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Title: A control chart using a copula-based Markov chain for attribute data Authors:  Xin-Wei Huang - National Central University (Taiwan) [presenting]
Takeshi Emura - Kurume University (Japan)
Abstract: Statistical process control (SPC) is a fundamental tool in industrial manufacturers, financial engineers, medical researchers, and others. The application of copula-based Markov chain to SPC is a recent approach, where a copula can capture serial dependence between observations. So far, only continuous data are considered to perform SPC under the copula-based Markov chain model. We propose a SPC method under the copula-based Markov chain model for attribute data that follow the binomial distribution. We develop methods to compute the maximum likelihood estimator and control limits that are necessary to draw an attribute control chart. We also develop simulation algorithms to generate dependent attribute data that can be used to compute the average run length of the proposed control chart. Furthermore, we propose a goodness-of-fit method and a copula selection method. We conduct simulation studies to check the accuracy of the proposed estimator and to compare our method with other methods. We demonstrate the proposed method by analyzing the Korean stock market data. We implement the proposed methods in the R Copula.Markov package so that users can easily apply the proposed methods.