隨著消費者意識抬頭，產品品質成為企業從競爭者中脫穎而出的關鍵，驗收抽樣計畫 (acceptance sampling plan) 為一實務上常見之品質管理工具，給予買賣雙方貨批判斷準則；由於科技進步，傳統以產品不良率衡量品質標準的方法在極低不良率製程下，須抽取大量樣本數以顯示實際製程能力，因此逐漸被製程能力指標 (Process Capability Indices, PCIs) 取代。為了提升檢驗效率並降低檢驗成本，許多學者發展出結合製程能力指標之計量型驗收抽樣計畫，當連續貨批之品質表現穩定且良好時，可使用跳批抽樣計畫 (Skip-lot Sampling Plan, SkSP) 進行檢驗，即檢驗時跳過部分貨批不檢驗，其中最常見之驗收抽樣計畫為以單次抽樣計畫為參考計畫 (reference plan) 之型二跳批抽樣計畫 (Skip-lot Sampling Plan of type 2, SkSP-2)。而本研究結合製程能力指標與跳批抽樣計畫概念與優點，發展出基於製程能力指標Cpmk之四種計量型跳批抽樣計畫，分別為型二跳批抽樣計畫、加入不同機制之跳批重複抽樣計畫 (SkSP-R)與廣義跳批抽樣計畫 (SkSP-V) 、改變參考計畫類型之重複群集型二跳批抽樣計畫 (SkSP-RGS)，利用指標估計值Cpmk_hat之真實抽樣分配建構數學模型，以兩點式操作特性曲線作為限制式、最小化平均樣本數作為目標式，在常見之不同品質水準與風險組合下進行參數求解，並透過不同績效衡量指標比較本研究提出之跳批抽樣計畫與單次抽樣計畫。最後，建構圖形化使用者介面，將之結合實際案例以輔助說明各計畫操作流程，以利實務應用。

With the rise of consumer awareness, quality of the product becomes the main factor for enterprises to stand out from the crowd. Acceptance sampling plan is a common tool used in quality control which provides both provider and consumer a criterion for lot sentencing. Owing to the development of technology, acceptance sampling plans are always proposed with process capability indices (PCIs) rather than with the number of nonconforming products to avoid a need of larger sample size under the process with extremely low nonconforming rate. Skip-lot sampling plan (SkSP) can enhance the efficiency of inspection and reduce the costs because it not only takes quality performance in the past into consideration but also inspects only a portion of the lots when the quality level of the submitted products is high. Among them, the most widely used plan is skip-lot sampling plan of type 2 (SkSP-2) which takes single sampling plan as reference plan. Therefore, the target of this paper is to intensify above advantages by arising four new sampling plans including SkSP-2, SkSP-R, SkSP-V and SkSP-RGS which are based on the concept of skip lot sampling and the process capability index Cpmk. The mathematic model is established to minimize the average sampling number under different combinations of quality levels and risk demand by exact sampling distribution which can avoid estimation bias. Moreover, the differences between the proposed plans and single sampling plan are also discussed via two different performance indices. Finally, a graphic user interface is built to describe the procedure of each plan to benefit the users by practical cases.

致謝 i
摘要 ii
Abstract iii
目錄 iv
圖目錄 vii
表目錄 xii
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
1.3 研究架構 4
第二章 文獻探討與回顧 7
2.1 製程能力指標 7
2.1.1 之估計量與抽樣分配 9
2.1.2 之假設檢定 11
2.2 驗收抽樣計畫 12
2.2.1 分類與發展 13
2.2.2 績效與評估 15
2.3 跳批抽樣計畫 18
2.3.1 型二跳批抽樣計畫 (SkSP-2) 19
2.3.2 跳批重複抽樣計畫 (SkSP-R) 22
2.3.3 廣義跳批抽樣計畫 (SkSP-V) 23
2.3.4 重複群集型二跳批抽樣計畫 (SkSP-RGS) 26
第三章 基於製程能力指標 之跳批抽樣計畫 28
3.1 基於製程能力指標 之型二跳批抽樣計畫 28
3.1.1 操作流程 29
3.1.2 允收機率函數與數學模型 30
3.1.3 參數求解結果與分析 33
3.2 基於製程能力指標 之跳批重複抽樣計畫 43
3.2.1 操作流程 44
3.2.2 允收機率函數與數學模型 45
3.2.3 參數求解結果與分析 47
3.3 基於製程能力指標 之廣義跳批抽樣計畫 57
3.3.1 操作流程 58
3.3.2 允收機率函數與數學模型 59
3.3.3 參數求解結果與分析 61
3.4 基於製程能力指標 之重複群集型二跳批抽樣計畫 71
3.4.1 操作流程 72
3.4.2 允收機率函數與數學模型 73
3.4.3 參數求解結果與分析 76
第四章 比較與分析 90
4.1 與單次抽樣計畫比較 90
4.1.1 型二跳批抽樣計畫與單次抽樣計畫 90
4.1.2 跳批重複抽樣計畫與單次抽樣計畫 93
4.1.3 廣義跳批抽樣計畫與單次抽樣計畫 96
4.1.4 重複群集型二跳批抽樣計畫與單次抽樣計畫 99
4.2 四種抽樣計畫比較 103
第五章 圖形化使用者介面與案例分析 106
5.1 基於製程能力指標之型二跳批抽樣計畫案例 108
5.2 基於製程能力指標之跳批重複抽樣計畫案例 113
5.3 基於製程能力指標之廣義跳批抽樣計畫案例 119
5.4 基於製程能力指標之重複群集型二跳批抽樣計畫案例 125
第六章 結論與未來展望 132
6.1 結論 132
6.2 未來展望 133
參考文獻 134
附錄 137

王沛安 (2018)。發展以製程能力指標為基礎之計量型跳批抽樣計畫。國立清華大學工業工程與工程管理學系碩士論文，未出版，新竹市。
黃儀珊 (2019)。基於單邊規格界限產品之計量型跳批抽樣計畫。國立清華大學工業工程與工程管理學系碩士論文，未出版，新竹市。
韋怡婷 (2020)。基於製程能力指標 之新型跳批抽樣計畫。國立清華大學工業工程與工程管理學系碩士論文，未出版，新竹市。
Aslam, M., Balamurali, S., Jun, C. H., & Ahmad, M. (2010). Optimal designing of a skip-lot sampling plan by two point method. Pakistan Journal of Statistics, 26(4), 585-592.
Aslam, M., Balamurali, S., Jun, C. H., Ahmad, M., & Rasool, M. (2012). Optimal designing of an Skip-V skip-lot sampling plans with double sampling plan as reference plan. International Journal of Advanced Manufacturing Technology, 60, 733–740.
Aslam, M., Balamurali, S., Jun, C. H., & Hussain, B. (2015). Design of SkSP-R variables sampling plans. Revista Colombiana de Estadística, 38(2), 413-429.
Aslam, M., Khan, N., & Khan, H. (2015). SkSP-V Acceptance sampling plan based on process capability index. Chiang Mai Journal of Science, 42(1),258-267.
Balamurali, S., Aslam, M., & Jun, C. H. (2014). A new system of skip-lot sampling plans including resampling. The Scientific World Journal.
Balamurali, S., Aslam, M., & Jun, C. H. (2015). Economic design of SkSP-R skip- lot sampling plans. Journal of Testing and Evaluation, 43(5), 1205-1210.
Balamurali, S., & Jun, C. H. (2006). Repetitive group sampling procedure for variables inspection. Journal of Applied Statistics, 33(3), 327-338.

Balamurali S., & Jun C. H. (2011). A new system of skip-lot sampling plans having a provision for reducing a normal inspection. Applied Stochastic Models in Business and Industry, 27(3), 348-363.
Balamurali, S., & Subramani, J. (2012). Optimal designing of skip-lot sampling plan of type SkSP-2 with double sampling plan as the reference plan. Journal of Statistical Theory and Practice, 6(2), 354-362.
Balamurali, S., & Subramani, J. (2018). Optimal designing of SkSP-2 skip-lot sampling plan for normally distributed quality characteristics. Transactions of the Institute of Measurement and Control, 40(7), 2240-2248.
Chan, L. K., Cheng, S. W., & Spring, F. A. (1988). A new measure of process capability: C_pm. Journal of Quality Technology, 20(3), 162-175.
Dodge, H. F., & Romig, H. G. (1929). A method of sampling inspection. Bell Labs Technical Journal, 8(4), 613-631.
Dodge, H. F. (1943). A sampling inspection plan for continuous production. Annals of Mathematical Statistics, 14(3), 264-279.
Dodge, H. F. (1955). Skip-lot sampling plan. Industrial Quality Control, 11(5), 3-5.
Govindaraju, K., & Ganesalingam, S. (1997). Sampling inspection for resubmitted lots. Communications in Statistics –Simulation and Computation, 26(3), 1163-1176.
Hamaker, H. C. (1979). Acceptance sampling for percent defective by variables and by attributes. Journal of Quality Technology, 11(3), 139-148.
Hussain, J., Balamurali, S., Aslam, M., & Jun, C. H. (2017). SkSP-R sampling plan based on process capability index. Communications in Statistics-Theory and Methods, 46(6), 2955-2966.
Juran, J. M., Gryna, F. M., & Bingham, R. S. (1974). Quality Control Handbook (Vol. 3). New York: McGraw-Hill.
Jessenberger, J., & Weihs, C. (2000). A note on the behavior of C_pmk with asymmetric specification limits. Journal of Quality Technology 32(4), 440-443.
Kane, V. E. (1986). Process capability indices. Journal of Quality Technology, 18(1), 41-52.
Koatpoothon, P., & Ayudthya, P. S. (2014). Comparison of skip-lot sampling plans (SkSP-V vs. SkSP-2). Songklanakarin Journal of Science and Technology, 36(4), 465–469.
Lin, C. J., & Pearn, W. L. (2010). Process selection for higher production yield based on capability index S_pk. Quality and Reliability Engineering International, 26(3), 247-258.
Montgomey, D. C. (2009) Introduction to Statsitical Quality Control; New York: John Wiley & Sons.
Muthulakshmi, S., & Lakshmi, B. (2011). Analysis of skip-lot sampling plans. International Journal of Microsystems Technology and its Applications, 1(1), 63-68.
Perry, R. L. (1973). Skip-lot sampling plans. Journal of Quality Technology, 5, 123-130.
Pearn, W. L., Kotz, S., & Johnson, N. L. (1992). Distributional and inferential properties of process capability indices. Journal of Quality Technology , 24, 216-231
Pearn, W. L., & Lin, P. C. (2002). Computer program for calculating the -value in testing process capability index C_pmk. Quality and Reliability Engineering International, 18(4), 333-342.
Pearn, W. L., & Kotz, S. (1994). Application of Clements’ method for calculation of second and third generation process capability indices for non-normal Pearsonian populations. Quality Engineering, 7(1), 139-145.
Pearn, W. L., & Wu, C. W. (2007). An effective decision making method for product acceptance. Omega, 35(1), 12-21.
Sherman, R. E. (1965). Design and evaluation of a repetitive group sampling plan. Technolometircs, 7(1), 11-21
Suresh, K. K., & Kavithamani, M. (2014). Optimal designing of skip-lot sampling plan of type SkSP-2 with double sampling plan as the reference plan under generalized exponential distribution. International Journal of Reliability and Applications, 15(2), 77-84.
Vännman, K., & Kotz, S. (1995). A superstructure of capability indices: Distributional properties and implications. Scandinavian Journal of Statistics, 22, 477-491
Wu, C. W., Aslam, M., Chen, J. C., & Jun, C. H. (2015). A repetitive group sampling plan by variables inspection for product acceptance determination. European Journal of Industrial Engineering, 9(3), 308–326.
Wu, C. W., Xie, M., & Wang, Z. (2001). Optimum rectifying inspection plans. International Journal of Production Research, 39(8), 1575-1588.