A control chart based on copula-based Markov time series models

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：9

、訪客IP：18.227.111.98

姓名

龍庭軒(Ting-Hsuan Long) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(A control chart based on copula-based Markov time series models)

相關論文

★ An improved nonparametric estimator of distribution function for bivariate competing risks model	★ Estimation and model selection for left-truncated and right-censored data: Application to power transformer lifetime modeling
★ A robust change point estimator for binomial CUSUM control charts	★ Maximum likelihood estimation for double-truncation data under a special exponential family
★ A class of generalized ridge estimator for high-dimensional linear regression	★ A copula-based parametric maximum likelihood estimation for dependently left-truncated data
★ A class of Liu-type estimators based on ridge regression under multicollinearity with an application to mixture experiments	★ Dependence measures and competing risks models under the generalized Farlie-Gumbel-Morgenstern copula
★ A review and comparison of continuity correction rules: the normal approximation to the binomial distribution	★ Likelihood inference on bivariate competing risks models under the Pareto distribution
★ Parametric likelihood inference with censored survival data under the COM-Poisson cure models	★ Likelihood-based analysis of doubly-truncated data under the location-scale and AFT models
★ Copula-based Markov chain model with binomial data	★ The Weibull joint frailty-copula model for meta-analysis with semi-competing risks data
★ A general class of multivariate survival models derived from frailty and copula models: application to reliability theory	★ Performance of a two-sample test with Mann-Whitney statistics under dependent censoring with copula models

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

不論在工業方面或是商業方面而言，統計製程管制(Statistical process control)皆是一個非常重要的品質管制工具。傳統的Shewhart管制圖僅是運用在獨立性的假設之下。然而，在現實生活中，存在著許多相關性假設的資料，因此，傳統的管制圖在現實生活中是不被接受且不實用的。在本文，我們主要的目的是以建立在copula之下的馬可夫鏈模型去衍伸我們的相關性假設資料。此外，我們提出了最大概似估計量的方法估計我們的未知參數，分別為管制上限(UCL)以及管制下限(LCL)。接著，我們使用蒙地卡羅模擬法做出平均串聯長度(Average run length)以用來表現管制圖的性質。最後，我們提出了降低變異數的方法去增加資料的準確性。

摘要(英)

Statistical process control is an important and convenient tool for business and industry. The traditional Shewhart control chart has been a popular tool for process control, which however is valid under the independence assumption of consecutive observations. In real world applications, there exist many types of dependent observations in which the traditional control charts cannot be used. In this paper, we apply a copula-based Markov chain to model the correlated observations. In particular, we proposed a maximum likelihood method to obtain the estimates of upper control limit (UCL) and lower control limit (LCL). It is shown by simulations that the proposed method provide more accurate estimates of the UCL and LCL than the existing procedure and traditional procedure. We also consider Monte Carlo simulations to compute the value of the average run length (ARL) of the proposed charts. Here, we suggest a variance reduction technique, called antithetic variables method to gain computational efficiency. Two datasets are analyzed for illustration.

關鍵字(中)

★ 平均串聯長度
★ Copula
★ 相關性資料
★ 馬可夫鏈
★ 降低變異數

關鍵字(英)

★ Average run length
★ Copula
★ correlated data
★ Markov chain
★ variance reduction

論文目次

摘要 i
Abstract ii
致謝詞 iii
List of Figures vii
List of Tables viii
Chapter 1 Introduction 1
Chapter 2 Background 4
Chapter 3 Estimation of process parameters 7
3.1. Chen and Fan’s method 8
3.2. Joe’s method (Proposed method) 9
3.2.1. Likelihood inference 9
3.2.2. Computational algorithm (Newton-Raphson) 10
3.3. Simulation result 12
3.3.1. Simulation method 12
3.3.2. The result for MSE 13
Chapter 4 Control chart based on Copula 19
4.1. 3 -Control Chart 19
4.2. Average Run Length Calculation 20
4.2.1. Monte Carlo and Data generation 20
4.2.2. Variance Reduction 21
4.3. Simulation Result 22
Chapter 5 Applications 26
5.1. Data Background 26
5.2. Numerical Result 26
Chapter 6 Conclusion and Discussion 35
Appendix A 37
A.1 Log-copula density 37
A.2 Likelihood function and its derivatives 37
A.3 R Codes for Joe’s Method 40
A.3.1 Description 40
A.3.2 Usage 40
A.3.3 Arguments 40
A.3.4 Definition and example 40
Reference 47

參考文獻

Bagshow, M., Johnson, R. A., 1975. The effect of serial correlation on the performance of CUSUM tests II. Technometrics 17, 73-80.
Chen, X., Fan, Y., 2006. Estimation of copula-based semiparametric time series models. Journal of Econometrics 130, 307-335.
Chernoff, H., Lehmann, E. L., 1954. The use of maximum likelihood estimates in chi-square tests for goodness of fit. The Annals of Mathematical Statistics 25, 579-586.
Darsow, W. F., Nguten B., Olsen, E. T., 1992. Copulas and Markov Processes. Illinois Journal of Mathematics 36, 600-642.
Dobric, J. Schmid, F., 2007. A Goodness of Fit Test for Copulas Based on Rosenblatt’s Transformation. Computational Statistics and Data Analysis 51, 4633-4642.
Efron B., 1979. Bootstrap methods: Another look at the jackknife. Ann. Statist 7, 1–26.
Emura, T. Lin C-W, Wang W., 2010. A Goodness-of-fit Test for Archimedean Copula Models in the Presence of Right Censoring. Computational Statistics and Data Analysis 54, 3033-3043.
Emura, T., Konno Y., 2012. A goodness-of-fit tests for parametric models based on dependently truncated data. Computational Statistics and Data Analysis 56, 2237-2250.
Frees, E. W., Valdez, E., 1998. Understanding the relationships using copulas. North American Actuarial Journal 2, 1-25.
Fuh, C. D., Teng, H. W., Wang, R. H., 2013. Efficient importance sampling for rare event simulation with application. Technical Report.
Genest, C., Remillard B., 2008. Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models. Annales de Institut Henri Poicare -Probabilites et Statistiques 44, 1096-1127.
Genest, C., Remillard, B., Beaudoin, D., 2009. Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics 44, 199-213.
Hryniewicz, O., 2012. On the robustness of the Shewhart control chart to different types of dependencies in data. Frontiers in Statistical Quality Control 10, 19-33.
Hung, Y. C., Tseng, N. F., 2012. Extracting informative variables in the validation of two-group causal relationship. Computational Statistics DOI 10, 1007/s00180-012-0351-z.
Joe, H., 1997. Multivariate Models and Dependence Concepts. CHAPMAN & HALL/CRC.
Johnson, R. A., Bagshaw, M., 1974. The effect of serial correlation on the performance of CUSUM tests. Technometrics 16, 103-112.
Knight, K., 2000. Mathematical Statistics. Chapman & Hall.
Kojadinovic, I., Yan, J., Holmes, M., 2011. Fast large-sample goodness-of-fit tests for copulas. Statistica Sinica 21, 841-871.
Montgomery, D. C., 2009. Statistical Quality Control, Sixth Edition. Wiley.
Nelsen, R. B., 2006. An Introduction to Copulas, 2nd Edition. Springer Series in Statistics, Springer-Verlag. New York.
Ross, S. M., 2006. Simulation, Fourth Edition. Elsevier.
Schmid, W., 2005. On the run length of a Shewhart chart for correlated data. Statistical Papers 36, 111-130.
Shewhart, W.A., 1931. Economic Control of Quality of Manufactured Product. New York: Macmillan.
Shumway, R. B., Stoffer, D. S., 2010. Time Series Analysis and Its Applications: With R Examples. Third Edition, Springer.
Sklar, A., 1959. Fonctions de re’partition a’ n dimensions et leurs marges. Publications de l’Intitut de Statistique de l’Universit de Paris 8, 229-231.
Stute, W., 1993. Bootstrap based goodness-of-fit test. Metrika 40, 243-256.

指導教授

江村剛志(Takeshi Emura)

審核日期

2013-6-19

推文