臺灣博碩士論文加值系統

允收抽樣一直是工業中廣泛運用的統計品質管制技術之一，當前的製造環境能夠大量批次的產品，在這個情況下，現存的單一抽樣計畫可能無法滿足生產者與消費者的需求，本論文提供了抽樣計畫的替代方案，像是專用單一屬性抽樣計畫、基於雙重允收標準的抽樣計畫和適用於常態與非常態分配的獨立混和抽樣分配， 研究目標計畫的執行並與現有計畫互相比較。本研究的績效指標包括樣本大小和抽樣計畫對於不符合單位之區分能力，針對零膨脹負二項分配，重新遞交了單一樣本計畫、重複性群組之抽樣計畫及多重依賴性之抽樣分配，而多重依賴性抽樣分配優於重新遞交之樣本計畫、重複性群組抽樣計畫和現存單一屬性之抽樣計畫，針對常態與膨脹型柏拉圖分配(Pareto distributions)，提出了基於雙重允收標準之抽樣分配，而此雙重允收標準之抽樣計畫優於單變量樣本計畫，具有邊際品質之獨立混合抽樣計畫優於沒有邊際品質及雙變量之抽樣計畫，而在擬議計畫中呈現良好的績效以確保滿足顧客的需求。此篇論文的說明案例是基於已發表論文和模擬資料所提供的真實數據，說明所提出的抽樣計畫的績效。

Acceptance sampling has been one of the widely used statistical quality control techniques enabling to ensure quality of industrial products. Due to the production of large size of lots in the current manufacturing environments and the various distributions of quality attributes, the traditional attributes and variables sampling plans may not be suitable for satisfying producer and consumer requirements. This dissertation presents alternative sampling plans such as special purpose single sampling plans by attributes, sampling plans based on dual acceptance criteria and independent mixed sampling plans that are suitable for normal and non-normal distributions. The performance measures such as sample size and the discriminating power of sampling plans are used to compare the proposed sampling plans with existing sampling plans. Resubmitted single sampling, repetitive group sampling and multiple dependent state sampling plans have been proposed for zero-inflated negative binomial distribution. Multiple dependent state sampling plan outperforms the resubmitted sampling plan, repetitive group sampling plan and existing single attributes sampling plan. Sampling plans based on dual acceptance criteria are proposed for normal and inflated Pareto distributions. The sampling plans based on dual acceptance criteria performs better than single variables sampling plans. Independent mixed sampling plan with marginal quality shows better performance in terms of sample size and discriminating power compared with the one without marginal quality and double variables sampling plan. The proposed plans show better performance to ensure the satisfaction of producer and customer needs. Illustrative examples are provided to illustrate the performance of the proposed sampling plans.

摘要 i
Abstract ii
Acknowledgment iii
Table of contents iv
List of figures vii
List of tables viii
Chapter One 1
Introduction 1
1.1. Background 1
1.2. Overview of the food industry 3
1.3. Statement of the problem 4
1.4. Objectives of the study 4
1.5. Organization of the dissertation 5
Chapter Two 6
Literature review 6
2.1. Overview of acceptance sampling plans 6
2.2. Classification of acceptance sampling plans 8
2.3. Sampling plans for microbiological study 9
2.3.1. Microbiological distributions 9
2.3.2. Microbiological sampling plans 11
2.4. Special purpose single sampling plans 12
2.5. Mixed sampling plans for normal and non-normal distributions 13
Chapter Three 16
Methodology 16
3.1. Statistical models and sampling plans 16
3.1.1. Description of the food quality measurement data 16
3.1.2. The statistical models 17
3.2. Attributes sampling plans for ZINB distribution 21
3.2.1. Single attributes sampling plan 21
3.2.2. The resubmitted single sampling plan 23
3.2.3. The repetitive group sampling plan 24
3.2.4. The multiple dependent state sampling plan 26
3.3. Review of sampling plans based on multiple acceptance criteria for normal distribution 27
3.3.1. Mixed sampling plans based on two stage sampling schemes 27
3.3.2. Acceptance probability based on three criteria with known variance 32
3.3.3. Acceptance probability based on dual criteria with unknown variance 33
3.4. Sampling plan based on dual acceptance criteria for normal distribution 34
3.4.1. Existing sampling plans 34
3.4.2. Proposed sampling plan based on dual acceptance criteria 35
3.5. Sampling plans based on dual acceptance criteria for inflated Pareto distribution 37
3.5.1. Existing single sampling plans 37
3.5.2. Proposed sampling plan based on dual acceptance criteria 39
3.6. Independent mixed sampling plans for inflated Pareto distribution 40
3.6.1. Existing double variables sampling plan 43
3.6.2. Proposed sampling plans 44
Chapter Four 49
Results and discussion 49
4.1. Performance evaluation of sampling plans 49
4.1.1. Single sampling plan for zero-inflated negative binomial distribution 50
4.1.2. Sampling plan based on dual acceptance criteria for normal distribution 59
4.1.3. Sampling plan based on dual acceptance criteria for inflated Pareto distribution 61
4.1.4. Performance comparison of independent mixed sampling plan for inflated Pareto data 64
4.2. Illustrative examples 70
Chapter Five 75
Conclusions and future study 75
5.1. Conclusions 75
5.2. Applications 76
5.3. Future study 77
Appendices 78
Appendix IA. The R-code for computing the plan parameters of SS and RSS plans 78
Appendix IB. The R-code for computing the plan parameters of RGS plan 79
Appendix IC. The R-code for computing the plan parameters of MDS sampling plan 80
Appendix ID. The R-code for computing the OC curves of sampling plans under ZINB distribution 82
Appendix IIA. The R-code for computing the OC curves of sampling plans under normal distribution 83
Appendix IIB. The approximation method for computing the joint probability 86
Appendix IIC. The R-code for computing the joint probability 87
Appendix IID. The R-code for computing the plan parameters of sampling plans for inflated Pareto 88
Appendix IIE. The R-code for computing the OC curves of sampling plans under inflated Pareto distribution 104
Appendix IIIA. The R code for computing the plan parameters double sampling plan by variables 105
Appendix IIIB. The R-code for computing plan parameters independent mixed sampling plans under inflated Pareto distribution 106
Appendix IIIC. The R code for computing plan parameters of independent mixed plans with marginal quality under inflated Pareto distribution 108

1. Agarwal, D. K., Gelfand, A. E., & Citron-Pousty, S. (2002). Zero-inflated models with application to spatial count data. Environmental and Ecological statistics, 9(4), 341-355.
2. Anscombe, F. J. (1950). Sampling theory of the negative binomial and logarithmic series distributions. Biometrika, 37(3/4), 358-382.
3. Arul, S. D., & Joyce, V. J. (2010). Selection of mixed sampling plans for second quality lots. Economic Quality Control, 25(1), 31-42.
4. Baksh, M. F., Böhning, D., & Lerdsuwansri, R. (2011). An extension of an over-dispersion test for count data. Computational Statistics & Data Analysis, 55(1), 466-474.
5. Balamurali, S., & Jun, C. H. (2006). Repetitive group sampling procedure for variables inspection. Journal of Applied Statistics, 33(3), 327-338.
6. Balamurali, S., & Jun, C. H. (2007). Multiple dependent state sampling plans for lot acceptance based on measurement data. European Journal of Operational Research, 180(3), 1221–1230.
7. Balamurali, S., Park, H., Jun, C. H., Kim, K. J., & Lee, J. (2005). Designing of variables repetitive group sampling plan involving minimum average sample number. Communications in Statistics - Simulation and Computation, 34(3), 799–809.
8. Bassett, J., Jackson, T., Jewell, K., Jongenburger, I., & Zwietering, M. H. (2010). Impact of microbial distributions on food safety. ILSI Europe.
9. Bowker, A. H., & Goode, H. P. (1952). Sampling inspectin by variables. New York: McGraw-Hill.
10. Bray, D. F., Lyon, D. A., & Burr, I. W. (1973). Three class attributes plans in acceptance sampling. Technometrics, 15(3), 575-585.
11. Cao, Y., & Subramaniam, V. (2013). Improving the performance of manufacturing systems with continuous sampling plans. IIE Transactions, 45(6), 575-590.
12. Collani, E. V. (1991). A note on acceptance sampling for variables. Metrika, 38(1), 19-36.
13. Constantine, A. G., Field, J. B. F., & Robinson, N. I. (2000). Theory & methods: probabilities of failure in mixed acceptance sampling schemes. Australian & New Zealand Journal of Statistics, 42(2), 225-233.
14. Couturier, D. L., & Victoria-Feser, M. P. (2010). Zero-inflated truncated generalized Pareto distribution for the analysis of radio audience data. The Annals of Applied Statistics, 4(4), 1824-1846.
15. Croarkin, M. C., & Yang, G. L. (1982). Acceptance probabilities for a sampling procedure based on the mean and an order statistic. Journal of Research of the National Bureau of Standards, 87(6), 485–511.
16. Czado, C., Erhardt, V., Min, A., & Wagner, S. (2007). Zero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent outsourcing rates. Statistical Modelling, 7(2), 125-153.
17. Dahms, S., & Hildebrandt, G. (1998). Some remarks on the design of three-class sampling plans. Journal of Food Protection, 61(6), 757-761.
18. Das, N. G., & Mitra, S. K. (1964). Effect of non-normality on plans for sampling inspection by variables. Sankhyā: The Indian Journal of Statistics, Series A, 26(2-3)169-176.
19. Dodge, H. F., & Romig, H. G. (1929). A method of sampling inspection. Bell System Technical Journal, 8(4), 613-631.
20. Dodge, H. F., & Romig, H. G. (1941). Single sampling and double sampling inspection tables. The Bell System Technical Journal, 20(1), 1-61.
21. Dodge, H. F., & Romig, H. G. (1959). Sampling inspection tables: single and double sampling. New York: Wiley.
22. Duarte, B. P., & Saraiva, P. M. (2008). An optimization-based approach for designing attribute acceptance sampling plans. International Journal of Quality & Reliability Management, 25(8), 824-841.
23. Duffuaa, S. O., Al-Turki, U. M., & Kolus, A. A. (2009). Process-targeting model for a product with two dependent quality characteristics using acceptance sampling plans. International Journal of Production Research, 47(14), 4031-4046.
24. Duncan, A. J. (1986). Quality control and industrial statistics. Homewood, Illinois: Richard D. Irwin, Inc.
25. Elder, R. S., & Muse, H. D. (1982). An approximate method for evaluating mixed sampling plans. Technometrics, 24(3), 207–211.
26. European Commission. Commission Regulation (EC) No 2073/2005 of 15 November 2005 on microbiological criteria for foodstuff. Official Journal of the European Union L. 2005; 338 (22), 1–26.
27. Fang, R. (2013). Zero-inflated negative binomial (ZINB) regression model for over-dispersed count data with excess zeros and repeated measures, an application to human microbiota sequence data. Doctoral dissertation, Denver, Colorado: University of Colorado.
28. Faroughi, P., & Ismail, N. (2017). Bivariate zero-inflated negative binomial regression model with applications. Journal of Statistical Computation and Simulation, 87(3), 457-477.
29. Figueiredo, F., Figueiredo, A., & Gomes, M. I. (2015). Acceptance sampling plans for inflated Pareto processes. In 4th international symposium on statistical process monitoring, ISSPM, Padua, Italy, 7–9, July, 2015.
30. Figueiredo, F., Figueiredo, A., & Gomes, M. I. (2018). Acceptance-Sampling Plans for Reducing the Risk Associated with Chemical Compounds. In Recent Studies on Risk Analysis and Statistical Modeling (pp. 99-111). Springer, Cham.
31. Gonzales-Barron, U., & Butler, F. (2011). A comparison between the discrete Poisson-gamma and Poisson-lognormal distributions to characterize microbial counts in foods. Food Control, 22(8), 1279-1286.
32. Gonzales-Barron, U., & Cadavez, V. (2017). Statistical Derivation of Sampling Plans for Microbiological Testing of Foods. In Microbial Control and Food Preservation (pp. 381-412). New York: Springer.
33. Gonzales-Barron, U., Kerr, M., Sheridan, J. J., & Butler, F. (2010). Count data distributions and their zero-modified equivalents as a framework for modelling microbial data with a relatively high occurrence of zero counts. International Journal of Food Microbiology, 136(3), 268-277.
34. Govindaraju, K, & Ganesalingam, S. (1997). Sampling inspection for resubmitted lots. Communications in Statistics - Simulation and Computation, 26(3), 1163–1176.
35. Govindaraju, K., & Kissling, R. (2015). A combined attributes–variables plan. Applied Stochastic Models in Business and Industry, 31(5), 575-583.
36. Govindaraju, K., & Subramani, K. (1990). Selection of multiple deferred state MDS-1 sampling plans for given acceptable quality level and limiting quality level involving minimum risks. Journal of Applied Statistics, 17(3), 427–434.
37. Greene, W. H. (1994). Accounting for excess zeros and sample selection in Poisson and negative binomial regression models. Working Paper #EC94-10. New York: New York University.
38. Hald, A. (1981). Statistical theory of sampling inspection by attributes. London: Academic Press.
39. Hamaker, H. C. (1958). Some basic principles of sampling inspection by attributes. Applied Statistics, 7(3), 149-159.
40. Hamaker, H. C. (1979). Acceptance sampling for percent defective by variables and by attributes. Journal of Quality Technology, 11(3), 139-148.
41. Hildebrandt, G., Böhmer, L., & Dahms, S. (1995). Three-class attributes plans in microbiological quality control: a contribution to the discussion. Journal of Food Protection, 58(7), 784-790.
42. ICMSF. (1986). Microorganisms in foods 2: Sampling for microbiological analysis; Principles and specific applications. Toronto: University of Toronto Press.
43. ICMSF. (2002). Microorganisms in foods 7: Microbiological testing in a system for managing food safety. New York: Kluwer Acad./Plenum Publishers.
44. ICMSF. (2011). Microorganisms in foods 8: Use of data for assessing process control and product acceptance. New York: Springer.
45. Jansakul, N., & Hinde, J. P. (2008). Score tests for extra-zero models in zero-inflated negative binomial models. Communications in statistics-simulation and computation, 38(1), 92-108.
46. Jarvis, B. (2016). Statistical aspects of the microbiological examination of foods. London: Academic Press.
47. Jennett, W. J., & Welch, B. L. (1939). The control of proportion defective as judged by a single quality characteristic varying on a continuous scale. Supplement to the Journal of the Royal Statistical Society, 6(1), 80-88.
48. Jongenburger, I., Reij, M. W., Boer, E. P. J., Gorris, L. G. M., & Zwietering, M. H. (2011). Random or systematic sampling to detect a localized microbial contamination within a batch of food. Food Control, 22(8), 1448-1455.
49. Jongenburger, I., Reij, M. W., Boer, E. P. J., Zwietering, M. H., & Gorris, L. G. M. (2012). Modelling homogeneous and heterogeneous microbial contaminations in a powdered food product. International Journal of Food Microbiology, 157(1), 35-44.
50. Kilsby, D. C., & Baird-Parker, A. C. (1983). Sampling programmes for microbiological analysis of food. In Food microbiology: Advances and prospects. Society for Applied Bacteriology Symposium series No. 11, (pp. 309-315). London: Academic Press.
51. Kilsby, D. C., Aspinall, L. J., & Baird‐Parker, A. C. (1979). A system for setting numerical microbiological specifications for foods. Journal of Applied Bacteriology, 46(3), 591-599.
52. Lachenbruch, P. A. (2001). Comparisons of two‐part models with competitors. Statistics in Medicine, 20(8), 1215-1234.
53. Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 34(1), 1-14.
54. Lauer, N. G. (1982). Probabilities of noncompliance for sampling plans in NBS Handbook 133. Journal of Quality Technology, 14(3), 162–165.
55. Lee, A. H., Wu, C. W., & Chen, Y. W. (2016). A modified variables repetitive group sampling plan with the consideration of preceding lots information. Annals of Operations Research, 238(1-2), 355–373.
56. Legan, J. D., Vandeven, M. H., Dahms, S., & Cole, M. B. (2001). Determining the concentration of microorganisms controlled by attributes sampling plans. Food Control, 12(3), 137-147.
57. Li, Y., Pu, X., & Xiang, D. (2011). Mixed variables-attributes test plans for single and double acceptance sampling under exponential distribution. Mathematical Problems in Engineering, 2011, 1-15.
58. Lieberman, G. J., & Resnikoff, G. J. (1955). Sampling plans for inspection by variables. Journal of the American Statistical Association, 50(270), 457-516.
59. Linkletter, C. D., Ranjan, P., Lin, C. D., Bingham, D. R., Brenneman, W. A., Lockhart, R. A., & Loughin, T. M. (2012). Compliance testing for random effects models with joint acceptance criteria. Technometrics, 54(3), 243–255.
60. Loganathan, A., & Shalini, K. (2014). Determination of single sampling plans by attributes under the conditions of zero-inflated Poisson distribution. Communications in Statistics-Simulation and Computation, 43(3), 538-548.
61. Ma, C., & Robinson, J. (2011). Lot acceptance and compliance testing based on the sample mean and minimum/maximum. Journal of Statistical Planning and Inference, 141(7), 2440 –2448.
62. Malik, M. B. (2012). Extensions and developments on the Schilling and Dodge mixed dependent acceptance sampling plans. Statistical Methodology, 9(4), 486-489.
63. Minami, M., Lennert-Cody, C. E., Gao, W., & Roman-Verdesoto, M. (2007). Modeling shark bycatch: the zero-inflated negative binomial regression model with smoothing. Fisheries Research, 84(2), 210-221.
64. Montgomery, D. C. (2013). Introduction to statistical quality control. New York: Wiley.
65. Mullahy, J. (1997). Heterogeneity, excess zeros, and the structure of count data models. Journal of Applied Econometrics, 12(3), 337-350.
66. Mussida, A., Gonzales-Barron, U., & Butler, F. (2013). Effectiveness of sampling plans by attributes based on mixture distributions characterising microbial clustering in food. Food Control, 34(1), 50-60.
67. Mwalili, S. M., Lesaffre, E., & Declerck, D. (2008). The zero-inflated negative binomial regression model with correction for misclassification: an example in caries research. Statistical Methods in Medical Research, 17(2), 123-139.
68. Newcombe, P. A., & Allen, O. B. (1988). A three-class procedure for acceptance sampling by variables. Technometrics, 30(4), 415-421.
69. Neyman, J. (1939). On a new class of" contagious" distributions, applicable in entomology and bacteriology. The Annals of Mathematical Statistics, 10(1), 35-57.
70. Owen, D. B. (1966). One-sided variables sampling plans. Industrial Quality Control, 22(3), 450-456.
71. Owen, D. B. (1967). Variables sampling plans based on normal distribution. Technometrics, 9(3), 417–423.
72. Owen, D. B. (1969). Summary of recent work on variables acceptance sampling with emphasis on non-normality. Technometrics, 11(4), 631-637.
73. Owen, W. J., & DeRouen, T. A. (1980). Estimation of the mean for lognormal data containing zeroes and left-censored values, with applications to the measurement of worker exposure to air contaminants. Biometrics, 707-719.
74. Palcat, F. A. (2006), Three-class sampling plans: a review with applications, Frontiers in Statistical Quality Control, 8, 34-52.
75. Perumean-Chaney, S. E., Morgan, C., McDowall, D., & Aban, I. (2013). Zero-inflated and over-dispersed: what is one to do? Journal of Statistical Computation and Simulation, 83(9), 1671-1683.
76. R Core Team. (2018). R: a language and environment for statistical computing. R Foundation for Statistical Computing: Vienna, Austria.
77. Ridout, M., Demétrio, C. G., & Hinde, J. (1998). Models for count data with many zeros. In Proceedings of the XIXth International Biometric Conference (pp.179-192). Cape Town, South Africa: International Biometric Society.
78. Santos-Fernández, E., Govindaraju, K., & Jones, G. (2014). A new variables acceptance sampling plan for food safety. Food Control, 44, 249-257.
79. Santos-Fernández,E.,Govindaraju, K., & Jones, G. (2016a). Quantity-based microbiological sampling plans and quality after inspection. Food Control, 63, 83-92.
80. Santos-Fernández, E., Govindaraju, K., Jones, G., & Kissling, R. (2017). New two-stage sampling inspection plans for bacterial cell counts. Food Control, 73, 503-510.
81. Santos‐Fernández, E., Kondaswamy, G., & Jones, G. (2016b). Compressed limit sampling inspection plans for food safety. Applied Stochastic Models in Business and Industry, 32(4), 469-484.
82. Schilling, E. G. (1985). The role of acceptance sampling in modern quality control. Communications in Statistics-Theory and Methods, 14(11), 2769-2783.
83. Schilling, E. (2005). Average run length and the OC curve of sampling plans. Quality Engineering, 17(3), 399-404.
84. Schilling, E. G., & Dodge, H. F. (1969). Procedures and tables for evaluating dependent mixed acceptance sampling plans. Technometrics, 11(2), 341-372.
85. Schilling, E.G., & Neubauer, D. V. (2017). Acceptance sampling in quality control. Boca Raton, FL: Chapman and Hall/CRC Press.
86. 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. Sankhyā: The Indian Journal of Statistics, Series B, 59(1), 96-107.
87. Soundararajan, V., & Vijayaraghavan, R. (1990). Construction and selection of multiple dependent (deferred) state sampling plan. Journal of Applied Statistics, 17(3), 397-409.
88. Suresh, K. K., & Devaarul, S. (2002). Designing and selection of mixed sampling plan with chain sampling as attribute plan. Quality Engineering, 15(1), 155-160.
89. Suresh, K. K., & Devaarul, S. (2003). Multidimensional mixed sampling plans. Quality Engineering, 16(2), 233-237.
90. Tian, L. (2005). Inferences on the mean of zero‐inflated lognormal data: the generalized variable approach. Statistics in Medicine, 24(20), 3223-3232.
91. Valero, A., Pasquali, F., De Cesare, A., & Manfreda, G. (2014). Model approach to estimate the probability of accepting a lot of heterogeneously contaminated powdered food using different sampling strategies. International Journal of Food Microbiology, 184, 35-38.
92. Vangel, M. G. (2002). Lot acceptance and compliance testing using the sample mean and an extremum. Technometrics, 44 (3), 242–249.
93. Van Schothorst, M., Zwietering, M. H., Ross, T., Buchanan, R. L., & Cole, M. B. (2009). Relating microbiological criteria to food safety objectives and performance objectives. Food Control, 20(11), 967-979.
94. Wallis, W. A. (1947). Use of variables in acceptance inspection for percent defective. Techniques of Statistical Analysis, 3-111.
95. Wang, F. K. (2018). Sampling plans by variables for inflated-Pareto data in the food industry. Food Control, 84, 97-105.
96. Wang, F. K., & Tamirat, Y. (2016). Two new independent mixed sampling plans for inspecting a product with linear profiles. Quality and Reliability Engineering International, 32(8), 2999-3009.
97. Whitaker, T. B., Doko, M. B., Maestroni, B. M., Slate, A. B., & Ogunbanwo, B. F. (2007). Evaluating the performance of sampling plans to detect fumonisin B1 in maize lots marketed in Nigeria. Journal of AOAC International, 90(4), 1050-1059.
98. Wilrich, P. T., & Weiss, H. (2011). Three-class sampling plans for the evaluation of bacterial contamination. Milchwissenschaft, 66(4), 413-416.
99. Wortham, A. W., & Baker, R. C. (1976). Multiple deferred state sampling inspection. International Journal of Production Research, 14(6), 719–731.
100. Yau, K. K., Wang, K., & Lee, A. H. (2003). Zero‐inflated negative binomial mixed regression modeling of over‐dispersed count data with extra zeros. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 45(4), 437-452.
101. Yee, T. W., & Dirnböck, T. (2009). Models for analysing species’ presence/absence data at two time points. Journal of Theoretical Biology, 259(4), 684-694.
102. Zidan, M., Wang, J. C., & Niewiadomska‐bugaj, M. (2011). Comparison of k independent, zero‐heavy lognormal distributions. Canadian Journal of Statistics, 39(4), 690-702.