簡易檢索 / 詳目顯示

研究生: 蕭裕翰
Siao, Yu-Han
論文名稱: 應用判別分析探討高可靠度產品之預燒試驗分類決策
Application of Discriminant Analysis for Classifying Highly Reliable Products in Burn-in Testing
指導教授: 胡政宏
Hu, Cheng-Hung
學位類別: 碩士
Master
系所名稱: 管理學院 - 工業與資訊管理學系
Department of Industrial and Information Management
論文出版年: 2024
畢業學年度: 112
語文別: 中文
論文頁數: 70
中文關鍵詞: 預燒試驗衰變分析Wiener過程衰變路徑判別分析
外文關鍵詞: burn-in test, degradation analysis, Wiener process, degradation path, Discriminant Analysis
相關次數: 點閱:51下載:0
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
  • 高可靠度時代已來臨,人們對產品的耐用度要求越來越高,進而衍生出所謂的高可靠度產品。在現今多樣化產品中,產品可靠度已成為消費者挑選產品之關鍵影響因素,而製造商也必要即時地提供顧客有關產品可靠度的資訊,以提升產品市場競爭力。為確保產品品質能符合消費者之長期需求,如何進行一有效的預燒試驗以及評估產品之壽命相關資訊,是所有生產者皆須面臨之重要決策問題。針對高可靠度產品,若存在一品質特徵值(quality characteristic, QC),並且其衰變量與對產品壽命具有高度相關,則可藉由所收集到的衰變資料來建構衰變模型,將是一個實際可行且有效率的方法,以解決失效樣本不足的問題。如今衰變模型已廣泛地被用來評估高可靠度產品的壽命資訊,而在本篇研究中,是以Tseng & Peng (2001)研究為發想,使用Wiener過程來描述產品品質特性的連續衰變路徑,考慮正常與瑕疵產品之衰變路徑變異不同下,應用判別分析提出一種分類方法,且以最小化錯誤分類成本為目標,求得一最佳分類切點,制定出判別產品良莠之分類準則。最後,修改以Tseng & Peng (2003)中的接觸式影像感測器(CIS)中的LED進行模擬,以亮度作為其品質特徵值,並說明其完整分類過程。此研究之成果,將有助於製造商節省預燒成本與縮短預燒時間。

    For high-reliability products, if there exists a quality characteristic (QC) whose degradation is highly correlated with product life, constructing a degradation model based on collected degradation data is a practical and efficient method to address the problem of insufficient failure samples. In this paper, we use the Wiener process to describe the continuous degradation path of product quality characteristics. This study is inspired by the research of Tseng & Peng (2001), considering the variance differences in the Wiener degradation model between normal and defective products, applies Discriminant Analysis to propose two classification methods, aiming to minimize misclassification cost (MC) and to determine an optimal cut-point for establishing classification criteria between normal and defective products, thus saving Burn-In costs and shortening Burn-In time. Finally, a simulation is performed using the LED of a contact image sensor from Tseng & Peng's study (2003), with brightness as its quality characteristic, and the complete classification process is illustrated.

    摘要I 致謝VII 目錄IX 表目錄XII 圖目錄XIII 第一章 緒論1 1.1 研究背景1 1.2 研究動機1 1.3 研究目的3 1.4研究前提假設與限制3 1.5研究架構4 第二章 文獻探討5 2.1預燒程序5 2.2衰變模型5 2.2.1隨機係數模型6 2.2.2隨機過程模型6 2.2.3 Wiener過程模型7 2.3判別分析8 2.3.1分類方法8 2.3.2最適分類法則8 2.3.3評估分類函數:混淆矩陣10 2.4預燒試驗分類11 2.5小結13 第三章 高可靠度產品之篩選試驗分類14 3.1參數符號與研究假設14 3.1.1符號總整理14 3.1.2本研究之假設16 3.2分類決策之問題描述18 3.2.1衰變模型19 3.2.2決定一最佳分類切點19 3.2.3分類評估指標:混淆矩陣20 3.3情況一(η_1>η_2且σ_1=σ_2)20 3.3.1衰變模型Y_1 (t)建構20 3.3.2最佳分類切點C_1^*21 3.3.3最佳預燒時間t_1^*23 3.3.4模擬情況一(η_1>η_2且σ_1=σ_2)之篩選過程24 3.4情況二(η_1=η_2且σ_1>σ_2):以最後一個觀測值分類28 3.4.1衰變模型Y_2 (t)建構30 3.4.2最佳分類切點上界C_2(1)^*與最佳分類切點下界C_2(2)^*31 3.4.3最佳預燒時間t_2^*35 3.5情況二(η_1=η_2且σ_1>σ_2):以樣本變異數分類35 3.5.1衰變模型Y_2 (t)建構36 3.5.2最佳分類切點C_3^*38 3.5.3最佳檢測時間點次數k^*41 第四章 模擬與分析43 4.1案例情境說明43 4.2模擬情況二:以最後一個觀測值分類之篩選過程43 4.3模擬情況二:以樣本變異數分類之篩選過程48 第五章 研究結論與未來方向51 5.1研究結論51 5.2未來方向51 參考文獻53

    中文文獻
    陳順宇. (2005). 多變量分析 (第4版). 臺北市: 華泰文化.
    英文文獻
    Anderson, T. W., & Mathématicien, E. U. (1958). An Introduction to Multivariate Statistical Analysis (Vol. 2, pp. 3-5). New York: Wiley.
    Chhikara, R. (1988). The inverse Gaussian distribution: theory: methodology, and applications (Vol. 95). CRC Press.
    Doksum, K. A., & Hbyland, A. (1992). Models for variable-stress accelerated life testing experiments based on wiener processes and the inverse gaussian distribution. Technometrics, 34(1), 74-82.
    Hoel, P. G., Port, S. C., & Stone, C. J. (1986). Introduction to stochastic processes. Waveland Press.
    Jensen, F., & Petersen, N. E. (1982). Burn-in. A Wiley-Interscience Publication.
    Johnson, R. A., & Wichern, D. W. (2002). Applied multivariate statistical analysis (5th ed.). Upper Saddle River, NJ: Prentice Hall.
    Leemis, L. M., & Beneke, M. (1990). Burn-in models and methods: A review. IIE Transactions, 22(2), 172-180.
    Lu, C. J., & Meeker, W. O. (1993). Using degradation measures to estimate a time-to-failure distribution. Technometrics, 35(2), 161-174.
    Meeker, W. Q., Escobar, L. A., & Pascual, F. G. (2022). Statistical methods for reliability data. John Wiley & Sons.
    Nelson, W. B. (1990). Accelerated testing: Statistical models, test plans, and data analysis. John Wiley & Sons.
    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, W., Li, Y. F., Yang, Y. J., Huang, H. Z., & Zuo, M. J. (2014). Inverse Gaussian process models for degradation analysis: A Bayesian perspective. Reliability Engineering & System Safety, 130, 175-189.
    Singpurwalla, N. D. (1995). Survival in dynamic environments. Statistical Science, 10(1), 86-103.
    Tseng, S. T., & Yu, H. F. (1997). A termination rule for degradation experiments. IEEE Transactions on Reliability, 46(1), 130-133.
    Tseng, S. (2001). Optimal burn-in time for highly reliable products. International Journal of Industrial Engineering: Theory, Applications and Practice, 8(4), 329-338.
    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.
    Tseng, S. T., & Peng, C. Y. (2004). Optimal burn-in policy by using an integrated Wiener process. IIE Transactions, 36(12), 1161-1170.
    Tsai, C. C., Tseng, S. T., & Balakrishnan, N. (2011). Mis-specification analyses of gamma and Wiener degradation processes. Journal of Statistical Planning and Inference, 141(12), 3725-3735.
    Wu, S., & Xie, M. (2007). Classifying weak, and strong components using ROC analysis with application to burn-in. IEEE Transactions on Reliability, 56(3), 552-561
    Wang, X., & Xu, D. (2010). An inverse Gaussian process model for degradation data. Technometrics, 52(2), 188-197
    Yu, H. F., & Tseng, S. T. (1999). Designing a degradation experiment. Naval Research Logistics (NRL), 46(6), 689-706.
    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.
    Yu, J., Yang, J., Tang, D., & Dai, J. (2018). An optimal burn-in policy for cellular phone lithium-ion batteries using a feature selection strategy and relevance vector machine. Energies, 11(11), 3021.

    無法下載圖示 校內:2026-07-30公開
    校外:2026-07-30公開
    電子論文尚未授權公開,紙本請查館藏目錄
    QR CODE