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Bias reduction in the two-stage method for degradation data analysis. (English) Zbl 07193035
Summary: Degradation data are usually collected for assessing the reliability of the product. We propose a new two-stage method to analyze degradation data. The degradation path is fitted by the nonlinear mixed effects model in the first stage, and the parameters in lifetime distribution are estimated by maximizing the asymptotic marginal distribution of pseudo lifetimes in the second stage. The new method has many advantages: (i) it does not require the distributions on random effects, (ii) the historical information about lifetime distribution of the product can be incorporated easily, and thus the estimated lifetime distribution has a closed form, (iii) bias correction term is automatically embedded into the asymptotic marginal distribution of pseudo lifetime. Finally, simulation studies and real data analysis are performed for illustration.
MSC:
62 Statistics
65 Numerical analysis
Software:
MEMSS; SPLIDA; S-PLUS
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[1] Lu, C.; William, W.; Escobar, L., A comparison of degradation and failure time analysis methods for estimating a time-to-failure distribution, Stat. Sin., 6, 531-546 (1996)
[2] Hong, Y.; Duan, Y.; Meeker, W.; Stanley, D.; Gu, X., Statistical methods for degradation data with dynamic covariates information and an application to outdoor weathering data, Technometrics, 57, 180-193 (2015)
[3] Ye, Z.; Chen, N., The inverse Gaussian process as a degradation model, Technometrics, 56, 302-311 (2014)
[4] Guan, Q.; Tang, Y.; Xu, A., Objective Bayesian analysis for accelerated degradation test based on wiener process models, Appl. Math. Model., 40, 2743-2755 (2016)
[5] Kharoufeh, J.; Solo, C.; Ulukus, M., Semi-Markov models for degradation-based reliability, IIE Trans., 42, 599-612 (2010)
[6] Byon, E.; Ding, Y., Season-dependent condition-based maintenance for a wind turbine using a partially observed Markov decision process, IEEE Trans. Power Syst., 25, 823-834 (2010)
[7] Xing, Y.; Ma, E.; Tsui, K.; Pecht, M., An ensemble model for predicting the remaining useful performance of lithium-ion batteries, Microelectron. Reliab., 53, 811-820 (2013)
[8] Ye, Z.; Xie, M., Stochastic modelling and analysis of degradation for highly reliable products, Appl. Stoch. Models Bus. Ind., 31, 16-32 (2015)
[9] Zhang, Z.; Si, X.; Hu, C.; Lei, Y., Degradation data analysis and remaining useful life estimation: a review on wiener-process-based methods, Eur. J. Oper. Res., 271, 775-796 (2018)
[10] He, D.; Wang, Y.; Chang, G., Objective Bayesian analysis for the accelerated degradation model based on the inverse gaussian process, Appl. Math. Model., 61, 341-350 (2018)
[11] Hao, S.; Yang, J.; Christophe, B., Degradation analysis based on an extended inverse gaussian process model with skew-normal random effects and measurement errors, Reliab. Eng. Syst. Saf., 189, 261-270 (2019)
[12] Jiang, P.; Wang, B.; Wu, F., Inference for constant-stress accelerated degradation test based on gamma process, Appl. Math. Model., 67, 123-134 (2019)
[13] Oliveira, R.; Loschi, R.; Freitas, M., Skew-heavy-tailed degradation models: an application to train wheel degradation, IEEE Trans. Reliab., 67, 129-141 (2018)
[14] Yuan, T.; Wu, X.; Bae, S.; Zhu, X., Reliability assessment of a continuous-state fuel cell stack system with multiple degrading components, Reliab. Eng. Syst. Saf., 189, 157-164 (2019)
[15] Wang, P.; Tang, Y.; Bae, S.; He, Y., Bayesian analysis of two-phase degradation data based on change-point wiener process, Reliab. Eng. Syst. Saf., 170, 244-256 (2018)
[16] Peng, W.; Li, Y.; Yang, Y.; Zhu, S.; Huang, H., Bivariate analysis of incomplete degradation observations based on inverse gaussian processes and copulas, IEEE Trans. Reliab., 65, 624-639 (2016)
[17] Xu, A.; Shen, L.; Wang, B.; Tang, Y., On modeling bivariate wiener degradation process, IEEE Trans. Reliab., 67, 897-906 (2018)
[18] Pinheiro, J.; Bates, D., Mixed-effects Models in S and S-PLUS (2000), Springer
[19] Hartford, A.; Davidian, M., Consequences of misspecifying assumptions in nonlinear mixed effects models, Comput. Stat. Data Anal., 34, 139-164 (2000)
[20] Meeker, W.; Escobar, L., Statistical methods for reliability data (1998), John Wiley & Sons
[21] Lu, C.; Meeker, W., Using degradation measures to estimate a time-to-failure distribution, Technometrics, 35, 161-174 (1993)
[22] Chen, Z.; Zheng, S., Lifetime distribution based degradation analysis, IEEE Trans. Reliab., 54, 3-10 (2005)
[23] Cox, D., Some remarks on failure-times, surrogate markers, degradation, wear, and the quality of life, Lifetime Data Anal., 5, 307-314 (1999)
[24] Wu, S.; Shao, J., Reliability analysis using the least squares method in nonlinear mixed-effect degradation models, Stat. Sin., 9, 855-877 (1999)
[25] Robinson, M.; Crowder, M., Bayesian methods for a growth-curve degradation model with repeated measures, Lifetime Data Anal., 6, 357-374 (2000)
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