當買方收到一批貨時需要判定是否允收此批貨物，用來判斷是否允收的方法可以分為三類，100%全檢、直接允收及允收抽樣計畫。直接允收風險過大，採取全檢又因耗時長且成本過高以至於不符合經濟效益。因此大多數的買方會採取允收抽樣計畫來進行判定，透過制定符合測試的抽樣計畫，利用抽取樣本得到的估計值來與訂定的允收條件做比對，若達到允收條件則允收該批貨物，反之則拒收。
隨著科技的日新月異，產品的可靠度越來越高，這使得在合理的時間內很難有效得到此類產品的故障數據。因此衍生出利用加速測試來收集產品的數據來克服此一障礙，加速壽命測試（Accelerated Life Testing , ALT）是將產品暴露在更艱困的環境下進行測試（例如高壓、高溫、高電流…等），來加速收集產品壽命的數據，但即使使用了加速壽命測試仍然可能難以在較短的測試時間內獲取足夠的故障數據。對於此類產品加速退化測試 (Accelerated Degradation Test , ADT) 是另一種有效的實驗方式，藉由在艱困的環境中測量產品中會隨著時間推移而退化的品質特性（Quality Characteristic , QC）（例如電路板上的電阻、LED的亮度…等）的退化數據來估算產品的使用壽命。
在上述的背景下，本研究受LED的數據啟發，希望建立一個加速退化測試退化模型的允收抽樣計畫，其中假設其退化過程服從Wiener衰退過程，並在模型中加入執行成本限制以及生產者及消費者所需承擔之抽樣風險使本模型更貼近現實情況。本模型的目的將探討滿足以上限制條件的情況下整個抽樣計畫所需的最低預算為多少，再根據最低預算求出樣本個數、記錄次數、記錄的時間間隔等決策變數使得估計值的變異數最小，再將結果與所訂定的允收標準做比對，判斷是否允收該項產品。最後以LED的數據來驗證此模型，最後再對其做敏感度分析。

When buyers receive a batch of goods, they need to decide whether to accept or reject them. Three methods are commonly used: 100% inspection, direct acceptance, and acceptance sampling plans. However, direct acceptance poses high risks, while 100% inspection is time-consuming and costly. Hence, most buyers opt for acceptance sampling plans. These plans involve developing suitable sampling methods, comparing estimated values from samples with acceptance criteria, and accepting or rejecting the batch accordingly.
With advancing technology, product reliability has increased, making it challenging to collect sufficient failure data in a reasonable timeframe. To overcome this, accelerated life testing (ALT) exposes products to harsher conditions to accelerate data collection on product lifespan. But obtaining enough data in a shorter testing time remains difficult. Accelerated degradation testing (ADT) offers an effective alternative by measuring the degradation of quality characteristics over time in harsh environments.
Inspired by LED data, this study aims to establish an acceptance sampling plan for constant-stress accelerated degradation testing models. The model assumes Wiener degradation and considers cost constraints and sampling risks for both producers and consumers. The objective is to determine the minimum budget required for the sampling plan and decide the number of samples, recorded measurements, and time intervals to minimize estimated value variance. The results are compared with acceptance criteria to decide whether to accept the product. Finally, the model is validated using LED data, followed by sensitivity analysis.

Amini, M., Shemehsavar, S., & Pan, Z. Q. (2016). Optimal Design for Step-Stress Accelerated Test with Random Discrete Stress Elevating Times Based on Gamma Degradation Process. Quality and Reliability Engineering International, 32(7), 2391-2402. https://doi.org/10.1002/qre.1943
Aslam, M., & Jun, C. H. (2009). A group acceptance sampling plan for truncated life test having Weibull distribution. Journal of Applied Statistics, 36(9), 1021-1027, Article Pii 915087967. https://doi.org/10.1080/02664760802566788
Aslam, M., Wu, C.-W., Azam, M., & Jun, C.-H. (2013). Variable sampling inspection for resubmitted lots based on process capability index Cpk for normally distributed items. Applied Mathematical Modelling, 37(3), 667-675. https://doi.org/10.1016/j.apm.2012.02.048
Aslam, M., Yen, C. H., Chang, C. H., Al-Marshadi, A. H., & Jun, C. H. (2019). A Multiple Dependent State Repetitive Sampling Plan Based on Performance Index for Lifetime Data with Type II Censoring. Ieee Access, 7, 49377-49391. https://doi.org/10.1109/access.2019.2909568
Balakrishnan, N., Leiva, V., & Lopez, J. (2007). Acceptance sampling plans from truncated life tests based on the generalized Birnbaum-Saunders distribution. Communications in Statistics-Simulation and Computation, 36(3), 643-656. https://doi.org/10.1080/03610910701207819
Balamurali, S., & Jun, C. H. (2007). Multiple dependent state sampling plans for lot acceptance based on measurement data. European Journal of Operational Research, 180(3), 1221-1230. https://doi.org/10.1016/j.ejor.2006.05.025
Chen, Z., Li, S., & Pan, E. S. (2016). Optimal Constant-Stress Accelerated Degradation Test Plans Using Nonlinear Generalized Wiener Process. Mathematical Problems in Engineering, 2016, Article 9283295. https://doi.org/10.1155/2016/9283295
Doksum, K. A., & Hoyland, A. (1992). MODELS FOR VARIABLE-STRESS ACCELERATED LIFE TESTING EXPERIMENTS BASED ON WIENER-PROCESSES AND THE INVERSE GAUSSIAN DISTRIBUTION. Technometrics, 34(1), 74-82. https://doi.org/10.2307/1269554
Dube, S., Pradhan, B., & Kundu, D. (2011). Parameter estimation of the hybrid censored log-normal distribution. Journal of Statistical Computation and Simulation, 81(3), 275-287, Article Pii 919678568. https://doi.org/10.1080/00949650903292650
Elsayed, E. A. (2012). Overview of Reliability Testing. Ieee Transactions on Reliability, 61(2), 282-291. https://doi.org/10.1109/tr.2012.2194190
Hu, C. H., Lee, M. Y., & Tang, J. (2015). Optimum step-stress accelerated degradation test for Wiener degradation process under constraints. European Journal of Operational Research, 241(2), 412-421. https://doi.org/10.1016/j.ejor.2014.09.003
Ibrahim, M. S., Fan, J. J., Yung, W. K. C., Wu, Z. Y., & Sun, B. (2019). Lumen Degradation Lifetime Prediction for High-Power White LEDs Based on the Gamma Process Model. Ieee Photonics Journal, 11(6), Article 8201316. https://doi.org/10.1109/jphot.2019.2950472
Kantam, R. R. L., Rosaiah, K., & Rao, G. S. (2001). Acceptance sampling based on life tests: log-logistic model. Journal of Applied Statistics, 28(1), 121-128. https://doi.org/10.1080/02664760120011644
Li, X. Y., Gao, P. F., & Sun, F. Q. (2015). Acceptance sampling plan of accelerated life testing for lognormal distribution under time-censoring. Chinese Journal of Aeronautics, 28(3), 814-821. https://doi.org/10.1016/j.cja.2015.03.007
Liao, C. M., & Tseng, S. T. (2006). Optimal design for step-stress accelerated degradation tests. Ieee Transactions on Reliability, 55(1), 59-66. https://doi.org/10.1109/tr.2005.863811
Liao, H., & Elsayed, E. A. (2006). Reliability inference for field conditions from accelerated degradation testing. Naval Research Logistics, 53(6), 576-587. https://doi.org/10.1002/nav.20163
Liu, H. Z., Huang, J. C., Guan, Y. H., & Sun, L. (2019). Accelerated Degradation Model of Nonlinear Wiener Process Based on Fixed Time Index. Mathematics, 7(5), Article 416. https://doi.org/10.3390/math7050416
Lu, C. J., & Meeker, W. Q. (1993). USING DEGRADATION MEASURES TO ESTIMATE A TIME-TO-FAILURE DISTRIBUTION. Technometrics, 35(2), 161-174. https://doi.org/10.2307/1269661
Ma, H. M., & Meeker, W. Q. (2008). Optimum step-stress accelerated life test plans for log-location-scale distributions. Naval Research Logistics, 55(6), 551-562. https://doi.org/10.1002/nav.20299
Mahmoud, M., Nassar, M. M., & Aefa, M. A. (2020). Bayesian Estimation and Prediction Based on Progressively First Failure Censored Scheme from a Mixture of Weibull and Lomax Distributions. Pakistan Journal of Statistics and Operation Research, 16(2), 357-372. https://doi.org/10.18187/pjsor.v16i2.2442
Seo, J. H., Jung, M., & Kim, C. M. (2009). Design of accelerated life test sampling plans with a nonconstant shape parameter. European Journal of Operational Research, 197(2), 659-666. https://doi.org/10.1016/j.ejor.2008.07.009
Si, X. S., Wang, W. B., Hu, C. H., Zhou, D. H., & Pecht, M. G. (2012). Remaining Useful Life Estimation Based on a Nonlinear Diffusion Degradation Process. Ieee Transactions on Reliability, 61(1), 50-67. https://doi.org/10.1109/tr.2011.2182221
Sohn, S. Y., & Jang, J. S. (2001). Acceptance sampling based on reliability degradation data. Reliability Engineering & System Safety, 73(1), 67-72. https://doi.org/10.1016/s0951-8320(01)00031-x
Tsai, C. C., Lin, C. T., & Balakrishnan, N. (2015). Optimal Design for Accelerated-Stress Acceptance Test Based on Wiener Process. Ieee Transactions on Reliability, 64(2), 603-612. https://doi.org/10.1109/tr.2015.2410191
Wang, H. W., Xu, T. X., & Mi, Q. L. (2015). Lifetime prediction based on Gamma processes from accelerated degradation data. Chinese Journal of Aeronautics, 28(1), 172-179. https://doi.org/10.1016/j.cja.2014.12.015
Whitmore, G. A., & Schenkelberg, F. (1997). Lifetime Data Analysis, 3(1), 27-45. https://doi.org/10.1023/a:1009664101413
Wu, S. J., & Kus, C. (2009). On estimation based on progressive first-failure-censored sampling. Computational Statistics & Data Analysis, 53(10), 3659-3670. https://doi.org/10.1016/j.csda.2009.03.010
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.2014.2315773
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.2063
Yu, H. F., & Tseng, S. T. (1999). Designing a degradation experiment. Naval Research Logistics (NRL), 46(6), 689-706.
Zhao, X., Wang, S. Q., & Sun, L. P. (2019). Single and Sequential Sampling Plans for Multi-Attribute Products and Multi-Class Lot in Reliability Test. Ieee Access, 7, 81145-81155. https://doi.org/10.1109/access.2019.2923316