簡易檢索 / 詳目顯示

回結果列表
研究生： 蕭鈺承
Xiao, Yu-Cheng
論文名稱： 伽瑪加速衰變試驗之標準化大中取小設計
Standardized Minimax Design for Gamma Accelerated Degradation Tests
指導教授： 李宜真
Lee, I-Chen
學位類別： 碩士
Master
系所名稱： 管理學院 - 統計學系
Department of Statistics
論文出版年： 2026
畢業學年度： 114
語文別： 英文
論文頁數： 50
中文關鍵詞： 伽瑪加速衰變試驗 、標準化大中取小設計 、參數不確定性 、粒子群最佳化 、精確設計
外文關鍵詞： Gamma accelerated degradation tests, Standardized minimax design, Parameter uncertainty, Particle swarm optimization, Exact design
相關次數： 點閱：110  下載：4 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 對於高可靠度產品而言，在有限試驗期間內於正常使用條件下觀察到失效事件通常相當困難。加速衰變試驗提供一種有效的方法，透過在較高應力水準下蒐集衰變資料，以推估產品壽命。在伽瑪加速衰變試驗的規劃中，局部最適設計常被用來提升壽命分位數估計的精確度。然而，此類設計依賴於事先指定的模型參數，而這些參數在試驗規劃階段通常是未知的。為了處理參數不確定性的問題，本論文針對伽瑪加速衰變試驗建立一套標準化大中取小設計架構。此架構利用漸近樣本比率，在合理的參數區域內評估設計表現，並使設計能夠抵禦最差情境下的影響。在本研究中，應力水準、檢測間隔以及分配比例皆同時被視為設計變數。由於所形成的準則涉及巢狀且不可微分的最佳化問題，本論文發展一套以粒子群最佳化為基礎的混合演算法，以求得近似標準化大中取小設計。為了實際執行試驗，進一步採用逐步網格搜尋演算法，將近似設計轉換為精確整數試驗計畫。數值研究與模擬結果顯示，所提出之設計在參數不確定性下能提供穩定的壽命分位數估計，且精確設計能良好維持其對應近似設計的表現。

    For highly reliable products, observing failures under normal-use conditions within a limited testing period is often difficult. Accelerated degradation tests (ADTs) provide an efficient approach for collecting degradation measurements under elevated stress levels and inferring product lifetime. In Gamma ADT planning, locally optimal designs are commonly used to improve the precision of lifetime quantile estimation. However, these designs depend on pre-specified model parameters, which are usually unknown at the planning stage. To address parameter uncertainty, this thesis develops a standardized minimax design framework for Gamma ADTs. The proposed framework evaluates design performance over a plausible parameter region using the asymptotic sample ratio and protects the design against worst-case scenarios. Stress levels, inspection intervals, and allocation proportions are simultaneously treated as decision variables. Since the resulting criterion involves a nested and non-differentiable optimization problem, a PSO-based hybrid algorithm is developed to obtain approximate standardized minimax designs. For practical implementation, a stepwise grid search algorithm is further applied to convert approximate designs into exact integer test plans. Numerical studies and simulations show that the proposed designs provide stable lifetime quantile estimation under parameter uncertainty, and the exact designs closely maintain the performance of their corresponding approximate designs.

    中文摘要 i Abstract ii 致謝 iii Contents iv List of Tables vi List of Figures vii 1 Introduction 1 1.1 Background 1 1.2 Experimental Design in ADTs 1 1.2.1 Modeling Approaches 1 1.2.2 Decision Variables 2 1.2.3 Design Methodologies 3 1.3 Particle Swarm Optimization and Hybrid Algorithms 3 1.4 Research Motivation 4 1.5 Thesis Organization 4 2 Design Framework for Gamma ADTs 6 2.1 Design Settings 6 2.2 Gamma ADT Model 7 2.3 Design Criteria 9 2.3.1 Asymptotic Variance 9 2.3.2 Asymptotic Sample Ratio 11 2.3.3 Equivalence Theorem 12 3 Computational Algorithms 14 3.1 Particle Swarm Optimization 14 3.2 PSO-based Hybrid Algorithm for Standardized Minimax Designs 15 3.2.1 Two-layer Optimization Formulation 15 3.2.2 Outer PSO Search 16 3.2.3 Inner Maximization 16 3.3 Stepwise Grid Search Algorithm for Exact Design 18 4 Numerical Results and Simulation Study 22 4.1 Stress Relaxation Data and Design Settings 22 4.2 Approximate Design Results 24 4.3 Exact Design Results 26 4.4 Simulation Study 28 4.4.1 Performance of Approximate Designs 28 4.4.2 Comparison Between Approximate and Exact Designs 30 5 Concluding Remarks 33 References 35 Appendix A: Derivation of Fisher Information 38 Appendix B: Derivation of Reparameterized Asymptotic Variance 41

    Boulanger, M. and Escobar, L. A. (1994). Experimental design for a class of accelerated degradation tests. Technometrics, 36(3):260–272.
    Chen, P.-Y. and Chen, R.-B. (2025). Globpso: Swarm Intelligence Optimization. R Package Version 1.3.1.
    Chen, P.-Y., Chen, R.-B., Tung, H.-C., and Wong, W. K. (2017). Standardized maximim d-optimal designs for enzyme kinetic inhibition models. Chemometrics and Intelligent Laboratory Systems, 169:79–86.
    Chen, P.-Y., Chen, R.-B., and Wong, W. K. (2023). Particle swarm optimization for finding efficient longitudinal exact designs for nonlinear models. The New England Journal of Statistics in Data Science, 1:299–313.
    Chen, R.-B., Chang, S.-P., Wang, W., Tung, H.-C., and Wong, W. K. (2015). Minimax optimal designs via particle swarm optimization methods. Statistics and Computing, 25(5):975–988.
    Chen, R.-B., Chen, P.-Y., Hsu, C.-L., and Wong, W. K. (2020). Hybrid algorithms for generating optimal designs for discriminating multiple nonlinear models under various error distributional assumptions. PLoS ONE, 15(10):e0239864.
    Ginebra, J. and Sen, A. (1998). Minimax approach to accelerated life tests. IEEE Transactions on Reliability, 47(3):261–267.
    Huang, M.-N. L. and Lin, C.-S. (2006). Minimax and maximin efficient designs for estimating the location-shift parameter of parallel models with dual responses. Journal of Multivariate Analysis, 97(1):198–210.
    Kennedy, J. and Eberhart, R. (1995). Particle swarmoptimization. In Proceedings of ICNN’95 - International Conference on Neural Networks, volume 4, pages 1942–1948.
    Laskari, E. C., Parsopoulos, K. E., and Vrahatis, M. N. (2002). Particle swarm optimization for minimax problems. In Proceedings of the 2002 Congress on Evolutionary Computation, volume 2, pages 1576–1581.
    Lee, I.-C., Chen, R.-B., andWong,W. K. (2025). Optimal robust strategies for accelerated life tests and fatigue testing of polymer composite materials. The Annals of Applied Statistics, 19(4):2578–2598.
    Lee, I.-C., Tseng, S.-T., and Hong, Y. (2020). Global planning of accelerated degradation tests based on exponential dispersion degradation models. Naval Research Logistics, 67(6):469–483.
    Lim, H. and Yum, B.-J. (2011). Optimal design of accelerated degradation tests based on wiener process models. Journal of Applied Statistics, 38(2):309–325.
    Liu, X. and Tang, L.-C. (2010). A bayesian optimal design for accelerated degradation tests. Quality and Reliability Engineering International, 26(8):863–875.
    Meeker,W. Q. and Escobar, L. A. (2004). Reliability: The other dimension of quality. Quality Technology & Quantitative Management, 1(1):1–25.
    Meeker,W. Q., Escobar, L. A., and Lu, C. J. (1998). Accelerated degradation tests: Modeling and analysis. Technometrics, 40(2):89–99.
    Meeker, W. Q., Escobar, L. A., and Pascual, F. G. (2022). Statistical Methods for Reliability Data. John Wiley & Sons.
    M¨uller, C. H. and P´azman, A. (1998). Applications of necessary and sufficient conditions for maximin efficient designs. Metrika, 48(1):1–19.
    Pascual, F. and Montepiedra, G. (2002). On minimax designs when there are two candidate models. Journal of Statistical Computation and Simulation, 72(11):841–862.
    Pascual, F. G., Meeker, W. Q., and Escobar, L. A. (2006). Accelerated life test models and data analysis. In Springer Handbook of Engineering Statistics, pages 397–426. Springer.
    Peng, C.-Y. and Cheng, Y.-S. (2021). Profile optimum planning for degradation analysis. Naval Research Logistics, 68(7):951–962.
    Peng, C.-Y., Nagatsuka, H., and Cheng, Y.-S. (2022). Optimum test planning for heterogeneous inverse gaussian processes. Lifetime Data Analysis, 28(3):401.
    Shi, Y. and Meeker, W. Q. (2011). Bayesian methods for accelerated destructive degradation test planning. IEEE Transactions on Reliability, 61(1):245–253.
    Tseng, S.-T. and Lee, I.-C. (2016). Optimum allocation rule for accelerated degradation tests with a class of exponential-dispersion degradation models. Technometrics, 58(2):244–254.
    Tung, H.-P. (2024). Optimizing two-variable gamma accelerated degradation tests with a semi-analytical approach. Naval Research Logistics, 71(4):499–508.
    Tung, H.-P. and Chen, Y.-W. (2025). Optimal designs for gamma degradation tests. European Journal of Operational Research.
    Tung, H.-P. and Lee, I.-C. (2026). Optimal designs and inspection time decisions for gamma accelerated degradation tests. Naval Research Logistics.
    Weaver, B. P. and Meeker,W. Q. (2014). Methods for planning repeated measures accelerated degradation tests. Applied Stochastic Models in Business and Industry, 30(6):658–671.
    Yang, G. (2007). Life Cycle Reliability Engineering. Ye, Z.-S., Chen, L.-P., Tang, L.-C., and Xie, M. (2014). Accelerated degradation test planning using the inverse gaussian process. IEEE Transactions on Reliability, 63(3):750–763.
    Ye, Z.-S., Chen, L.-P., Tang, L.-C., and Xie, M. (2014). Accelerated degradation test planning using the inverse gaussian process. IEEE Transactions on Reliability, 63(3):750–763.
    Ye, Z.-S. and Xie, M. (2015). Stochastic modelling and analysis of degradation for highly reliable products. Applied Stochastic Models in Business and Industry, 31(1):16–32.

    下載圖示
    校外：立即公開
    QR CODE