Control charts of mean and variance using copula Markov SPC and conditional distribution by copula

We propose control charts of mean and variance by using the Emura, Long, and Sun (2017) copula Markov statistical process control (SPC) and conditional distribution with diverse copula functions. To verify our new method, we generate bivariate simulated data by an asymmetric copula function and then make the conditional uniform transformed data by employing diverse copula distributions. We apply the conditional uniform transformed data to the Emura, Long, and Sun (2017) copula Markov SPC chart to investigate how copula directional dependence and copula tail dependence can affect the control charts of the mean and variance. For an illustrated example, we use Major League Baseball (MLB) batting average (BA) and earned run average (ERA) data from 1998 to 2016 seasons to detect a large abnormal variation of MLB statistics by using the proposed method. We show that the average run lengths (ARLs) of the control charts of conditional variance are affected by directional dependence by using the Gaussian copula beta regression (Kim and Hwang, 2017) and copula tail dependence.