Remaining Useful Life (RUL) is one of the most important indicators to detect a component failure. RUL can be predicted by historical data by adopting a model-based method. The stochastic process models have become the most popular way to model degradation data for high-quality products, such as the Wiener process, gamma process and inverse Gaussian process. However, this leads to poor reliability assessment if the model is misspecified. Application of the Tweedie exponential dispersion (TED) process, including the above-mentioned classical stochastic processes as special cases, transforms the model selection problem into a parameter estimation problem dexterously. In this paper, we propose a TED process with random drifts for degradation data and a TED process with random drifts and covariates for accelerated degradation data. A hierarchical Bayesian method is adopted to estimate the parameters of the proposed models. We also derive the failure-time distribution and the remaining useful life distribution for the proposed models. The simulation study shows that the proposed model outperforms the wrongly specified models. Two illustrative examples demonstrate the performance of the proposed TED process with random drifts and the TED process with random drifts and covariates.

References

• Bae, S. J., Kuo, W., & Kvam, P. H. (2007). Degradation models and implied lifetime distributions. Reliability Engineering & System Safety, 92(5), 601–608. https://doi.org/10.1016/j.ress.2006.02.002
• Balakrishnan, N., & Kundu, D. (2019). Birnbaum–Saunders distribution: A review of models, analysis, and applications. Applied Stochastic Models in Business and Industry, 35(1), 4–49. https://doi.org/10.1002/asmb.v35.1
• Bernardo, J. M., & Smith, A. (1994). Bayesian Theory. JohnWiley & Sons.
• Chen, Z., Xia, T., Li, Y., & Pan, E. (2019). Tweedie exponential dispersion processes for degradation modeling, prognostic, and accelerated degradation test planning. IEEE Transactions on Reliability, 69(3), 887–902. https://doi.org/10.1109/TR.24
• Chen, Z., Xia, T., Li, Y., & Pan, E. (2021). Random-effect models for degradation analysis based on nonlinear Tweedie exponential-dispersion processes. IEEE Transactions on Reliability, 71(1), 47–62. https://doi.org/10.1109/TR.2021.3107050
• Daniels, H. E. (1954). Saddlepoint approximations in statistics. The Annals of Mathematical Statistics, 25(4), 631–650. https://doi.org/10.1214/aoms/1177728652
• dos Santos, T. R., & Colosimo, E. A. (2015). A modified approximate method for analysis of degradation data. Journal of Applied Statistics, 42(6), 1322–1331. https://doi.org/10.1080/02664763.2014.999651
• Duan, F., & Wang, G. (2018). Exponential-dispersion degradation process models with random effects and covariates. IEEE Transactions on Reliability, 67(3), 1128–1142. https://doi.org/10.1109/TR.24
• Dunn, P. K., & Smyth, G. K. (2008). Evaluation of Tweedie exponential dispersion model densities by Fourier inversion. Statistics and Computing, 18(1), 73–86. https://doi.org/10.1007/s11222-007-9039-6
• Fang, G., Pan, R., & Wang, Y. (2022). Inverse Gaussian processes with correlated random effects for multivariate degradation modeling. European Journal of Operational Research, 300(3), 1177–1193. https://doi.org/10.1016/j.ejor.2021.10.049
• Hong, L., & Ye, Z. (2017). When is acceleration unnecessary in a degradation test?Statistica Sinica, 27(3), 1461–1483.
• Jørgensen, B. (1986). Some properties of exponential dispersion models. Scandinavian Journal of Statistics, 13(3), 187–197.
• Jørgensen, B. (1997). The Theory of Dispersion Models. CRC Press.
• Lawless, J., & Crowder, M. (2004). Covariates and random effects in a Gamma process model with application to degradation and failure. Lifetime Data Analysis, 10(3), 213–227. https://doi.org/10.1023/B:LIDA.0000036389.14073.dd
• Lim, H., & Yum, B.-J. (2011). Optimal design of accelerated degradation tests based on Wiener process models. Journal of Applied Statistics, 38(2), 309–325. https://doi.org/10.1080/02664760903406488
• Limon, S., Yadav, O. P., & Liao, H. (2017). A literature review on planning and analysis of accelerated testing for reliability assessment. Quality and Reliability Engineering International, 33(8), 2361–2383. https://doi.org/10.1002/qre.v33.8
• Lu, C. J., & Meeker, W. O. (1993). Using degradation measures to estimate a time-to-failure distribution. Technometrics, 35(2), 161–174. https://doi.org/10.1080/00401706.1993.10485038
• Luo, C., Shen, L., & Xu, A. (2022). Modelling and estimation of system reliability under dynamic operating environments and lifetime ordering constraints. Reliability Engineering & System Safety, 218,108136. https://doi.org/10.1016/j.ress.2021.108136
• Meeker, W. Q., Escobar, L. A., & Lu, C. J. (1998). Accelerated degradation tests: Modeling and analysis. Technometrics, 40(2), 89–99. https://doi.org/10.1080/00401706.1998.10485191
• Peng, C.-Y. (2015). Inverse Gaussian processes with random effects and explanatory variables for degradation data. Technometrics, 57(1), 100–111. https://doi.org/10.1080/00401706.2013.879077
• Shat, H. (2024). Optimal design of stress levels in accelerated degradation testing for multivariate linear degradation models. Journal of Applied Statistics, 51(3), 534–554. https://doi.org/10.1080/02664763.2022.2140332
• Shi, Y., & Meeker, W. Q. (2011). Bayesian methods for accelerated destructive degradation test planning. IEEE Transactions on Reliability, 61(1), 245–253. https://doi.org/10.1109/TR.2011.2170115
• Tseng, S.-T., & Lee, I.-C. (2016). Optimum allocation rule for accelerated degradation tests with a class of exponential-dispersion degradation models. Technometrics, 58(2), 244–254. https://doi.org/10.1080/00401706.2015.1033109
• Wang, X. (2008). A pseudo-likelihood estimation method for nonhomogeneous Gamma process model with random effects. Statistica Sinica, 18(3), 1153–1163.
• Wang, X. (2010). Wiener processes with random effects for degradation data. Journal of Multivariate Analysis, 101(2), 340–351. https://doi.org/10.1016/j.jmva.2008.12.007
• Yang, G. (2007). Life Cycle Reliability Engineering. John Wiley & Sons.
• Ye, Z.-S., Chen, L.-P., Tang, L. C., & Xie, M. (2014). Accelerated degradation test planning using the inverse Gaussian process. IEEE Transactions on Reliability, 63(3), 750–763. https://doi.org/10.1109/TR.24
• Ye, Z.-S., & Xie, M. (2015). Stochastic modelling and analysis of degradation for highly reliable products. Applied Stochastic Models in Business and Industry, 31(1), 16–32. https://doi.org/10.1002/asmb.v31.1
• Zhou, S., & Xu, A. (2019). Exponential dispersion process for degradation analysis. IEEE Transactions on Reliability, 68(2), 398–409. https://doi.org/10.1109/TR.24

To cite this article: Pingping Wang & Yincai Tang (29 Sep 2025): Remaining useful life prediction based on exponential dispersion process with random drifts, Statistical Theory and Related Fields, DOI: 10.1080/24754269.2025.2555043

To link to this article: https://doi.org/10.1080/24754269.2025.2555043