預燒試驗中，衰退試驗係使用產品特性的衰退資料預測失效、衡量好壞。由於衰退試驗非直接觀察產品的失效，適合應用在現今許多高可靠度產品上。合適的衰退試驗可為製造商帶來良好的品質提升效果，已有眾多學者提出相關研究。
至今，「設計最佳衰退試驗」相關之研究大致分為兩類，第一類考量「最大化平均剩餘壽命」，第二類則考量「最小化成本」。僅考量上述任一面向可能有失公允，因此有學者在壽命試驗中提出考量「最小化單位時間的預燒期望成本（Minimize Burn-in Cost Per Unit Time）」，以同時衡量剩餘使用壽命及相關成本。本研究以Wiener過程為例，針對衰退試驗，提出與試驗時間（Burn-in time）及判斷標準（Cut-off level）有關之可靠度函數及平均剩餘壽命估計法。考量試驗本身的設定對於通過率的影響，並考量保固成本，使決策更貼近實際應用。最終提出於衰退試驗考量「最小化單位時間的預燒期望成本」之方法，亦提供了衰退試驗進行加速時的剩餘使用壽命、相關成本等估計方式，及決策最佳加速衰退試驗之方法。
本研究使用一案例，分別使用傳統搜尋法及基因演算法求解，驗證此二法之結果相同。進一步，將此個案分別以「最大化平均剩餘壽命」、「最小化成本」設計最佳試驗，且將本研究提出的模型與此二者相互評比，得出本研究提出的模型在產品分類上有良好的表現。然而，目前仍未找到含有加速成本數據的實際案例，待未來有實際案例方能驗證。

In the degradation test, without directly observing the products, the data of product characteristics can predict failure and evaluate quality. Therefore, it is suitable for many high-reliability products.
Researches about the optimal degradation test can be roughly divided into two categories. One considers "maximize mean residual life (MRL)", and the other considers "minimize costs." However, it may be unfair to consider only any of the above aspects. In this research, we put forward "minimize mean burn-in cost per unit time" to consider the residual useful life and related costs simultaneously. Wiener process was used as a demonstration.
For the degradation test, we proposed a reliability function related to both burn-in time and cut-off level to estimate the MRL. In addition, we considered the test's setting impact on the probability of passing, and took the field failure cost into account to make the decision closer to the actual application. Finally, a degradation test model and designing method was proposed. We also provided the optimal test designing method for the accelerated degradation test.
A case was used and solved using traditional search methods and genetic algorithms respectively. It verified that the two methods have the same result. Further, we changed the objective function to "maximize MRL" and "minimize costs". Comparing the model proposed in this study with the two, it is concluded that the model proposed in this study has a good performance in product classification.

[1] 林揚承、李佩熹和童超塵(2009). 決定加速預燒試驗的最佳時間和溫度條件. 品質學報, 16(4), 281-290.
[2] Banjevic, D. (2009). Remaining Useful Life in Theory and Practice. Metrika, 69(2-3), 337-349.
[3] Chang, D. S. (2000). Optimal Burn-in Decision for Products with an Unimodal Failure Rate Function. European Journal of Operational Research, 126(3), 534-540.
[4] Chhikara, R. S., & Folks, J. L. (1977). The Inverse Gaussian Distribution as a Lifetime Model. Technometrics, 19(4), 461-468.
[5] Fan, J. J., Yung, K. C., & Pecht, M. (2012). Lifetime Estimation of High-Power White LED Using Degradation-Data-Driven method. IEEE Transactions on Device and Materials Reliability, 12(2), 470-477.
[6] Hall, W., & Wellner, J. A. (1981). Mean Residual Life. Statistics and Related Topics, 169, 184.
[7] Kim, T., & Kuo, W. (1998). Optimal Burn‐in Decision Making. Quality and Reliability Engineering International, 14(6), 417-423.
[8] Kuehnel, W., & Sherman, S. (1994). A Surface Micromachined Silicon Accelerometer with On-Chip Detection Circuitry. Sensors and Actuators A: Physical, 45(1), 7-16.
[9] Kuo, W. (1984). Reliability Enhancement through Optimal Burn-in. IEEE Transactions on Reliability, 33(2), 145-156.
[10] Lawrence, M. J. (1966). An Investigation of the Burn-in Problem. Technometrics, 8(1), 61-71.
[11] Lee, P. H., Torng, C. C., & Lin, Y. C. (2011). Determination of the Optimal Accelerated Burn-In Time Under Arrhenius–Lognormal Distribution Assumption. Applied Mathematical Modelling, 35(8), 4023-4030.
[12] Leemis, L. M., & Beneke, M. (1990). Burn-in Models and Methods :a Review. IIE Transactions, 22(2), 172-180.
[13] 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.
[14] Mosayebi Omshi, E., & Shemehsavar, S. (2018). An Optimal Burn‐in policy Based on a Degradation Model. Applied Stochastic Models in Business and Industry, 34(4), 486-498.
[15] Nelson, W. B. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analysis (Vol. 344): John Wiley & Sons.
[16] Nguyen, D. G., & Murthy, D. N. (1982). Optimal Burn-in Time to Minimize Cost for Products Sold under Warranty. IIE transactions, 14(3), 167-174.
[17] Park, J. I., & Bae, S. J. (2010). Direct Prediction Methods on Lifetime Distribution of Organic Light-Emitting Diodes From Accelerated Degradation Tests. IEEE Transactions on Reliability, 59(1), 74-90.
[18] Peng, H., Feng, Q., & Coit, D. W. (2009). Simultaneous Quality and Reliability Optimization for Microengines Subject to Degradation. IEEE Transactions on Reliability, 58(1), 98-105.
[19] Plesser, K. T., & Field, T. O. (1977). Cost-Optimized Burn-in Duration for Repairable Electronic Systems. IEEE Transactions on Reliability, 26(3), 195-197.
[20] Schmitt, L. M. (2001). Theory of Genetic Algorithms. Theoretical Computer Science, 259(1-2), 1-61.
[21] Si, X. S., Wang, W., Hu, C. H., & Zhou, D. H. (2011). Remaining Useful Life Estimation–a Review on the Statistical Data Driven Approaches. European Journal of Operational Research, 213(1), 1-14.
[22] Si, X. S., Wang, W. B., Chen, M. Y., Hu, C. H., & Zhou, D. H. (2013a). A Degradation Path-Dependent Approach for Remaining Useful Life Estimation with an Exact and Closed-Form Solution. European Journal of Operational Research, 226(1), 53-66.
[23] Si, X. S., Wang, W. B., Hu, C. H., Chen, M. Y., & Zhou, D. H. (2013b). A Wiener-Process-Based Degradation Model with a Recursive Filter Algorithm for Remaining Useful Life Estimation. Mechanical Systems and Signal Processing, 35(1-2), 219-237.
[24] Tang, L. C., Yang, G. Y., & Xie, M. (2004). Planning of Step-Stress Accelerated Degradation Test. Paper presented at the Annual Symposium Reliability and Maintainability, 2004 - RAMS.
[25] 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.
[26] Tseng, S. T., Tang, J., & Ku, I. H. (2003). Determination of Burn‐in Parameters and Residual Life for Highly Reliable Products. Naval Research Logistics, 50(1), 1-14.
[27] Unal, N., & Weschsung, R. (1998). Inkjet Printheads: an Example of MST Market Reality. Micromachine Devices, 3(1), 1-6.
[28] Wang, F. K., & Chu, T. P. (2012). Lifetime Predictions of LED-Based Light Bars by Accelerated Degradation Test. Microelectronics Reliability, 52(7), 1332-1336.
[29] Wang, X., & Xu, D. H. (2010). An Inverse Gaussian Process Model for Degradation Data. Technometrics, 52(2), 188-197.
[30] Watson, G. S., & Wells, W. T. (1961). On the Possibility of Improving the Mean Useful Life of Items by Eliminating those with Short Lives. Technometrics, 3(2), 281-298.
[31] Whitbeck, C. W., & Leemis, L. M. (1989). Component vs System Burn-in Techniques for Electronic Equipment. IEEE Transactions on reliability, 38(2), 206-209.
[32] Xu, Z. B., Hong, Y. L., & Jin, R. (2016). Nonlinear General Path Models for Degradation Data with Dynamic Covariates. Applied Stochastic Models in Business and Industry, 32(2), 153-167.
[33] 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.
[34] 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.
[35] Zhai, Q., Ye, Z.-S., Yang, J., & Zhao, Y. (2016). Measurement Errors in Degradation-Based Burn-in. Reliability Engineering & System Safety, 150, 126-135.
[36] Zhang, Y. (2015). Wiener and Gamma Processes Overview for Degradation Modelling and Prognostic. (Master's thesis), NTNU.