# Data Generator for Risk-based Control Charts data_gen function simulate the data set from a specified distribution used in the risk based control charts. ```r data_gen(obs, mu, va, sk, ku) ``` ## Arguments - `obs`: The total number of observations of a process( a numeric value). - `mu`: The means of p characteristics/measurement errors (a numeric vector). - `va`: The variances of p characteristics/measurement errors (a numeric vector). - `sk`: The skewness of distribution of p characteristics/measurement errors (a numeric vector). - `ku`: The kurtosis of distribution of p characteristics/measurement errors (a numeric vector). ## Returns Return the data vector/matrix and the measurement error vector/matrix used in the risk-based control charts functions. ## References Katona, A. I., Saghir, A., Hegedűs, C., & Kosztyán, Z. T. (2023). Design of Risk-Based Univariate Control Charts with Measurement Uncertainty. IEEE Access. 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 `rbcc`, `rbcc_opt`, `rbcusumcc`, `rbcusumcc_opt`, `rbewmacc`, `rbewmacc_opt`, `rbmacc`, `rbmacc_opt`, `rbmcc`, `rbmcc_opt`, `plot.rbcc`, `summary.rbcc`. ## Examples ```r # Data Generation and Xbar chart. ## Example for generation of data vector X and measuremenet error vector UC. obs <- 200 # Total number of observations of a process. mu_X <- c(0) # Define data mean. va_X <- c(1) # Define data standard deviation. sk_X <- c(0) # Define data skewness. ku_X <- c(3) # Define data kurtosis. mu_UC <- c(0) # Define mean of measurement errors. va_UC <- c(1) # Define standard deviation of measurement errors. sk_UC <- c(0) # Define skewness of measurement errors. ku_UC <- c(3) # Define kurtosis of measurement errors. # Simulation of 200 obervations of 1 variable. X <- data_gen (obs, mu_X, va_X, sk_X, ku_X) # Simulation of 200 muasurement erros related to 1 variable. UC <- data_gen(obs,mu_UC, va_UC, sk_UC, ku_UC) # Construction of risk-based Xbar chart with default vector of decision costs C <- c(1,1,1,1) # vector of decision costs H <- rbcc(X, UC, C, n=3, type="xbar") # for subgroups of size 3 # Data Generation and multivariate T2 chart. # Data generation for a 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. # Example for generation of data matrix X of 200 obervations of 3 variables. X <- data_gen (obs, mu_X, va_X, sk_X, ku_X) # 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 with 3 variables. 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 # optimal risk-based multivariate control chart H_opt <- rbmcc_opt(X, UC, C) # 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) ```