An evidence theory based model fusion method for degradation modeling and statistical analysis. (English) Zbl 1465.62030
Summary: Several methods have been proposed to handle uncertainty issues, including process uncertainty and parameter uncertainty, in stochastic-process based degradation modeling and statistical analysis. However, these methods oftentimes do not address the uncertainty issues well under small sample conditions. Hence, due to the powerful ability of evidence theory to describe uncertainty, especially under small sample conditions, an evidence theory based model fusion method is proposed. The candidate models are considered as different evidence sources and give evidences about the evaluated product based on likelihood. Considering the heterogeneous characteristics of the evidences predicted from different candidate models, the reliability degree is introduced to convert the evidences and estimated based on goodness-of-fit. By fusing converted evidences, inferences and estimations of reliability, degradation mean, degradation variance, and mean time to failure are obtained. The effectiveness of the proposed method is verified by previously published degradation datasets and comparing to Bayesian model averaging method and model selecting method. The degradation mean and variance estimations are more precise and more stable compared to the other two methods under small sample conditions. Furthermore, the proposed method can be used to consider the uncertainty issues by belief, plausibility and uncertainty measure, even though under extremely small sample conditions.
MSC:
| 62B10 | Statistical aspects of information-theoretic topics |
| 62R07 | Statistical aspects of big data and data science |
Software:
SPLIDAReferences:
| [1] | Ivanov, V.; Reznik, A.; Succi, G., Comparing the reliability of software systems: a case study on mobile operating systems, Inf. Sci., 423, 398-411 (2018) |
| [2] | Khorshidi, H. A.; Gunawan, I.; Ibrahim, M. Y., Data-driven system reliability and failure behavior modeling using FMECA, IEEE Trans. Ind. Inf., 12, 1253-1260 (2016) |
| [3] | Volk, M.; Junges, S.; Katoen, J. P., Fast dynamic fault tree analysis by model checking techniques, IEEE Trans. Ind. Inf., 14, 370-379 (2018) |
| [4] | Nelson, W. B., Accelerated Testing: Statistical Models, Test Plans, and Data Analysis (2009), John Wiley & Sons: John Wiley & Sons New York, US |
| [5] | Meeker, W. Q.; Escobar, L. A.; Lu, C. J., Accelerated Degradation Tests: Modeling and Analysis, Technometrics, 40, 89-99 (1998) |
| [6] | Bae, S. J.; Kvam, P. H., A nonlinear random-coefficients model for degradation testing, Technometrics, 46, 460-469 (2004) |
| [7] | Ye, Z.; Tang, L. C.; Xu, H. Y., A distribution-based systems reliability model under extreme shocks and natural degradation, IEEE Trans. Reliab., 60, 246-256 (2011) |
| [8] | Matsumoto, E. Y.; Del-Moral-Hernandez, E., Improving regression predictions using individual point reliability estimates based on critical error scenarios, Inf. Sci., 374, 65-84 (2016) · Zbl 1428.68247 |
| [9] | Cabuz, S.; Abreu, G., Causal inference for multivariate stochastic process prediction, Inf. Sci., 448, 134-148 (2018) · Zbl 1447.62063 |
| [10] | Peng, C. Y., Inverse Gaussian processes with random effects and explanatory variables for degradation data, Technometrics, 57, 100-111 (2015) |
| [11] | Tseng, S. T.; Balakrishnan, N.; Tsai, C. C., Optimal step-stress accelerated degradation test plan for gamma degradation processes, IEEE Trans. Reliab., 58, 611-618 (2009) |
| [12] | Park, C.; Padgett, W. J., Accelerated degradation models for failure based on geometric Brownian motion and gamma processes, Lifetime Data Anal., 11, 511-527 (2005) · Zbl 1120.62088 |
| [13] | Li, X. Y.; Wu, J. P.; Ma, H. G.; Li, X.; Kang, R., A Random Fuzzy Accelerated Degradation Model and Statistical Analysis, IEEE Trans. Fuzzy Syst., 26, 1638-1650 (2018) |
| [14] | Ye, Z. S.; Chen, L. P.; Tang, L. C.; Xie, M., Accelerated degradation test planning using the inverse Gaussian process, IEEE Trans. Reliab., 63, 750-763 (2014) |
| [15] | Liu, L.; Li, X. Y.; Zio, E.; Rui, K., Model uncertainty in accelerated degradation testing analysis, IEEE Trans. Reliab., 66, 603-615 (2017) |
| [16] | Wang, Y.; Peng, Y.; Zi, Y.; Tsui, K. L., A two-stage data-driven-based prognostic approach for bearing degradation problem, IEEE Trans. Ind. Inf., 12, 924-932 (2016) |
| [17] | Ye, Z. S.; Chen, N., The inverse Gaussian process as a degradation model, Technometrics, 56, 302-311 (2014) |
| [18] | Adrian, E. R.; David, M.; Jennifer, A., Bayesian model averaging for linear regression models, J. Am. Stat. Assoc., 92, 179-191 (1997) · Zbl 0888.62026 |
| [19] | Lin, Y. H.; Li, Y. F.; Zio, E., A framework for modeling and optimizing maintenance in systems considering epistemic uncertainty and degradation dependence based on PDMPs, IEEE Trans. Ind. Inf., 14, 210-220 (2018) |
| [20] | Zeng, Z.; Kang, R.; Wen, M.; Zio, E., A model-based reliability metric considering aleatory and epistemic uncertainty, IEEE Access, 5, 15505-15515 (2017) |
| [21] | Peng, W.; Li, Y. F.; Yang, Y. J.; Huang, H. Z.; Zuo, M. J., Inverse Gaussian process models for degradation analysis: a Bayesian perspective, Reliab. Eng. Syst. Saf., 130, 175-189 (2014) |
| [22] | Peng, W.; Li, Y. F.; Yang, Y. J.; Mi, J.; Huang, H. Z., Leveraging degradation testing and condition monitoring for field reliability analysis with time-varying operating missions, IEEE Trans. Reliab., 64, 1367-1382 (2015) |
| [23] | Peng, W.; Li, Y. F.; Yang, Y. J.; Mi, J.; Huang, H. Z., Bayesian degradation analysis with inverse Gaussian process models under time-varying degradation rates, IEEE Trans. Reliab., 66, 84-96 (2017) |
| [24] | Ye, Z. S.; Chen, N.; Shen, Y., A new class of Wiener process models for degradation analysis, Reliab. Eng. Syst. Saf., 139, 58-67 (2015) |
| [25] | Wu, J.; Yan, S.; Zuo, M. J., Evaluating the reliability of multi-body mechanisms: a method considering the uncertainties of dynamic performance, Reliab. Eng. Syst. Saf., 149, 96-106 (2016) |
| [26] | Hurvich, C. M.; Tsai, C. L., Regression and time series model selection in small samples, Biometrika, 76, 297-307 (1989) · Zbl 0669.62085 |
| [27] | Sugiura, N., Further analysis of the data by Akaike’s information criterion and the finite corrections, Commun. Stat., Theory Methods, 7, 13-26 (1978) · Zbl 0382.62060 |
| [28] | Zio, E.; Apostolakis, G. E., Two methods for the structured assessment of model uncertainty by experts in performance assessments of radioactive waste repositories, Reliab. Eng. Syst. Saf., 54, 225-241 (1996) |
| [29] | Wang, L. Z.; Pan, R.; Li, X. Y.; Jiang, T. M., A Bayesian reliability evaluation method with integrated accelerated degradation testing and field information, Reliab. Eng. Syst. Saf., 112, 38-47 (2013) |
| [30] | Park, I.; Amarchinta, H. K.; Grandhi, R. V., A Bayesian approach for quantification of model uncertainty, Reliab. Eng. Syst. Saf., 95, 777-785 (2013) |
| [31] | Tseng, S. T.; Lee, I. C., Optimum allocation rule for accelerated degradation tests with a class of exponential dispersion degradation models, Technometrics, 58, 244-254 (2016) |
| [32] | Droguett, E.; Mosleh, A., Bayesian methodology for model uncertainty using model performance data, Risk Anal., 28, 1457-1476 (2008) |
| [33] | Park, I.; Amarchinta, H. K.; Grandhi, R. V., A Bayesian approach for quantification of model uncertainty, Reliab. Eng. Syst. Saf., 95, 777-785 (2010) |
| [34] | Park, I.; Grandhi, R. V., A Bayesian statistical method for quantifying model form uncertainty and two model combination methods, Reliab. Eng. Syst. Saf., 129, 46-56 (2014) |
| [35] | Liu, L.; Li, X. Y.; Zio, E.; Rui, K., Model uncertainty in accelerated degradation testing analysis, IEEE Trans. Reliab., 99, 1-13 (2017) |
| [36] | Kabir, G.; Tesfamariam, S.; Sadiq, R., Predicting water main failures using Bayesian model averaging and survival modelling approach, Reliab. Eng. Syst. Saf., 142, 498-514 (2015) |
| [37] | Dempster, A. P., A generalization of Bayesian inference, J. Roy. Stat. Soc. B, 30, 205-247 (1968) · Zbl 0169.21301 |
| [38] | Yang, D.; Ji, H. B.; Gao, Y. C., A robust D-S fusion algorithm for multi-target multi-sensor with higher reliability, Information Fusion, 47, 32-44 (2019) |
| [39] | Baraldi, P.; Zio, E., A comparison between probabilistic and Dempster-Shafer theory approaches to model uncertainty analysis in the performance assessment of radioactive waste repositories, Risk Anal., 30, 1139-1156 (2010) |
| [40] | Reinert, J. M.; Apostolakis, G. E., Including model uncertainty in risk-informed decision making, Ann. Nucl. Energy, 33, 354-369 (2006) |
| [41] | Riley, M. E., Evidence-based quantification of uncertainties induced via simulation-based modeling, Reliab. Eng. Syst. Saf., 133, 79-86 (2015) |
| [42] | Park, I.; Grandhi, R. V., Quantification of model-form and parametric uncertainty using evidence theory, Struct. Saf., 39, 44-51 (2012) |
| [43] | Jiang, C.; Zhang, Z.; Han, X.; Liu, J., A novel evidence-theory-based reliability analysis method for structures with epistemic uncertainty, Comput. Struct., 129, 1-12 (2013) |
| [44] | Zhang, Z.; Jiang, C.; Wang, G. G.; Han, X., First and second order approximate reliability analysis methods using evidence theory, Reliab. Eng. Syst. Saf., 137, 40-49 (2015) |
| [45] | Deng, Y., Deng entropy, Chaos, Solitons Fractals, 91, 549-553 (2016) · Zbl 1372.94368 |
| [46] | Jiang, W., A correlation coefficient for belief functions, Int. J. Approximate Reasoning, 103, 94-106 (2018) · Zbl 1448.68419 |
| [47] | Jiang, W.; Huang, C.; Deng, X., A new probability transformation method based on a correlation coefficient of belief functions, Int. J. Intell. Syst., 34, 6, 1337-1347 (2019) |
| [48] | Liu, Y.; Jiang, W., A new distance measure of interval-valued intuitionistic fuzzy sets and its application in decision making, Soft. Comput., 1-17 (2019) |
| [49] | Liu, D.; Wang, S. P.; Zhang, C.; Tomovic, M. M., Bayesian model averaging based reliability analysis method for monotonic degradation dataset based on inverse Gaussian process and Gamma process, Reliab. Eng. Syst. Saf., 18, 25-38 (2018) |
| [50] | Shafer, G., A Mathematical Theory of Evidence (1976), Princeton University Press: Princeton University Press Princeton, US · Zbl 0359.62002 |
| [51] | Sentz, K.; Ferson, S., Combination of Evidence in Dempster-Shafer Theory (2002), Sandia National Laboratories: Sandia National Laboratories Albuquerque, US |
| [52] | Yager, R. R.Y.; Liu, L. P., Classic Works of the Dempster-Shafer Theory of Belief Functions (2008), Springer: Springer Berlin, Germany · Zbl 1135.68051 |
| [53] | Yager, R. R.; Elmore, P.; Petry, F., Soft likelihood functions in combining evidence, Information Fusion, 36, 185-190 (2017) |
| [54] | Lefevre, E.; Colot, O.; Vannoorenberghe, P., Belief function combination and conflict management, Information Fusion, 3, 149-162 (2002) |
| [55] | (Smets, P.; Mamdani, E. H.; Dubois, D.; Prade, H., Non-Standard Logics for Automated Reasoning (1988), Academic Press: Academic Press London, UK) · Zbl 0669.03002 |
| [56] | Frikha, A., On the use of a multi-criteria approach for reliability estimation in belief function theory, Information Fusion, 18, 20-32 (2014) |
| [57] | A. Martin, A.L. Jousselme, C. Osswald, Conflict measure for the discounting operation on belief functions, In: U. Hanebeck (Ed.), Proc. 11th Int. Conf. Information Fusion, IEEE, Cologne, Germany, 2008, pp. 1-8. |
| [58] | Chen, L. Z.; Shi, W. K.; Deng, Y. Z.; Zhu, Z. F., A new fusion approach based on distance of evidences, J. Zhejiang Univ.-Sci. A, 6, 476-482 (2005) |
| [59] | W. Jiang, A. Zhang, Q. Yang, A new method to determine evidence discounting coefficient, In: D.S. Huang, D.C. WunschII, D.S. Levine, K.H. Jo(Eds.), Proc. 4th, Int. Conf. Intelligent Computing, Springer, Berlin, Germany, 2008, pp. 882-887. |
| [60] | Shannon, C. E., A mathematical theory of communication, Bell Syst. Tech. J., 27, 379-423 (1948) · Zbl 1154.94303 |
| [61] | K.T.P. Nguyen, Fouladirad M, A. Grall. Model selection for degradation modeling and prognosis with health monitoring data. Reliability Engineering & System Safety 169(2018) 105-116. |
| [62] | Meeker, W. Q.; Escobar, L. A., Statistical Methods for Reliability Data (1998), Wiley: Wiley New York, US · Zbl 0949.62086 |
| [63] | Wang, X., Wiener processes with random effects for degradation data, J. Multivariate Anal., 101, 340-351 (2010) · Zbl 1178.62091 |
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