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Optimal plan for Wiener constant-stress accelerated degradation model. (English) Zbl 07203990
Summary: This paper explores inferential procedures for the Wiener constant-stress accelerated degradation model under degradation mechanism invariance. The exact confidence intervals are obtained for the parameters of the proposed accelerated degradation model. The generalized confidence intervals are also proposed for the reliability function and \(p\) th quantile of the lifetime at the normal operating stress level. In addition, the prediction intervals are developed for the degradation characteristic, lifetime and remaining useful life of the product at the normal operating stress level. The performance of the proposed generalized confidence intervals and the prediction intervals is assessed by the Monte Carlo simulation. Furthermore, a new optimum criterion is proposed based on minimizing the mean of the upper prediction limit for the degradation characteristic at the design stress level. The exact optimum plan is also derived for the Wiener accelerated degradation model according to the proposed optimal criterion. The proposed interval procedures and optimum plan are the free of the equal testing interval assumption. Finally, two examples are provided to illustrate the proposed interval procedures and exact optimum plan. Specifically, based on the degradation data of LEDs, some interval estimates of quantities related to reliability indicators are obtained. For the degradation data of carbon-film resistors, the optimal allocation of test units is derived in terms of the proposed optimal criterion.
MSC:
62 Statistics
74 Mechanics of deformable solids
Software:
SPLIDA
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[1] Meeker, W. Q.; Escobar, L. A., Statistical Methods for Reliability Data (1998), John Wiley & Sons: John Wiley & Sons New York · Zbl 0949.62086
[2] Shiau, J. H.; Lin, H. H., Analyzing accelerated degradation data by nonparametric regression, IEEE Trans. Reliab., 48, 2, 149-158 (1999)
[3] Padgett, W. J.; Tomlinson, M. A., Inference from accelerated degradation and failure data based on gaussian process models, Lifetime Data Anal., 10, 2, 191-206 (2004) · Zbl 1058.62090
[4] Mohammadian, S. H.; Aït-Kadi, D. D.; Routhier, F., Quantitative accelerated degradation testing: Practical approaches, Reliab. Eng. Sys. Saf., 95, 2, 149-159 (2010)
[5] Zhang, Z. X.; Si, X. S.; Hu, C. H.; Zhang, Q.; Li, T. M.; Xu, C. Q., Planning repeated degradation testing for products with three-source variability, IEEE Trans. Reliab., 65, 1, 640-647 (2016)
[6] Meeker, W. Q.; Escobar, L. A.; Lu, C. J., Accelerated degradation tests: modeling and analysis, Technometrics, 40, 2, 89-99 (1998)
[7] Shi, Y.; Meeker, W. Q., Bayesian methods for accelerated destructive degradation test planning, IEEE Trans. Reliab., 61, 1, 245-253 (2012)
[8] Zhang, Z. X.; Si, X. S.; Hu, C. H.; Lei, Y. G., Degradation data analysis and remaining useful life estimation: A review on wiener-process-based methods, Eur. J. Oper. Res., 271, 775-796 (2018) · Zbl 1403.60073
[9] Jiang, P. H.; Wang, B. X.; Wu, F. T., Inference for constant-stress accelerated degradation test based on gamma process, Appl. Math. Model., 67, 123-134 (2019) · Zbl 07183419
[10] Ye, Z. S.; Chen, N., The inverse gaussian process as a degradation model, Technometrics, 56, 3, 302-311 (2014)
[11] Liao, C. M.; Tseng, S. T., Optimal design for step-stress accelerated degradation tests, IEEE Trans. Reliab., 55, 1, 59-66 (2006)
[12] Lim, H.; Yum, B. J., Optional design of accelerated degradation tests based on wiener process models, J. Appl. Stat., 38, 2, 309-325 (2011)
[13] Liao, H. T.; Elsayed, E. A., Reliability inference for field conditions from accelerated degradation testing, Nav. Res. Log., 53, 6, 576-587 (2006) · Zbl 1104.62110
[14] Whitmore, G. A.; Schenkelberg, F., Modeling an acceleerated degradatin data using wiener diffusion with a time scale transformation, Lifetime Data Anal., 3, 1, 27-45 (1997) · Zbl 0891.62071
[15] Escobar, L. A.; Meeker, W. Q., A review of accelerated test models, Stat. Sci., 21, 4, 552-577 (2006) · Zbl 1129.62090
[16] Hu, C. H.; Lee, M. Y.; Tang, J., Optimum step-stress accelerated degradation test for wiener degradation process under constraints, Eur. J. Oper. Res., 241, 2, 412-421 (2015) · Zbl 1339.90107
[17] Tang, L. C.; Yang, G. Y.; Xie, M., Planning of step-stress accelerated degradation test, Proceedings of the Annual Reliability and Maintainability Symposium, 287-292 (2004)
[18] Weerahandi, S., Generalized Inference in Repeated Measures: Exact Methods in MANOVA and Mixed Models (2004), Wiley: Wiley New York · Zbl 1057.62041
[19] Luo, M.; Yan, H. C.; Hu, B.; Zhou, J. H.; Pang, C. K., A data-driven two-stage maintenance framework for degradation prediction in semiconductor manufacturing industries, Comput. Ind. Eng., 85, 414-422 (2015)
[20] Wang, B. X.; Yu, K., Optimum plan for step-stress model with progressive type-II censoring, Test, 18, 115-135 (2009) · Zbl 1203.62176
[21] Meneghini, M.; Tazzoli, A.; Mura, G.; Meneghesso, G.; Zanoni, E., A review on the physical mechanisms that limit the reliability of gan-based LEDs, IEE E. T. Electron. Dev., 57, 1, 108-118 (2010)
[22] Bae, S. J.; Kvam, P. H., A nonlinear random-coefficients model for degradation testing, Technometrics, 46, 4, 460-469 (2004)
[23] Hong, L.; Ye, Z. S.; Sari, J. K., Interval estimation for wiener processes based on accelerated degradation test data, IISE Transactions, 50, 12, 1043-1057 (2018)
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