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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 廖振鐸(Chen-Tuo Liao) | |
dc.contributor.author | Chien-Lang Chen | en |
dc.contributor.author | 陳建郎 | zh_TW |
dc.date.accessioned | 2021-06-15T13:39:58Z | - |
dc.date.available | 2016-02-15 | |
dc.date.copyright | 2016-02-15 | |
dc.date.issued | 2015 | |
dc.date.submitted | 2016-01-14 | |
dc.identifier.citation | [1] I. Affleck and F. D. M. Haldane. Critical theory of quantum spin chains. Physical Review B, 36:5291–5300, 1987.
[2] Agresti, A., and Coull, B. A. Approximate is better than exact for interval estimation of binomial proportions. The American Statistician, 52:119–126, 1998. [3] Beall, G. Approximate methods in calculating discriminant functions. Psychometrika, 10:205–217, 1945. [4] Bernardo, J. M. and Irony, T. Z.. A general multivariate bayesian process capability index. The Statistician, 45:487–502, 1996. [5] Brown, L. D., Cai, T. T., and DasGupta, A. Interval estimation for a binomial pro¬portion. Statistical Science, 16:101–117, 2001. [6] Brown, L. D., Cai, T. T., and Dasgupta, A. Confidence intervals for a binomial and asymptotic expansions. Annals of Statistics, 30:160–201, 2002. [7] Chen, H. A multivariate process capability index over a rectangular solid tolerance zone. Statistica Sinca, 4:749–758, 1994. [8] Gamage, J., Mathew, T., and Weerahandi, S. Generalized p-values and generalized confidence regions for the multivariate behrensvfisher problem and MANOVA. Journal of Multivariate Analysis, 88:177–189, 2004. [9] Graybill, F. A., and Wang, C. M. Confidence intervals on nonnegative linear com-binations of variances. Journal of the American Statistical Association, 75:869–873, 1980. [10] Hannig, J. On generalized fiducial inference. Statistica Sinica, 19:491–544, 2009. [11] Hannig, J., Iyer, H., and Patterson, P. Fiducial generalized confidence intervals. Journal of the American Statistical Association, 101:254–269, 2006. [12] Hoffman, D., and Kringle, R. Two-sided tolerance intervals for balanced and unbalanced random effects models. Journal of Biopharmaceutical Statistics, 15:283–293, 2005. [13] Howe, W. G. Two-sided tolerance limits for normal populations, some improvements. Journal of the American Statistical Association, 64:610–620, 1969. [14] Iyer, H. K., and Patterson, P.. A recipe for constructing generalized pivotal quantities and generalized confidence intervals. Colorado State University Department of Statistics Technical Report, 10, 2002. [15] Johnson, R. A., and Wichern, D. W. Applied Multivariate Statistical Analysis. Engle-wood Cliffs, NJ: Prentice hall, 1992. [16] Kotz, S., and Johnson, N. L. Process capability indices: A review, 1992-2000. discussions. Journal of Quality Technology, 34:2–53, 2002. [17] Krishnamoorthy, K. and Mathew, T. Statistical Tolerance Regions: Theory, Applications, and Computation. John Wiley & Sons, 2009. [18] Lee, H. I., and Liao, C. T. Estimation for conformance proportions in a normal variance components model. Journal of Quality Technology, 44:63–79, 2012. [19] Lee, H. I., and Liao, C. T. Unilateral conformance proportions in balanced and unbalanced normal random effects models. Journal of Agricultural, Biological, and Environmental Statistics, 19:202–218, 2014. [20] Lee, Y., Shao, J. and Chow, S. C. Modified large-sample confidence intervals for linear combinations of variance components: extension, theory, and application. Journal of the American Statistical Association, 99:467–478, 2004. [21] Liao, C. T., and H. K. Iyer. A tolerance interval for the normal distribution with several variance components. Statistica Sinica, 14:217–230, 2004. [22] Liao, C. T., Lin, T. Y. and Iyer, H. K. One-and two-sided tolerance intervals for general balanced mixed models and unbalanced one-way random models. Technometrics, 47:323–335, 2005. [23] Lin, T. Y., Liao, C. T., and Iyer, H. K. Tolerance intervals for unbalanced one-way random effects models with covariates and heterogeneous variances. Journal of Agricultural, Biological, and Environmental Statistics, 13:221–241, 2008. [24] Lubischew, A. A. On the use of discriminant functions in taxonomy. Biometrics, 18:455–477, 1962. [25] Newcombe, R. G. . Confidence intervals for proportions and related measures of effect size. CRC Press., 2012. [26] Perakis, M. and Xekalaki, E. A process capability index that is based on the proportion of conformance. Journal of Statistical Computation and Simulation, 27:707–718, 2002. [27] Perakis, M., and Xekalaki, E. A process capability index that is based on the proportion of conformance. Journal of Statistical Computation and Simulation, 72:707–718, 2002. [28] Rencher, Alvin C. Methods of Multivariate Analysis. John Wiley & Sons, 2003. [29] Shahriari, H., and Abdollahzadeh, M. A new multivariate process capability vector. Quality Engineering, 21:290–299, 2009. [30] Smith, R. W. The use of random-model tolerance intervals in environmental monitoring and regulation. Journal of agricultural, biological, and environmental statistics, 7:74– 94, 2002. [31] Wald Abraham, and J. Wolfowitz. Tolerance limits for a normal distribution. The Annals of Mathematical Statistics, 17:208–215, 1946. [32] Wang, C. M., and Iyer, H. K. Tolerance intervals for the distribution of true values in the presence of measurement errors. Technometrics, 36:162–170, 1994. [33] Wang, C. M., and Lam, C. T. Confidence limits for proportion of conformance. Journal of quality technology, 28:439–445, 1996. [34] Weerahandi, S. Generalized confidence intervals. Journal of the American Statistical Association, 88:899–905, 1993. [35] Weerahandi, S. Generalized inference in repeated measures: exact methods in MANOVA and mixed models. John Wiley & Sons, 2004. [36] Wilks, S. S. Determination of sample sizes for setting tolerance limits. The Annals of Mathematical Statistics, 12:91–96, 1941. [37] Wilson, E. B.. Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22:209–212, 1927. [38] Yum, B. J., and Kim, K. W. A bibliography of the literature on process capability indices: 2000–2009. Quality and Reliability Engineering International, 27:251–268, 2011. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/51585 | - |
dc.description.abstract | 工業產品的產製過程,對於產品的品質特徵值(quality characteristic)的要求通常是期望高過所期望的一定高之比例的產品落入預定的規格(specification acceptance region)內,符合此要求的產品之比例(proportion),即是所謂的良質率(conformance proportion)。對應到統計學上,即是以一個隨機變數(random variable)來代表此一品質特徵值,此隨機變數落於某個給定的規格範圍(specification limits)的比例即為良質率。由於實際產製過程,產品的品質往往是由多個品質特徵值(multiple quality characteristics)決定,所以本論文的研究著重於多變量下之良質率的區間估計。我們提出兩類型的估計方法,第一類型是依照廣義樞紐量(Fiducial Generalized Pivotal Quantity)(FGPQ)的概念推導出的方法(FGPQ-based method),另一類型則是利用二項分佈推導出的方法(Binominal-distribution-based method)。本論文的第二章討論單一個多變量常態分佈(multivariate normal distribution)之良質率的區間估計,此處我們建構信賴下界(lower confidence limit),對此良質率進行右尾假設檢定。第三章則是建構兩個良質率之差異(difference)的信賴區間(two-sided confidence interval) 以進行雙尾假設檢定。我們利用統計模擬來評估各個方法的表現,實際應用時,若無給定的規格範圍,則使用容許區間(statistical tolerance intervals)去建構適當的規格範圍,除了與製程良率相關的實例外,本論文亦討論台灣地區空氣品質及物種判別的實際資料分析。 | zh_TW |
dc.description.abstract | An industrial product is considered to be actually usable, but not scrap or defective, it usually needs to meet multiple performance requirements, which are referred to as quality characteristics. The individual component of such quality characteristics may be qualitative (nominal or ordinal) or quantitative (discrete or continuous). In specificity, the performance requirement of each single quantitative characteristic is often specified by a target value along with a conformance region or an acceptance region, which is described by means of a lower and an upper specification limit. A product is deemed to be a conforming product if all of the quality characteristics fall into these specification limits. Confidence limits for the conformance proportion are usually required not only to perform statistical significance test, but also to provide useful information for determining practical significance.
In this dissertation, we develop approaches for computing confidence limits for the conformance proportion of multiple quality characteristics that are assumed to be distributed as a multivariate normal distribution. Based on the concept of a fiducial generalized pivotal quantity (FGPQ) and on the Binomial distribution by treating it as the success proportion of a binary population. We first focus on a single conformance proportion, and then extend to the situation of a difference between two the conformance proportions. The estimation performance of the proposed methods is evaluated through detailed simulation studies. Some real data examples are collected to illustrate the application of the conformance proportion, including manufacture process data, air quality data and flea beetle species data, etc. | en |
dc.description.provenance | Made available in DSpace on 2021-06-15T13:39:58Z (GMT). No. of bitstreams: 1 ntu-104-D96621201-1.pdf: 1179862 bytes, checksum: 43249ebd8f73608d52a5ce57b75101ca (MD5) Previous issue date: 2015 | en |
dc.description.tableofcontents | I INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . 1
1.1 Statement of Problems . . . . . . . . . . . . . . . . 1 1.2 Literature Review . . . . . . . . . . . . . . . . . . 3 1.3 The Plan of the Dissertation. . . . . . . . . . . . . 4 II A SINGLE CONFORMANCE PROPORTION . . . . . . . . . . . 5 2.1 Estimation Methods. . . . . . . . . . . . . . . . . . 5 2.1.1 Fiducial Generalized Pivotal Quantity Based Method .5 2.1.2 Binomial-Distribution-Based Methods . . . . . . . . 8 2.2 Simulation Studies . . . . . . . . . . . . . . . . . 10 2.3 Illustrative Examples . . . . . . . . . . . . . . . . 17 2.4 Concluding Remarks. . . . . . . . . . . . . . . . . . 20 III THE DIFFERENCE OF TWO CONFORMANCE PROPORTIONS . . . .21 3.1 Estimation Methods . . . . . . . . . . . . . . . . . 21 3.1.1 Fiducial Generalized Pivotal Quantity based Method. 21 3.1.2 Binomial-Distribution-Based Methods . . . . . . . . 23 3.2 Simulation Studies . . . . . . . . . . . . . . . . . 25 3.3 Illustrative Examples . . . . . . . . . . . . . . . . 32 3.4 Concluding Remarks . . . . . . . . . . . . . . . . . 43 IV FURTHER RESEARCH . . . . . . . . . . . . . . . . . . . 47 References . . . . . . . . . . . . . . . . . . . . . . . 48 | |
dc.language.iso | en | |
dc.title | 多變量良質率之區間估計 | zh_TW |
dc.title | Interval Estimation for the Multivariate Conformance Proportion | en |
dc.type | Thesis | |
dc.date.schoolyear | 104-1 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 劉仁沛,林彩玉,高振宏,劉力瑜 | |
dc.subject.keyword | 二項分佈,廣義樞紐量,多變量常態分佈,製程能力分析,容許區間, | zh_TW |
dc.subject.keyword | Binomial distribution,Generalized pivotal quantity,Multivariate normal distribution,Process capability analysis,Tolerance interval, | en |
dc.relation.page | 51 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2016-01-15 | |
dc.contributor.author-college | 生物資源暨農學院 | zh_TW |
dc.contributor.author-dept | 農藝學研究所 | zh_TW |
顯示於系所單位: | 農藝學系 |
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