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

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/60081

Title:	A control chart based on copula-based Markov time series models
Authors:	龍庭軒;Long,Ting-Hsuan
Contributors:	統計研究所
Keywords:	平均串聯長度;Copula;相關性資料;馬可夫鏈;降低變異數;Average run length;Copula;correlated data;Markov chain;variance reduction
Date:	2013-06-19
Issue Date:	2013-07-10 12:04:53 (UTC+8)
Publisher:	國立中央大學
Abstract:	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。 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.
Appears in Collections:	[Graduate Institute of Statistics] Electronic Thesis & Dissertation

Files in This Item:

File	Description	Size	Format
index.html		0Kb	HTML	639	View/Open

社群 sharing

Loading...