Stochastic modelling and analysis of degradation for highly reliable products

Applied Stochastic Models in Business and Industry

Volumn 31, Issue 1, 2015, Pages 16-32

  Yea, Zhi Sheng ^a   Xie, Min ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Data driven methods; Degradation based burn in; General path models; Stochastic process models; Wiener processes

Indexed keywords

DECISION MAKING; RANDOM PROCESSES; STOCHASTIC SYSTEMS;

BURN-IN; DATA-DRIVEN METHODS; PATH MODELS; STOCHASTIC PROCESS MODEL; WIENER PROCESS;

STOCHASTIC MODELS;

EID: 84923355419     PISSN: 15241904     EISSN: 15264025     Source Type: Journal    
DOI: 10.1002/asmb.2063     Document Type: Article

References (126)

1. Si XS,Wang W, Hu CH, Zhou DH. Remaining useful life estimation - a review on the statistical data driven approaches. European Journal of Operational Research 2011; 213(1):1-14.
2. Jardine AKS, Lin D, Banjevic D. A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical Systems and Signal Processing 2006; 20(7):1483-1510.
3. Whitmore GA, Schenkelberg F. Modelling accelerated degradation data usingWiener diffusion with a time scale transformation. Lifetime Data Analysis 1997; 3(1):27-45.
4. Park C, Padgett WJ. Accelerated degradation models for failure based on geometric Brownian motion and gamma processes. Lifetime Data Analysis 2005a; 11(4):511-527.
5. Doksum KA, Hóyland A. Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution. Technometrics 1992; 34(1):74-82.
6. Park C, Padgett WJ. New cumulative damage models for failure using stochastic processes as initial damage. IEEE Transactions on Reliability 2005b; 54(3):530-540.
7. Wang Y, Ye ZS, Tsui KL. Stochastic evaluation of magnetic head wears in hard disk drives. IEEE Transactions on Magnetics 2014; 50(5):1-7.
8. Whitmore GA. Estimating degradation by a Wiener diffusion process subject to measurement error. Lifetime Data Analysis 1995; 1(3):307-319.
9. Ye ZS, Wang Y, Tsui KL, Pecht M. Degradation data analysis using Wiener processes with measurement errors. IEEE Transactions on Reliability 2013a; 62(4):772-780.
10. Ye ZS, Chen LP, Xie M, Tang LC. Accelerated degradation test planning using the inverse Gaussian process. IEEE Transactions on Reliability 2014a; 63(3):750-763.
11. Tang S, Yu C, Wang X, Guo X, Si X. Remaining useful life prediction of lithium-ion batteries based on the wiener process with measurement error. Energies 2014; 7(2):520-547.
12. Peng CY, Hsu SC. A note on a Wiener process with measurement error. Applied Mathematics Letters 2012; 25(4):729-732.
13. Peng CY, Tseng ST. Mis-specification analysis of linear degradation models. IEEE Transactions on Reliability 2009; 58(3):444-455.
14. Doksum KA, Normand SLT. Gaussian models for degradation processes - part I: methods for the analysis of biomarker data. Lifetime Data Analysis 1995; 1(2):131-144.
15. Tang LC, Yang G, Xie M. Planning of step-stress accelerated degradation test. Annual Reliability and Maintainability Symposium, 2004, 287-292.
16. Liao CM, Tseng ST. Optimal design for step-stress accelerated degradation tests. IEEE Transactions on Reliability 2006; 55(1):59-66.
17. Lim H, Yum BJ. Optimal design of accelerated degradation tests based on Wiener process models. Journal of Applied Statistics 2011; 38(2):309-325.
18. Padgett WJ, Tomlinson MA. Inference from accelerated degradation and failure data based on Gaussian process models. Lifetime Data Analysis 2004; 10(2):191-206.
19. Tsai CC, Tseng ST, Balakrishnan N. Optimal design for degradation tests based on Gamma processesWith random effects. IEEE Transactions on Reliability 2012a; 61(1):604-613.
20. Joseph VR, Yu IT. Reliability improvement experiments with degradation data. IEEE Transactions on Reliability 2006; 55(1):149-157.
21. Liao H, Elsayed EA. Reliability inference for field conditions from accelerated degradation testing. Naval Research Logistics 2006; 53(6):576-587.
22. Peng CY, Tseng ST. Progressive-stress accelerated degradation test for highly-reliable products. IEEE Transactions on Reliability 2010; 59(1):30-37.
23. Ye ZS, Hong Y, Xie Y. How do heterogeneities in operating environments affect field failure predictions and test planning The Annals of Applied Statistics 2013b; 7(4):2249-2271.
24. Meeker WQ, Escobar LA. Statistical Methods for Reliability Data. Wiley: New York, 1998.
25. Si XS, Wang W, Hu CH, Zhou DH, Pecht MG. Remaining useful life estimation based on a nonlinear diffusion degradation process. IEEE Transactions on Reliability 2012; 61(1):50-67.
26. Tsai CC, Tseng ST, Balakrishnan N. Mis-specification analyses of gamma and Wiener degradation processes. Journal of Statistical Planning and Inference 2011a; 141(12):3725-3735.
27. Si XS, Wang W, Hu CH, Chen MY, Zhou DH. A Wiener-process-based degradation model with a recursive filter algorithm for remaining useful life estimation. Mechanical Systems and Signal Processing 2013; 35(1):219-237.
28. Wang X, Jiang P, Guo B, Cheng Z. Real-time reliability evaluation with a general Wiener process-based degradation model. Quality and Reliability Engineering International 2013; 30(2):205-220.
29. Bian L, Gebraeel N. Computing and updating the first-passage time distribution for randomly evolving degradation signals. IIE Transactions 2012; 44(11):974-987.
30. Liao H, Tian Z. A framework for predicting the remaining useful life of a single unit under time-varying operating conditions. IIE Transactions 2013; 45(9):964-980.
31. Bian L, Gebraeel N. Stochastic framework for partially degradation systems with continuous component degradation-rate-interactions. Naval Research Logistics 2014; 61(4):286-303.
32. Peng CY, Tseng ST. Statistical lifetime inference with Skew-Wiener linear degradation models. IEEE Transactions on Reliability 2013; 62(2):338-350.
33. Wang X. Wiener processes with random effects for degradation data. Journal of Multivariate Analysis 2010; 101(2):340-351.
34. Wang X. Nonparametric estimation of the shape function in a Gamma process for degradation data. Canadian Journal of Statistics 2009; 37(1):102-118.
35. Si X, Hu CH, Kong X, Zhou DH. A residual storage life prediction approach for systems with operation state switches. IEEE Transactions on Industrial Electronics 2014; 61(11):6304-6315.
36. Singpurwalla ND. Survival in dynamic environments. Statistical Science 1995; 10(1):86-103.
37. van Noortwijk JM. A survey of the application of gamma processes in maintenance. Reliability Engineering & System Safety 2009; 94(1):2-21.
38. Singpurwalla N. Gamma processes and their generalizations: an overview. In Engineering Probabilistic Design and Maintenance for Flood Protection. Springer: Dordrecht, The Netherlands, 1997; 67-75.
39. Bagdonavicius V, Nikulin MS. Estimation in degradation models with explanatory variables. Lifetime Data Analysis 2001; 7(1):85-103.
40. Park C, Padgett WJ. Stochastic degradation models with several accelerating variables. IEEE Transactions on Reliability 2006; 55(2):379-390.
41. Lawless JF, Crowder MJ. Covariates and random effects in a gamma process model with application to degradation and failure. Lifetime Data Analysis 2004; 10(3):213-227.
42. Wang X. Semiparametric inference on a class of Wiener processes. Journal of Time Series Analysis 2009; 30(2):179-207.
43. Wang X. A pseudo-likelihood estimation method for nonhomogeneous gamma process model with random effects. Statistica Sinica 2008; 18(3):1153-1163.
44. Ye ZS, Chen N, Tsui KL. A Bayesian approach to condition monitoring with imperfect inspections. Quality & Reliability Engineering International 2014b. DOI: 10.1002/qre.1609, to appear.
45. Kallen MJ, van Noortwijk JM. Optimal maintenance decisions under imperfect inspection. Reliability Engineering & System Safety 2005; 90(2):177-185.
46. Zhou Y, Sun Y, Mathew J, Wolff R, Ma L. Latent degradation indicators estimation and prediction: a Monte Carlo approach. Mechanical Systems and Signal Processing 2011; 25(1):222-236.
47. Lu D, Pandey MD, Xie WC. An efficient method for the estimation of parameters of stochastic gamma process from noisy degradation measurements. Journal of Risk and Reliability 2013; 227(4):425-433.
48. Wang X, Xu D. An inverse Gaussian process model for degradation data. Technometrics 2010; 52(2):188-197.
49. Ye ZS, Chen N. The inverse Gaussian process as a degradation model. Technometrics 2014; 56(3):302-311.
50. Ye ZS. On the conditional increments of degradation processes. Statistics & Probability Letters 2013; 83(11):2531-2536.
51. Peng W, Li YF, Yang YJ, Huang HZ, Zuo MJ. Inverse Gaussian process models for degradation analysis: a Bayesian perspective. Reliability Engineering & System Safety 2014; 130:175-189.
52. Lu CJ, Meeker WQ. Using degradation measures to estimate a time-to-failure distribution. Technometrics 1993; 35(2):161-174.
53. Freitas MA, de Toledo MLG, Colosimo EA, Pires MC. Using degradation data to assess reliability: a case study on train wheel degradation. Quality and Reliability Engineering International 2009; 25(5):607-629.
54. Su C, Lu JC, Chen D, Hughes-Oliver JM. A random coefficient degradation model with ramdom sample size. Lifetime Data Analysis 1999; 5(2):173-183.
55. Weaver BP, Meeker WQ, Escobar LA, Wendelberger JR. Methods for planning repeated measures degradation studies. Technometrics 2013; 55(2):122-134.
56. Boulanger M, Escobar LA. Experimental design for a class of accelerated degradation tests. Technometrics 1994; 36(3):260-272.
57. Bae SJ, Kvam PH. A nonlinear random-coefficients model for degradation testing. Technometrics 2004; 46(4):460-469.
58. Bae SJ, Kuo W, Kvam PH. Degradation models and implied lifetime distributions. Reliability Engineering & System Safety 2007; 92(5):601-608.
59. Yu HF. Designing an accelerated degradation experiment with a reciprocal Weibull degradation rate. Journal of Statistical Planning and Inference 2006; 136(1):282-297.
60. Shiau JJH, Lin HH. Analyzing accelerated degradation data by nonparametric regression. IEEE Transactions on Reliability 1999; 48(2):149-158.
61. Zhou R, Serban N, Gebraeel N. Degradation-based residual life prediction under different environments. The Annals of Applied Statistics 2014. http://www.e-publications.org/ims/submission/AOAS/user/submissionFile/16350?confirm=05fabeee, to appear.
62. Lu JC, Park J, Yang Q. Statistical inference of a time-to-failure distribution derived from linear degradation data. Technometrics 1997; 39(4):391-400.
63. Yuan XX, Pandey M. A nonlinear mixed-effects model for degradation data obtained from in-service inspections. Reliability Engineering & System Safety 2009; 94(2):509-519.
64. Lin TI, Lee JC. On modelling data from degradation sample paths over time. Australian & New Zealand Journal of Statistics 2003; 45(3):257-270.
65. Meeker WQ, Escobar LA, Lu JC. Accelerated degradation tests: modeling and analysis. Technometrics 1998; 40(2):89-99.
66. Robinson ME, Crowder MJ. Bayesian methods for a growth-curve degradation model with repeated measures. Lifetime Data Analysis 2000; 6(4):357-374.
67. Hamada MS. Using degradation data to assess reliability. Quality Engineering 2005; 17(4):615-620.
68. Pan R, Crispin T. A hierarchical modeling approach to accelerated degradation testing data analysis: a case study. Quality and Reliability Engineering International 2011; 27(2):229-237.
69. Chen N, Tsui KL. Condition monitoring and remaining useful life prediction using degradation signals: revisited. IIE Transactions 2013; 45(9):939-952.
70. Shi Y, Escobar LA, Meeker WQ. Accelerated destructive degradation test planning. Technometrics 2009; 51(1):1-13.
71. Tang LC, Liu X. Planning and inference for a sequential accelerated life test. Journal of Quality Technology 2010; 42(1):103-118.
72. Lindstrom MJ. Linear and Nonlinear Mixed-Effects Models for Repeated Measures Data. PhD thesis, University ofWisconsin-Madison, 1987.
73. Hong Y, Duan Y, Meeker WQ, Stanley DL, Gu X. Statistical methods for degradation data with dynamic covariates information and an application to outdoor weathering data. Technometrics 2014. DOI: 10.1080/00401706.2014.915891, to appear.
74. Wang W. An overview of the recent advances in delay-time-based maintenance modelling. Reliability Engineering & System Safety 2012; 106:165-178.
75. Ye ZS, Tang LC, Xie M. A burn-in scheme based on percentiles of the residual life. Journal of Quality Technology 2011a; 43(4):334-345.
76. Esary J, Marshall A. Shock models and wear processes. The Annals of Probability 1973; 1(4):627-649.
77. Gut A. Mixed shock models. Bernoulli 2001; 7(3):541-555.
78. Lam Y. A geometric process-shock maintenance model. IEEE Transactions on Reliability 2009; 58(2):389-396.
79. Li G, Luo J. Shock model in Markovian environment. Naval Research Logistics 2005; 52(3):253-260.
80. Nakagawa T. Shock and Damage Models in Reliability Theory. Springer: London, 2007.
81. Soro IW, Nourelfath M, Ait-Kadi D. Performance evaluation of multi-state degraded systems with minimal repairs and imperfect preventive maintenance. Reliability Engineering & System Safety 2010; 95(2):65-69.
82. Yin ML, Angus JE, Trivedi KS. Optimal preventive maintenance rate for best availability with hypo-exponential failure distribution. IEEE Transactions on Reliability 2013; 62(2):351-361.
83. Zhong C, Jin H. A novel optimal preventive maintenance policy for a cold standby system based on semi-Markov theory. European Journal of Operational Research 2014; 232(2):405-411.
84. Kharoufeh JP. Explicit results for wear processes in a Markovian environment. Operations Research Letters 2003; 31(3):237-244.
85. Kharoufeh JP, Cox SM. Stochastic models for degradation-based reliability. IIE Transactions 2005; 37(6):533-542.
86. Kharoufeh JP, Solo CJ, Ulukus MY. Semi-Markov models for degradation-based reliability. IIE Transactions 2010; 42(8):599-612.
87. Xu Z, Ji Y, Zhou D. Real-time reliability prediction for a dynamic system based on the hidden degradation process identification. IEEE Transactions on Reliability 2008; 57(2):230-242.
88. Byon E, Ding Y. Season-dependent condition-based maintenance for a wind turbine using a partially observedMarkov decision process. IEEE Transactions on Power Systems 2010; 25(4):1823-1834.
89. Gebraeel N, Lawley M, Liu R, Parmeshwaran V. Residual life predictions from vibration-based degradation signals: a neural network approach. IEEE Transactions on Industrial Electronics 2004; 51(3):694-700.
90. Sotiris VA, Tse PW, Pecht MG. Anomaly detection through a Bayesian support vector machine. IEEE Transactions on Reliability 2010; 59(2):277-286.
91. Hamada MS, Wilson A, Reese CS, Martz H. Bayesian Reliability . Springer: New York, 2008.
92. Peng W, Huang HZ, Xie M, Yang Y, Liu Y. A Bayesian approach for system reliability analysis with multilevel pass-fail, lifetime and degradation data sets. IEEE Transactions on Reliability 2013; 62(3):689-699.
93. Chinnam RB. A neuro-fuzzy approach for estimating mean residual life in condition-based maintenance systems. International Journal of Materials and Product Technology 2004; 20(1):166-179.
94. Wang D, Miao Q, Kang R. Robust health evaluation of gearbox subject to tooth failure with wavelet decomposition. Journal of Sound and Vibration 2009; 324(3):1141-1157.
95. Miller AJ. A New Wavelet Basis for the Decomposition of Gear Motion Error Signals and Its Application to Gearbox Diagnostics. The Pennsylvania State University: PA, 1999.
96. Lin D, Wiseman M, Banjevic D, Jardine AKS. An approach to signal processing and condition-based maintenance for gearboxes subject to tooth failure. Mechanical Systems and Signal Processing 2004; 18(5):993-1007.
97. Miao Q, Makis V. Condition monitoring and classification of rotating machinery using wavelets and hidden Markov models. Mechanical Systems and Signal Processing 2007; 21(2):840-855.
98. Miao Q, Wang D, Pecht M. A probabilistic description scheme for rotating machinery health evaluation. Journal of Mechanical Science and Technology 2010; 24(12):2421-2430.
99. Miao Q, Huang HZ, Fan X. Singularity detection in machinery health monitoring using Lipschitz exponent function. Journal of Mechanical Science and Technology 2007; 21(5):737-744.
100. Wang D, Tse PW, GuoW,Miao Q. Support vector data description for fusion of multiple health indicators for enhancing gearbox fault diagnosis and prognosis. Measurement Science and Technology 2011; 22(2):025102.
101. Saha B, Goebel K, Christophersen J. Comparison of prognostic algorithms for estimating remaining useful life of batteries. Transactions of the Institute of Measurement and Control 2009a; 31(3-4):293-308.
102. Saha B, Goebel K, Poll S, Christophersen J. Prognosticsmethods for battery health monitoring using a Bayesian framework. IEEE Transactions on Instrumentation and Measurement 2009b; 58(2):291-296.
103. Santhanagopalan S, White RE. State of charge estimation using an unscented filter for high power lithium ion cells. International Journal of Energy Research 2010; 34(2):152-163.
104. Wang D, Tse P. Prognostics of oil sand pumps based on a moving-average wear degradation index and a general sequential Monte Carlo method. Mechanical Systems and Signal Processing 2014. to appear.
105. He W,Williard N, Osterman M, PechtM. Prognostics of lithium-ion batteries based on Dempster-Shafer theory and the Bayesian Monte Carlo method. Journal of Power Sources 2011; 196:10314-10321.
106. Xing Y, Ma EWM, Tsui KL, Pecht M. An ensemble model for predicting the remaining useful performance of lithium-ion batteries. Microelectronics Reliability 2013; 53(6):811-820.
107. Miao Q, Xie L, Cui H, Liang W, Pecht M. Remaining useful life prediction of lithium-ion battery with unscented particle filter technique. Microelectronics Reliability 2013; 53(6):805-810.
108. Baussaron J, Barreau-Guérin M, Gerville-Réache L, Schimmerling P. Degradation test plan for Wiener degradation processes. Annual Reliability and Maintainability Symposium, 2011, 1-6.
109. Ye ZS, Revie M, Walls LA. A load sharing system reliability model with managed component degradation. IEEE Transactions on Reliability 2014c; 63(3):721-730.
110. Tseng ST, BalakrishnanN, Tsai CC. Optimal step-stress accelerated degradation test plan for Gamma degradation processes. IEEE Transactions on Reliability 2009; 58(4):611-618.
111. Tsai TR, Lin CW, Sung YL, Chou PT, Chen CL, Lio Y. Inference from lumen degradation data under Wiener diffusion process. IEEE Transactions on Reliability 2012b; 61(3):710-718.
112. Ye ZS, Xie M, Tang LC, Chen N. Efficient semiparametric estimation of gamma processes for deteriorating products. Technometrics 2014d. DOI: 10.1080/00401706.2013.869261, to appear.
113. Tseng ST, Yu HF. A termination rule for degradation experiments. IEEE Transactions on Reliability 1997; 46(1):130-133.
114. Yu HF, Chiao CH. An optimal designed degradation experiment for reliability improvement. IEEE Transactions on Reliability 2002; 51(4):427-433.
115. Kim SJ, Bae SJ. Cost-effective degradation test plan for a nonlinear random-coefficients model. Reliability Engineering & System Safety 2013; 110:68-79.
116. Marseguerra M, Zio E, Cipollone M. Designing optimal degradation tests via multi-objective genetic algorithms. Reliability Engineering & System Safety 2003; 79(1):87-94.
117. Shi Y, Meeker WQ. Bayesian methods for accelerated destructive degradation test planning. IEEE Transactions on Reliability 2012; 61(1):245-253.
118. Yang G, Yang K. Accelerated degradation-tests with tightened critical values. IEEE Transactions on Reliability 2002; 51(4):463-468.
119. Ye ZS, Tang LC, Xu HY. A distribution-based systems reliability model under extreme shocks and natural degradation. IEEE Transactions on Reliability 2011b; 60(1):246-256.
120. Tseng ST, Tang J. Optimal burn-in time for highly reliable products. International Journal of Industrial Engineering 2001; 8(4):329-338.
121. Tseng ST, Tang J, Ku IH. Determination of burn-in parameters and residual life for highly reliable products. Naval Research Logistics 2003; 50(1):1-14.
122. Tseng ST, Peng CY. Optimal burn-in policy by using an integrated Wiener process. IIE Transactions 2004; 36(12):1161-1170.
123. Ye ZS, Shen Y, Xie M. Degradation-based burn-in with preventive maintenance. European Journal of Operational Research 2012a; 221(2):360-367.
124. Tsai CC, Tseng ST, Balakrishnan N. Optimal burn-in policy for highly reliable products using Gamma degradation process. IEEE Transactions on Reliability 2011b; 60(1):234-245.
125. Ye ZS, Xie M, Tang LC, Shen Y. Degradation-based burn-in planning under competing risks. Technometrics 2012b; 54(2):159-168.
126. Wang W. A prognosis model for wear prediction based on oil-based monitoring. Journal of the Operational Research Society 2007; 58(7):887-893.