隨著科技與製造技術的持續進步，消費者對於產品可靠性與品質的要求日益提高，如何提升產品品質又同時控制成本，成為製造商面臨的重要課題。在產品的生產過程中，製造商可透過各種不同方法以提高產品良率。其中，在產品出貨前，製造商可利用預燒測試（Burn-in test）模擬嚴苛環境條件加速產品老化，藉此篩選早期失效的不良品，進而提升出貨品質與市場信任度，同時降低後續維修與召回成本。
然而，傳統的預燒分類方法多以單一品質特徵作為判斷依據，未能充分考慮多品質特徵間的退化相關性，導致誤判風險與成本增加。過往研究指出，若能為產品配置合適的退化模型，可更真實地模擬產品的退化行為，獲得更準確的可靠度資訊。若進一步結合最適分類法則，並同時考量先驗機率與誤判成本，則可發展出使總分類成本最小化的預燒策略，兼顧品質與經濟效益。
因此，本研究提出一套基於二維 Wiener 退化過程的預燒分類方法，利用二維退化模型描述兩個品質特徵的聯合退化行為，以更完整地捕捉特徵間的相關性。再透過線性投影技術，將多維退化資訊轉換為一維指標，簡化後續分類分析，並結合成本敏感判別分析，建立一套兼具數學解析性與實務應用性的分類決策架構。本研究在不同共變異數假設下推導最佳分類閾值與預燒時間，以最小化總期望成本為目標，同時考量誤判成本與測試成本，最終提出最適化決策方案，作為製造商預燒測試與品質決策的重要參考。

With the continuous advancement of technology and manufacturing techniques, consumers increasingly demand higher product reliability and quality. How to improve quality while controlling costs has become a critical challenge for manufacturers. Among various approaches, burn-in testing accelerates product aging under harsh conditions to screen out early failures, thereby enhancing quality and market trust while reducing recall costs.
However, traditional burn-in classification methods typically rely on a single quality characteristic, failing to consider the degradation dependencies among multiple attributes, which increases misclassification risks and costs. Prior studies indicate that adopting appropriate degradation models can better simulate actual product behavior and provide more accurate reliability information. Furthermore, integrating optimal classification rules with prior probabilities and misclassification costs can develop strategies that minimize total classification costs, balancing quality and economic efficiency. Therefore, this study proposes a burn-in classification method based on a two-dimensional Wiener degradation process to describe the joint degradation behavior of two quality characteristics, better capturing their interdependencies.
Using linear projection, multi-dimensional degradation information is transformed into a one-dimensional indicator to simplify subsequent analysis. Combined with cost-sensitive discriminant analysis, this approach establishes a mathematically tractable and practical decision framework. Optimal classification thresholds and burn-in times are derived to minimize total expected costs, providing manufacturers with important guidance for burn-in testing and quality decision-making.

蔡志群. (2009). Gamma 衰變過程之設計與分析. 清華大學統計學研究所學位論文, 2009, 1-98.
Chen, N., Ye, Z. S., Xiang, Y., & Zhang, L. (2015). Condition-based maintenance using the inverse Gaussian degradation model. European Journal of Operational Research, 243(1), 190-199.
Crowder, M., & Lawless, J. (2007). On a scheme for predictive maintenance. European Journal of Operational Research, 176(3), 1713-1722.
Jensen, F., & Petersen, N. E. (1982). Burn-in. A Wiley-Interscience Publication.
Jiang, P., Wang, B. X., Wang, X., & Qin, S. (2020). Optimal plan for Wiener constant-stress accelerated degradation model. Applied Mathematical Modelling, 84, 191-201.
Jin, G., & Matthews, D. (2014). Measurement plan optimization for degradation test design based on the bivariate Wiener process. Quality and Reliability Engineering International, 30(8), 1215-1231.
Johnson, D. E. (1998). Applied multivariate methods for data analysts.
Johnson, R. A., & Wichern, D. W. (2007). Applied multivariate statistical analysis.
Lawless, J., & Crowder, M. (2004). Covariates and random effects in a gamma process model with application to degradation and failure. Lifetime data analysis, 10, 213-227.
LEEMIS, L. M., & BENEKE, M. (1990). Burn-in models and methods： a review. IIE transactions, 22(2), 172-180.
Li, X., Liu, Z., Wang, Y., & Li, M. (2019). Optimal burn-in strategy for two-dimensional warranted products considering preventive maintenance. International Journal of Production Research, 57(17), 5414-5431.
Pan, Z., Balakrishnan, N., Sun, Q., & Zhou, J. (2013). Bivariate degradation analysis of products based on Wiener processes and copulas. Journal of Statistical Computation and Simulation, 83(7), 1316-1329.
Park, C., & Padgett, W. J. (2005). Accelerated degradation models for failure based on geometric Brownian motion and gamma processes. Lifetime Data Analysis, 11, 511-527.
Peng, C. Y., & Tseng, S. T. (2009). Mis-specification analysis of linear degradation models. IEEE Transactions on Reliability, 58(3), 444-455.
Sharma, S. (1995). Applied multivariate techniques. John Wiley & Sons, Inc..
Tsai, C. C., Tseng, S. T., & Balakrishnan, N. (2010). Optimal burn-in policy for highly reliable products using gamma degradation process. IEEE Transactions on Reliability, 60(1), 234-245.
Tseng, S. T., Tang, J., & Ku, I. H. (2003). Determination of burn‐in parameters and residual life for highly reliable products. Naval Research Logistics (NRL), 50(1), 1-14.
Wang, X. L., Guo, B., Cheng, Z. J., & Jiang, P. (2013). Residual life estimation based on bivariate Wiener degradation process with measurement errors. Journal of Central South University, 20(7), 1844-1851.
Wang, X., & Xu, D. (2010). An inverse Gaussian process model for degradation data. Technometrics, 52(2), 188-197.
Wang, X., Guo, B., & Cheng, Z. (2014). Residual life estimation based on bivariate Wiener degradation process with time-scale transformations. Journal of Statistical Computation and Simulation, 84(3), 545-563.
Whitmore, G. A., Crowder, M. J., & Lawless, J. F. (1998). Failure inference from a marker process based on a bivariate Wiener model. Lifetime data analysis, 4, 229-251.
Xu, A., Shen, L., Wang, B., & Tang, Y. (2018). On modeling bivariate Wiener degradation process. IEEE Transactions on Reliability, 67(3), 897-906.
Yan, B., Wang, H., Ma, X., & Wang, Y. (2022). Correlation-driven bivariate Wiener process modeling subjects to random effects. In 12th International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (QR2MSE 2022) (Vol. 2022, pp. 152-159). IET.
Yang, C. H., Hsu, Y. H., & Hu, C. H. (2024). Mis-specification analyses and optimum degradation test plan for Wiener and inverse Gaussian processes. Communications in Statistics-Theory and Methods, 53(2), 700-717.
Ye, Z. S., & Chen, N. (2014). The inverse Gaussian process as a degradation model. Technometrics, 56(3), 302-311.
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.
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.
Ye, Z. S., Xie, M., Tang, L. C., & Shen, Y. (2012). Degradation-based burn-in planning under competing risks. Technometrics, 54(2), 159-168.
Zhai, Q., Ye, Z. S., Yang, J., & Zhao, Y. (2016). Measurement errors in degradation-based burn-in. Reliability Engineering & System Safety, 150, 126-135.
Zhang, Z., Si, X., Hu, C., & Lei, Y. (2018). Degradation data analysis and remaining useful life estimation： A review on Wiener-process-based methods. European Journal of Operational Research, 271(3), 775-796.