# Optimized Risk-based Univariate Control Charts Calculate Optimized Risk-based Univariate Control Chart ```r rbcc_opt(X, UC, C, n, type=c("xbar", "R", "S"),confidence_level=0.9973, K_init=0,LKL=0,UKL=5) ``` ## Arguments - `X`: vector of variable (numeric vector). Either can be simulated using data_gen or defined by using available data set. - `UC`: vector of measuerement error (numeric vector).Either can be simulated using data_gen or defined by using available previous information. - `C`: vector of decision costs (default value is vector of 1). - `n`: the sample size for grouping. For individual obervations use n=1). - `type`: a character string specifying the type of Shewhart control chart. Available types are; "Xbar", "R"and "S". - `confidence_level`: the (1-alpha)percent confidence level(default value is 0.9973) - `K_init`: a correction component (default value is 0). - `LKL`: Lower limit of K parameter (default value is 0) - `UKL`: Upper limit of K parameter (default value is 5) ## Returns - **cost0**: Total cost of a monitoring process - **cost1**: Total cost of correct acceptance related to a process monitoring - **cost2**: Total cost of decision error type 2 related to a process monitoring - **cost3**: Total cost of decision error type 1 related to a process monitoring - **cost4**: Total cost of correct reject related to a process monitoring - **LCLx**: Lower Control Limit of a Shewhart univariate 'type' chart for a given data - **UCLx**: Upper Control Limit of a Shewhart univariate 'type' chart for a given data - **LCLy**: Lower Control Limit of an Optimal Risk-based univariate 'type' chart for a given data - **UCLy**: Upper Control Limit of an Optimal Risk-based univariate 'type' chart for a given data - **real**: Real values of plotting statistic for a given data - **Observed**: Observed plotting statistic for a given data with measurement errors - **par**: Optimal 'K' parameter of risk-based univariate 'type' chart ## 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 `data_gen`, `rbcc`, `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 summary(H) # summarize the results plot(H) # plot RBCC # optimal risk-based xbar control chart H_opt <- rbcc_opt(X, UC, C, n=3, type="xbar") summary(H_opt) ```

rbcc_opt function