# Optimized Risk-based Multivariate Control Chart Calculate Optimized Risk-based Multivariate Control Chart ```r rbmcc_opt(X, UC, C, n=1, confidence_level=0.99, K_init=0,LKL=-5,UKL=5) ``` ## Arguments - `X`: matrix of variables (numeric matrix). Either can be simulated using data_gen or defined by using available data set. - `UC`: matrix of measuerement error (numeric matrix). - `C`: vector of decision costs (default value is vector of 1). - `n`: The sample size for grouping. For individual obervations use n=1). - `confidence_level`: The (1-alpha)percent confidence level (default value is 0.99) - `K_init`: Set correction component to 0 by default (default value is 0) - `LKL`: Lower limit of K parameter (default value is -5) - `UKL`: Upper limit of K parameter (default value is -5) ## Returns - **cost0**: Total cost of a monitoing process - **cost1**: Total cost of correct acceptance related to a process monitoring - **cost2**: Total cost of decision error type 1 related to a process monitoring - **cost3**: Total cost of decision error type 2 related to a process monitoring - **cost4**: Total cost of correct reject related to a process monitoring - **baselimit**: UCL of T^2 chart for a given data - **limit**: UCL of optimized risk based multivariate control chart for a given data - **real**: Real values of T2 statistic for a given data - **Observed**: Observed T2 with measurement errors for a given data - **Kopt**: Optimal K paramater of risk-based multivariate control chart for a given data ## References Katona, A. I., Saghir, A., Hegedűs, C., & Kosztyán, Z. T. (2023). Design of Risk-Based Univariate Control Charts with Measurement Uncertainty. IEEE Access, 11, 97567-97573. Kosztyán, Z. T., & Katona, A. I. (2016). Risk-based multivariate control chart. Expert Systems with Applications, 62, 250-262. ## Author(s) Aamir Saghir, Attila I. Katona, Zsolt T. Kosztyan* e-mail: kzst@gtk.uni-pannon.hu ## See Also `data_gen`, `rbcc`, `rbcc_opt`, `rbcusumcc`, `rbcusumcc_opt`, `rbewmacc`, `rbewmacc_opt`, `rbmacc`, `rbmacc_opt`, `rbmcc`, `plot.rbcc`, `summary.rbcc`. ## Examples ```r # Data generation for matrix X mu_X <- c(0,1,2) # vector of means. va_X <- c(1,2, 0.5) # vector of standard deviation. sk_X <- c(0,0.5, 0.8) # vector of skewness. ku_X <- c(3,3.5, 4) # vector of kurtosis. obs <- 200 # Total number of observations of a process. X <- data_gen (obs, mu_X, va_X, sk_X, ku_X) # generate data pints # Data generation for measurement error matrix UC mu_UC <- c(0,0,0) # vector of means of measurement errors. va_UC <- c(1,2, 0.5) # vector of standard deviation of measurement errors. sk_UC <- c(0,0,0) # Vector of skewness of measurement errors. ku_UC <- c(3,3,3) # Vector of kurtosis of measurement errors. # example for generation of measurement error matrix UC <- data_gen(obs,mu_UC, va_UC, sk_UC, ku_UC) # with default vector of decision costs C <- c(1,1,1,1) # vector of decision costs H <- rbmcc(X, UC, C) # for subgroups of size 1 plot(H) # plot RBMCC H_opt <- rbmcc_opt(X, UC, C) # optimal risk-based multivariate control chart # with vector of proportional decision costs C <- c(1, 5, 60, 5) # vector of decision costs H <- rbmcc(X, UC, C) # for subgroups of size 1 H_opt <- rbmcc_opt(X, UC, C) # optimal risk-based multivariate control chart # with vector of proportional decision costs and sugbroup size 3 C <- c(1, 5, 60, 5) # vector of decision costs H <- rbmcc(X, UC, C, 3) # for subgroups of size 3 H_opt <- rbmcc_opt(X, UC, C, 3) # optimal risk-based multivariate control chart # Plot of Hotelling's T2 and optimal risk based multivariate control charts plot(H_opt) # Example of considering the real sample data("t2uc") # load the dataset X <- as.matrix(t2uc[,1:2]) # get optical measurements ar "real" values UC <- as.matrix(t2uc[,5:6]) # get measurement errors C <- c(1,20,160,5) # define cost structure # Fit optimized RBT2 control chart R <- rbmcc_opt(X, UC, C, 1,confidence_level = 0.99) summary(R) # summarize the results plot(R) # plot the result ```

rbmcc_opt function