# Optimized Risk-based EWMA Control Charts Calculate Optimized Risk-based Univariate exponentially weighted moving average Control Chart ```r rbewmacc_opt(X, UC, C, n=1, lambada=0.20, nsigmas=3, 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). - `lambada`: a weight or smoothing constant for EWMA control charts. The value is between (0,1). The defualt value is 0.20. - `nsigmas`: the charting multiplier(default value is 3) - `K_init`: Set correction component to 0 by default (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 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 a EWMA chart for a given data - **limit**: UCL of optimized risk based EWMA control chart for a given data - **real**: Real values of plotting statistic for a given data - **Observed**: Observed plotting statistic with measurement errors for a given data - **Kopt**: Optimal 'K' paramater of risk-based EWMA 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`, `rbmacc`, `rbmacc_opt`, `rbmcc`, `rbmcc_opt`, `plot.rbcc`, `summary.rbcc`. ## Examples ```r # Data generation for vector X 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. obs <- 200 # Total number of observations of a process. X <- data_gen (obs, mu_X, va_X, sk_X, ku_X) # Data generation for measurement error vector UC 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. UC <- data_gen(obs,mu_UC, va_UC, sk_UC, ku_UC) C <- c(1,1,1,1) # Define a vector of decision costs. H <- rbewmacc(X, UC, C) # for subgroups of size 1 # fit optimal risk-based EWMA control chart H_opt <- rbewmacc_opt(X, UC, C, n=1,lambada=0.20,nsigmas=3,K_init= 0,LKL=0,UKL=5) plot(H_opt) # plot RBEWMACC # with vector of proportional decision costs C <- c(1, 5, 60, 5) # vector of decision costs H <- rbewmacc(X, UC, C) # traditional risk-based EWMA control chat # fit optimal risk-based EWMA control chart H_opt <- rbewmacc_opt(X, UC, C, n=1,lambada=0.20,nsigmas=3,K_init= 0,LKL=0,UKL=5) plot(H_opt) # plot RBEWMACC ```

rbewmacc_opt function