Long, TingHsuan and Emura, Takeshi (2014): A control chart using copulabased Markov chain models. Forthcoming in: Journal of the Chinese Statistical Association
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Abstract
Statistical process control is an important and convenient tool to stabilize the quality of manufactured goods and service operations. The traditional Shewhart control chart has been used extensively for process control, which is valid under the independence assumption of consecutive observations. In real world applications, there are many types of dependent observations in which the traditional control chart cannot be used. In this paper, we propose to apply a copulabased Markov chain to perform statistical process control for correlated observations. In particular, we consider three methods to obtain the estimates of upper control limit (UCL) and lower control limit (LCL) for the control chart. It is shown by simulations that Joe’s parametric maximum likelihood method provides the most reliable estimates of the UCL and LCL compared to the other methods. We also propose simulation techniques to compute the average run length (ARL) of the proposed charts, which can be used to set the UCL and LCL for a given value of ARL. The piston rings data are analyzed for illustration.
Item Type:  MPRA Paper 

Original Title:  A control chart using copulabased Markov chain models 
English Title:  A control chart using copulabased Markov chain models 
Language:  English 
Keywords:  Average run length, Clayton model, correlated data, Kendall’s tau, Markov chain 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General 
Item ID:  57419 
Depositing User:  takeshi emura 
Date Deposited:  19 Jul 2014 04:43 
Last Modified:  26 Sep 2019 13:52 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/57419 
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