隨著市場競爭日漸激烈，產品品質成為生產者及消費者考量的重要因素。在電子業，由於產品的壽命隨著品質的提升越來越長，因此，為了節省產品品質的檢驗成本及時間，同時確保產品壽命能符合所需求的品質水準，常利用截略壽命檢驗結合驗收抽樣計畫作為判決貨批允收的工具。目前在截略壽命檢驗下的單次或雙次驗收抽樣計畫下，已有學者針對不同分配進行相關研究，但這些研究大多僅考量消費者風險，而未同時考慮生產者風險，且在固定允收數的情況下，來建構二項分配的數學模型，求解最小抽樣樣本數。而本研究將針對四個產品壽命常見的非常態分配，瑞利分配、指數分配、 廣義瑞利分配及廣義指數分配，整合相關理論，在考量生產者及消費者風險下撿購基於截略壽命檢驗之截略壽命檢驗的單次驗收抽樣計畫及雙次驗收抽樣計畫，並求解允收數和最小的抽樣樣本數。此外，也分析在各種不同的品質水準條件下，使用單次驗收抽樣計畫及雙次驗收抽樣計畫的平均樣本數之差別。最後，本研究提供不同品質水準、風險組合及終止檢驗時間因子的單次及雙次驗收抽樣計畫參數表，並進一步發展常見分配之圖形化使用者介面，結合案例操作說明，提供使用者操作參考。

With the increasingly fierce market competition, product quality has become an important factor to both producers and consumers, especially in the electronics industry. As product lifespans increase with improved quality, there is a need to optimize the inspection cost and time while ensuring that products meet the required quality standards. To address this, truncated life tests in conjunction with acceptance sampling plans are commonly employed for batch acceptance decisions. Existing studies have focused on different distributions under truncated life tests and single or double acceptance sampling plans. However, these studies often emphasize consumer risks while neglecting producer risks and primarily concentrate on finding the acceptance number to determine the minimum sample size. This study focuses on four common non-normal lifetime distributions, namely Rayleigh, Exponential, Generalized Rayleigh, and Generalized Exponential distributions. By integrating relevant theories, we construct single and double acceptance sampling plans under truncated life tests, considering both producer and consumer risks. The study aims to determine the acceptance number and minimum sample size for these plans. Furthermore, a comparative analysis of the average sample sizes between single and double acceptance sampling plans is conducted under various quality level conditions. Finally, this study provides parameter tables for single and double acceptance sampling plans based on different quality levels, risk combinations, and experimental termination times. Additionally, we develop a user-friendly graphical interface for practical implementation and present two practical examples for reference.

目錄
摘要 i
Abstract ii
致謝 iii
目錄 iv
表目錄 vii
圖目錄 1
第一章 緒論 3
1.1 研究背景與動機 3
1.2 研究目的 5
1.3 研究架構 6
第二章 文獻回顧 8
2.1 驗收抽樣計畫 8
2.1.1 操作特性曲線 10
2.1.2 計數型與計量型抽樣計畫 13
2.1.3 驗收抽樣計畫之抽樣方式 14
2.1.4 平均樣本數 16
2.2 截略壽命檢驗 16
2.2.1 截略壽命檢驗和設限壽命檢驗比較 17
2.2.2 截略壽命檢驗下的驗收抽樣計畫 18
2.3 截略壽命檢驗之常用分配 20
2.3.1 瑞利分配 20
2.3.2 廣義瑞利分配 22
2.3.3 指數分配 25
2.3.4 廣義指數分配 27
第三章 常見分配產品壽命之截略壽命檢驗的單次驗收抽樣計畫 30
3.1 單次驗收抽樣計畫操作流程 31
3.2 瑞利分配及廣義瑞利分配 33
3.2.1 允收機率函數 33
3.2.2 計畫參數之數學模型 35
3.3 指數和廣義指數分配 37
3.3.1 允收機率函數 37
3.3.2 計畫參數之數學模型 39
3.4 常見分配計畫參數分析與討論 39
第四章 常見分配產品壽命之截略壽命檢驗的雙次驗收抽樣計畫 48
4.1 雙次驗收抽樣計畫操作流程 49
4.2 雙次驗收抽樣計畫的允收機率函數 51
4.3 雙次驗收抽樣計畫的計畫參數之數學模型 52
4.4 常見分配計畫參數分析與討論 53
第五章 案例分析 66
5.1 深溝滾珠軸承案例 66
5.2 汽車車內子系統案例 71
第六章 結論與未來研究方向 73
6.1 結論 73
6.2 未來研究方向 74
參考文獻 75
附錄A 77

1. Aslam, M. (2005). Double acceptance sampling based on truncated life tests in Rayleigh distribution. Editorial Advisory Board e, 17(4), 605-610.
2. Aslam, M., Jun, C.-H., & Ahmad, M. (2010). Design of a time-truncated double sampling plan for a general life distribution. Journal of Applied Statistics, 37(8), 1369-1379.
3. Aslam, M., Jun, C.-H., Rasool, M., & Ahmad, M. (2010). A time truncated two-stage group sampling plan for Weibull distribution. CSAM (Communications for Statistical Applications and Methods), 17(1), 89-98.
4. Aslam, M., Kundu, D., & Ahmad, M. (2010). Time truncated acceptance sampling plans for generalized exponential distribution. Journal of Applied Statistics, 37(4), 555-566.
5. Bjerkedal, T. (1960). Acquisition of Resistance in Guinea Pies infected with Different Doses of Virulent Tubercle Bacilli. American Journal of Hygiene, 72(1), 130-148.
6. Epstein, B. (1954). Truncated life tests in the Exponential case. The Annals of Mathematical Statistics, 555-564.
7. Epstein, B. and Sobel, M. (1953). Life testing. Journal of the American Statistical Association, 48(263), 486-502.
8. Goode, H. P. and Kao, J. H. (1961). Sampling procedures and tables for life and reliability testing： based on the Weibull distribution. Office of the Assistant Secretary of Defense (Installations and Logistics).
9. Gupta, R. D. and Kundu, D. (1999). Theory & methods： Generalized Exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188.
10. Gupta, S. S. and Gupta, S. S. (1961). Gamma distribution in acceptance sampling based on life tests. Journal of the American Statistical Association, 56(296), 942-970.
11. Hamaker, H. C. (1979). Acceptance sampling for percent defective by variables and by attributes. Journal of Quality Technology, 11(3), 139-148.
12. Kao, J. H. (1971). MIL-STD-414 sampling procedures and tables for inspection by variables for percent defective. Journal of Quality Technology, 3(1), 28-37.
13. Kundu, D. and Gupta, R. D. (2011). An extension of the Generalized Exponential distribution. Statistical Methodology, 8(6), 485-496.
14. Lieblein, J. and Zelen, M. (1956). Statistical investigation of the fatigue life of deep-groove ball bearings. Journal of Research of The National Bureau of Standards, 57(5), 273-316.
15. Montgomery, D. C. (2009). Statistical Quality Control (Vol. 7). Wiley New York.
16. Ramaswamy, A. and Anburajan, P. (2012). Double acceptance sampling based on truncated life tests in Generalized Exponential distribution. Applied Mathematical Sciences, 6(64), 3199-3207.
17. Rayleigh, L. (1880). XII. On the resultant of a large number of vibrations of the same pitch and of arbitrary phase. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 10(60), 73-78.
18. Rosaiah, K. and Kantam, R. (2005). Acceptance sampling based on the inverse Rayleigh distribution. Economic Quality Control 20(2), 277-286
19. Shanker, R., Hagos, F. and Sujatha, S. (2015). On modeling of Lifetimes data using Exponential and Lindley distributions. Biometrics & Biostatistics International Journal, 2(5), 1-9.
20. Sobel, M. and Tischendrof, J. (1959). Acceptance sampling with new life test objectives. Proceedings of fifth National Symposium on Reliability and Quality Control, 108-118.
21. Tsai, T. R. and Wu, S. J. (2006). Acceptance sampling based on truncated life tests for Generalized Rayleigh distribution. Journal of Applied Statistics, 33(6), 595-600.
22. Vodă, V. G. (1976). Inferential procedures on a Generalized Rayleigh variate. I. Aplikace matematiky, 21(6), 395-412.
23. Zoramawa, A., Gulumbe, S., RRL, K. and Musa, Y. (2018). Developing double acceptance sampling plans for percentiles based on the inverse Rayleigh distribution. International Journal of Statistics and Applied Mathematics. 2018a, 3(1), 39-44.
24. Wu, C. W.; Shu, M. H.; Wu, N. Y. (2021). Acceptance sampling schemes for two-parameter Lindley lifetime products under a truncated life test. Quality Technology & Quantitative Management, 18(3), 382-395.