; 54(2): 318–327.
82.
ChenYYLiZH. An extended extreme shock maintenance model for a deteriorating system. Reliab Eng Syst Safe2008; 93(1): 1123–1129.
83.
WangYPhamH. A multi-objective optimization of imperfect preventive maintenance policy for dependent competing risk systems with hidden failure. IEEE T Reliab2011; 60(4): 770–781.
84.
PengHFengQCoitDW. Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes. IIE Trans2011; 43(1): 12–22.
85.
HuynhKTBarrosABrenguerC. A periodic inspection and replacement policy for system subject to degradation and traumatic events. Reliab Eng Syst Safe2011; 96(4): 497–508.
86.
FanHDHuCHChenMY. Cooperative predictive maintenance of repairable systems with dependent failure modes and resource constraint. IEEE T Reliab2011; 61(1): 144–157.
87.
PerfettiGAubertTWildeboerW. Influence of handling and storage conditions on morphological and mechanical properties of polymer-coated particles: characterization and modeling. Powder Technol2011; 206(1): 99–111.
88.
KharoufehJ. Explicit results for wear processes in a Markovian environment. Oper Res Lett2003; 31(3): 237–244.
89.
KharoufehJMixonD. On a Markov-modulated shock and wear process. Nav Res Log2009; 56(6): 563–576.
90.
JeffreyPStevenM. Stochastic models for degradation-based reliability. IIE Trans2005; 37(6): 533–542.
91.
SiXSHuCHKongXY. A residual storage life prediction approach for systems with operation state switches. IEEE T Ind Electron2014; 61: 6304–6315.
92.
HawkesACuiLZhengZ. Modeling the evolution of system reliability performance under alternative environments. IIE Trans2011; 43(11): 761–772.
93.
HuynhKBarrosABérenguerC. Adaptive condition-based maintenance decision framework for deteriorating systems operating under variable environment and uncertain condition monitoring. Proc IMechE, Part O: J Risk and Reliability2012; 226(6): 602–623.
94.
ScarfPA. A framework for condition monitoring and condition based maintenance. Qual Technol Quant Manag2007; 4(2): 301–312.
95.
WangH. A survey of maintenance policies of deteriorating systems. Eur J Oper Res2002; 139(1): 469–489.
96.
WangW. An inspection model for a process with types of inspections and repairs. Reliab Eng Syst Safe2009; 94(1): 526–533.
97.
LamY. An optimal inspection-repair-replacement policy for standby systems. J Appl Probab1995; 32(1): 212–223.
98.
EndrenyiJAndersGJLeite da SilvaAM. Probabilistic evaluation of the effect of maintenance on reliability: an application. IEEE T Power Syst1998; 13(2): 576–583.
MartorellSSanchezASerradellV. Age-dependent reliability model considering effects of maintenance and working conditions. Reliab Eng Syst Safe1999; 64(1): 19–31.
101.
ZhouXJXiLFLeeJ. Reliability-centered predictive maintenance scheduling for a continuously monitored system subject to degradation. Reliab Eng Syst Safe2007; 92(1): 530–534.
WangZQHuCHWangW. A simulation-based remaining useful life prediction method considering the influence of maintenance activities. In: Prognostics and system health management conference (PHM2014), Zhangjiajie, China, 24–27 August 2014. New York: IEEE.
105.
BagdonaviciusVNikulinMS. Accelerated life models: modeling and statistical analysis. Boca Raton, FL: Chapman and Hall/CRC, 2002.
106.
CouallierV. Some recent results on joint degradation and failure time modeling. In: NikulinMCommengesDHuberC (eds) Probability, statistics and modelling in public health. New York: Springer US, 2006, pp.73–89.
107.
EddahechABriatOVinassaJM. Lithium-ion battery performance improvement based on capacity recovery exploitation. Electrochim Acta2013; 114: 750–757.
108.
LiuDTPangJYZhouJB. Prognostics for state of health estimation of lithium-ion batteries based on combination Gaussian process functional regression. Microelectron Reliab2013; 53(1): 832–839.
109.
RaoKSMohapatraYN. Disentangling degradation and auto-recovery of luminescence in Alq3 based organic light emitting diodes. J Lumin2014; 145(1): 793–796.
BaraldiPMangiliFZioE. Investigation of uncertainty treatment capability of model-based and data-driven prognostic methods using simulated data. Reliab Eng Syst Safe2013; 112(1): 94–108.
112.
BaraldiPMangiliFZioE. A Kalman filter-based ensemble approach with application to turbine creep prognostics. IEEE T Reliab2012; 61(4): 966–977.
113.
SahaBGoebelK. Uncertainty management for diagnostics and prognostics of batteries using Bayesian techniques. In: IEEE aerospace conference, Big Sky, MT, 1–8 March 2008. New York: IEEE.
114.
RafteryAEKárnýMEttlerP. Online prediction under model uncertainty via dynamic model averaging: application to a cold rolling mill. Technometrics2010; 52(1): 52–66.
115.
TangLKacprzynskiGJGoebelK. Methodologies for uncertainty management in prognostics. In: IEEE aerospace conference, Big Sky, MT, 7–14 March 2009. New York: IEEE.
116.
SaxenaACelayaJSahaB. Evaluating prognostics performance for algorithms incorporating uncertainty estimates. In: IEEE aerospace conference, Big Sky, MT, 6–13 March 2010. New York: IEEE.
