Degradation is an unavoidable phenomenon in industrial systems. Hidden Markov models (HMMs) have been used for degradation modeling. In particular, segmental HMMs have been developed to model the explicit relationship between degradation signals and hidden states. However, existing segmental HMMs deal only with univariate cases, whereas in real systems, signals from various sensors are collected simultaneously, which makes it necessary to adapt the segmental HMMs to deal with multivariate processes. Also, to make full use of the information from the sensors, it is important to differentiate stable signals from deteriorating ones, but there is no good way for this, especially in multivariate processes. In this paper, the multivariate exponentially weighted moving average (MEWMA) control chart is employed to identify deteriorating multivariate signals. Specifically, the MEWMA statistic is used as a comprehensive indicator for differentiating multivariate observations. Likelihood Maximization is used to estimate the model parameters. To avoid underflow, the forward and backward probabilities are normalized. In order to assess degradation, joint probabilities are defined and derived. Further, the occurrence probability of each degradation state at the current time, as well as in the future, is derived. The Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset of NASA is employed for comparative analysis. In terms of degradation assessment and prediction, the proposed model performs very well in general. By sensitivity analysis, we show that in order to improve further the performance of the method, the weight of the chart should be set relatively small, whereas the method is not sensitive to the change of the in-control average run length (ARL).
TangDYuJChenX, et al. An optimal condition-based maintenance policy for a degrading system subject to the competing risks of soft and hard failure. Comput Ind Eng2015; 83: 100–110.
3.
SongCLiuKZhangX. Integration of data-level fusion model and kernel methods for degradation modeling and prognostic analysis. IEEE Trans Reliab2018; 67(2): 640–650.
4.
DongYXiaTFangX, et al. Prognostic and health management for adaptive manufacturing systems with online sensors and flexible structures. Comput Ind Eng2019; 133: 57–68.
5.
LiYChenZPanE. Joint economic design of CUSUM control chart and age-based imperfect preventive maintenance policy. Math Prob Eng2018; 2018. article id. 9246372
6.
TangDMakisVJafariL, et al. Optimal maintenance policy and residual life estimation for a slowly degrading system subject to condition monitoring. Reliab Eng Syst Safety2015; 134: 198–207.
7.
OuyangLChenJParkC, et al. Bayesian closed-loop robust process design considering model uncertainty and data quality. IISE Trans2020; 52(8): 288–300.
8.
MeekeWQLuValleMJ. An accelerated life test model based on reliability kinetics. Technometrics1995; 37(2): 133–146.
9.
XuMBaraldiPAl-DahidiS, et al. Fault prognostics by an ensemble of Echo State Networks in presence of event_based measurements. Eng Appl Artif Intell2020; 87: 103346.
10.
OuyangLZhengWZhuY, et al. An interval probability-based FMEA model for risk assessment: a real-world case. Qual Reliab Eng Int2020; 36(1): 125–143.
11.
ChinnamRB. On-line reliability estimation for individual components using statistical degradation signal models. Qual Reliab Eng Int2002; 18(1): 53–73.
12.
RobinsonMECrowderMJ. Bayesian methods for a growth-curve degradation model with repeated measures. Lifetime Data Anal2000; 6(4): 357–374.
13.
YanJHLeeJ. Degradation assessment and fault modes classification using logistic regression. J Manuf Sci Eng Trans ASME2005: 127(4): 912–914.
14.
HuangWDietrichDL. An alternative degradation reliability modeling approach using maximum likelihood estimation. IEEE Trans Reliab2005; 54(2): 310–317.
15.
JiangRJardineAKS. Health state evaluation of an item: a general framework and graphical representation. Reliab Eng Syst Safety2008; 93(1): 89–99.
16.
SunQZhouJZhongZ, et al. Gauss–Poisson joint distribution model for degradation failure. IEEE Trans Plasma Sci2004; 32(5): 1864–1868.
17.
WangWDragomir-DaescuD. Reliability quantification of induction motors- accelerated degradation testing approach. In: Annual reliability and maintainability symposium, Seattle, Washington, USA, January 2002, pp.325–331. IEEE.
18.
WangXBalakrishnanNGuoB. Residual life estimation based on a generalized wiener degradation process. Reliab Eng Syst Safety2014; 124: 13–23.
19.
TsaiCCLinCTBalakrishnanN. Optimal design for accelerated-stress acceptance test based on wiener process. IEEE Trans Reliab2015; 64(2): 603–612.
20.
ZhangCLuXTanY, et al. Reliability demonstration methodology for products with gamma process by optimal accelerated degradation testing. Reliab Eng Syst Safety2015; 142: 369–377.
21.
BordesLParoissinCSalamiA. Parametric inference in a perturbed gamma degradation process. Commun Stat-Theory Meth2016; 45(9): 2730–2747.
22.
GaoHZioEGuoJ, et al. Dynamic probabilistic-based LCF damage assessment of turbine blades regarding time-varying multi-physical field loads. Eng Fail Anal2020; 108:104193.
23.
GaoHWangAZioE, et al. An integrated reliability approach with improved importance sampling for low-cycle fatigue damage prediction of turbine disks. Reliab Eng Syst Safety2020; 199: 106819.
24.
RaimondK. Minimizing error in tool wear estimation using artificial neural network. In: IEEE international conference on industrial technology, Bombay, INDIA, December 2006. IEEE.
25.
DimlaDESrListerPM. On-line metal cutting tool condition monitoring.: II: tool-state classification using multi-layer perceptron neural networks. Int J Machine Tools Manuf2000; 40(5): 769–781.
26.
ZhaoRYanRWangJ, et al. Learning to monitor machine health with convolutional bi-directional LSTM networks. Sensors2017; 17(2): 273.
27.
Al-DulaimiAZabihiSAsifA, et al. A multimodal and hybrid deep neural network model for Remaining Useful Life estimation. Comput Ind2019; 108: 186–196.
28.
SongYXiaTZhengY, et al. A remaining useful life prediction framework integrating multiple time window convolutional neural networks. J Grey Syst2020; 32(3): 34–37.
29.
XiaTSongYZhengY, et al. An ensemble framework based on convolutional bi-directional LSTM with multiple time windows for remaining useful life estimation. Comput Ind2020; 115: 103182.
30.
LiXDingQSunJ. Remaining useful life estimation in prognostics using deep convolution neural networks. Reliab Eng Syst Safety2018; 172: 1–11.
31.
LiJZhangXZhouX, et al. Reliability assessment of wind turbine bearing based on the degradation-hidden-Markov model. Renew Energy2019; 132: 1076–1087.
32.
ChenZLiYXiaT, et al. Hidden Markov model with auto-correlated observations for remaining useful life prediction and optimal maintenance policy. Reliab Eng Syst Safety2019; 184: 123–136.
33.
RebelloSYuHMaL. An integrated approach for system functional reliability assessment using dynamic Bayesian network and hidden Markov model. Reliab Eng Syst Safety2018; 180: 124–135.
34.
LeTTChatelainFBerenguerC. Multi-branch hidden Markov models for remaining useful life estimation of systems under multiple deterioration modes. Proc IMechE, Part O: J Risk Reliability2016; 230(5): 473–484.
35.
LiuTZhuKZengL. Diagnosis and prognosis of degradation process via hidden semi-Markov model. IEEE-ASME Trans Mechatron2018; 23(3): 1456–1466.
36.
GeramifardOXuJZhouJ, et al. A physically segmented hidden Markov model approach for continuous tool condition monitoring diagnostics and prognostics. IEEE Trans Ind Inform2012; 8(4): 964–973.
37.
ChenZXiaTPanE. Remaining useful life estimation based on a segmental hidden Markov model with continuous observations. In: 12th ASME international manufacturing science and engineering conference, Los Angeles, CA, USA, June 2017.
38.
ChenZXiaTLiY, et al. Degradation modeling and classification of mixed populations using segmental continuous hidden Markov models. Quality Reliab Eng Int2018; 34(5): 807–823.
39.
MontgomeryDC. Statistical quality control: a modern introduction. 6th ed.New York, NY: John Wiley & Sons, Inc., 2009.
40.
FangXPaynabarKGebraeelN. Multi-stream sensor fusion-based prognostics model for systems with single failure modes. Reliab Eng Syst Safety2017; 159: 322–331.
41.
ZhangHZhouDChenM, et al. FBM-based remaining useful life prediction for degradation processes with long-range dependence and multiple modes. IEEE Trans Reliab2019; 68(3): 1021–1033.
42.
RossSM. Introduction to probability models. 11th ed. Beijing, China: Posts & Telecom Press, 2015.
43.
PrabhuSSRungerGC. Designing a multivariate EWMA control chart. J Quality Technol1997; 29(1): 8–15.
44.
RabinerLR. A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE1989; 77(2): 257–286.
45.
LiYPanEXiaoY. On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes. Qual Reliab Eng Int2020; 36: 2351–2369.
46.
LucasJMSaccucciMS. Exponentially weighted moving average control schemes: properties and enhancements. Technometrics1999; 32(1): 1–12.
47.
CrowderSV. Design of exponentially weighted moving average schemes. J Quality Technol1989; 21(3): 155–162.
48.
HunterJS. A one-point plot equivalent to the Shewhart chart with western electric rules. Quality Eng1989; 2(1): 13–19.
