允收抽樣在品質管理的領域中扮演著很重要的角色，且適用於各式的檢驗。允收抽樣計畫是指透過所需的樣本大小及允收條件來對產品進行判決。本研究主要是以考量良率損失下，提出一個基於製程能力指標 Cpmk 之計量型重複遞交抽樣計畫之研究。相較於計數型抽樣計畫，計量型抽樣計畫主要用於衡量連續型數據的品質特性，並且同時保障買賣雙方各自所能承受的風險，但使用較小量的檢測抽樣數。尤其當檢驗成本非常昂貴或破壞性實驗時，計量型抽樣計畫顯得更為有利。
本研究中，抽樣計畫的主要參數：樣本大小及判斷之臨界值，係透過求解非線性之聯立方程式而得。其中，組成兩條非線性方程式之操作特性曲線 (OC curve) ，則是透過精確的抽樣分配而得。因此，這能使批判產品允收的決策更加準確及可靠。此外，因應實務之應用，透過不同品質要求與風險要求下的組合，文中列出了參數表以供查詢使用，並且針對所提出的方法做一系列之討論。
最後，本研究透過一個實際案例來說明如何將所提出的重複遞交之計量型抽樣計畫的執行步驟。

Acceptance sampling is one of the important parts of the field of quality control and used primarily for any kinds of inspection. Acceptance sampling plans state the required sample size and the required acceptance or rejection criteria for lots sentencing. This thesis proposes a variables sampling plan for resubmitted lots based on a process capability index Cpmk that covers modern quality improvement philosophy where reduction of variation from the target value is the guiding principle to reduce the fraction on nonconformities, as it takes into account both process yield and process loss. Variables sampling plans will measure the quality characteristics on a numerical scale, with several advantages of having smaller sample size than attributes sampling plans under the same level of protection for both producer and customer. This is especially beneficial when the inspection is costly and destructive. The required sample size and critical acceptance value are developed based on the exact sampling distribution rather than the approximation; hence the decisions made are more accurate and reliable. For practical purpose, tables for the required sample size and critical acceptance value of various combinations of quality levels, producer’s risk and consumer’s risk are constructed by solving two non-linear simultaneous equations. Moreover, the behaviors of the proposed sampling plans with various conditions are also shown and discussed. A numerical example is provided to illustrate and demonstrate how to use the variables sampling plan for resubmitted lots based on Cpmk in the real applications.

Aslam, M., Jun, C.H., Lio, Y.L., Munir, A. and Rasool, M. (2011). Group acceptance sampling plans for resubmitted lots under burr-type XII distributions. Journal of the Chinese Institute of Industrial Engineers, 28:8, 606-615.

Aslam, M., Wu, C.W., Azam, M. and Jun, C.H. (2012a). Variable sampling inspection for resubmitted lots based on process capability index Cpk for normally distributed items. Applied Mathematical Modelling, 37, 667-675.

Aslam, M., Balamurali, S., Jun, C.H. and Munir, A. (2012b). Bayesian sampling inspection for resubmitted lots under gamma-poisson distribution. Research Journal of Applied Sciences, Engineering and Technology, 4(23), 5171-5176.

Balamurali, S., and Jun, C.H. (2007). Multiple dependent state sampling plans for lot acceptance based on measurement data. European Journal of Operational Research, 180, 1221-1230.

Govindaraju, K. and Ganesalingam, S. (1997). Sampling inspection for resubmitted lots. Communications in Statistics-Simulation and Computation, 26(3), 1163-1176.

Itay, N., Yisrael, P. and Edna, S. (2009). Developing a sampling plan based on Cpk. Quality Engineering, 21:3, 306-318.

Jozani, M.J. and Mirkamali, S.J. (2010). Improved attribute acceptance sampling plans based on maxima nomination sampling. Journal of Statistics Planning and Inference, 140, 2448-2460.

Kotz, S. and Lovelace, C.R. (1998). Process Capability Indices in Theory and Practice. Oxford University Press Inc, New York.

Montgomery, D.C. (2009). Introduction to Statistical Quality Control, Sixth edition. John Wiley & Sons, New York.

Muthuraj, D. and Snthilkumar, D. (2006). Designing and construction of tightened- normal-tightened variable sampling scheme. Journal of Applied Statistics, 33, 101-111.

Owen, D.B. (1967). Variables sampling plans based on the normal distribution. Technometrics, 9, 19-36.

Pearn, W.L. and Kotz, S. and Johnson N.L. (1992). Distributional and inferential properties of process capability indices. Journal of Quality Technology, 24, 216-231.

Pearn, W.L. and Kotz, S. (2006). Encyclopedia and Handbook of Process Capability Indices, Vol.12. World Scientific Publishing, Singapore.

Pearn, W.L. and Lin, P.C. (2002). Computer program for calculating the p-value in testing process capability index Cpmk. Quality and Reliability Engineering International, 18, 333-342.

Pearn, W.L. and Shu, M.H. (2004). Measuring manufacturing capability based on lower confidence bounds of Cpmk applied to current transmitter process. International Journal Advanced Manufacturing Technology, 23, 116-125.

Pearn, W.L. and Wu, C.W. (2006). Variables sampling plans with PPM fraction of defectives and process loss consideration. Journal of the Operational Research Society, 57(4), 450-459.

Pearn, W.L. and Wu, C.W. (2007). An effective decision making method for product acceptance. Omega, 35, 12-21.

Seidel, W. (1997). Is sampling by variables worse than sampling by attributes? A decision theoretic analysis and a new mixed strategy for inspecting individual lots. The Indian Journal of Statistics, 59, 96-107.

Schilling, E.G. and Neubauer, D.V. (2009). Acceptance Sampling in Quality Control, Second edition. CRC Press, New York.

Wu, C.W. (2012). An efficient inspection scheme for variables based on taguchi capability index. European Journal of Operational Research, 223, 116-122.

Wu, C.W. and Pearn, W.L. (2008). A variable sampling plan based on Cpmk for product acceptance determination. European Journal of Operational Research, 184, 549-560.

Wu, C.W., Pearn, W.L. and Kotz, S. (2009). An overview of theory and practice on process capability indices for quality assurance. International Journal of Production Economics, 117(2), 338-359.

Wu, C.W., Aslam, M. and Jun, C.H. (2012). Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk. European Journal of Operational Research, 217, 560-566.

Yen, C.H. and Chang, C.H. (2009). Designing variables sampling plans with process loss consideration. Communications in Statistics‒Simulation and Computation, 38, 1579-1591.