Risk-Based Control Charts

Implements univariate and multivariate risk-based control charts for statistical process control in the presence of measurement uncertainty. Available charts include Shewhart X-bar, R, and S charts, moving-average charts, exponentially weighted moving-average charts, cumulative-sum charts, and Hotelling T-squared charts. Chart parameters can be optimized by minimizing the total cost of the four decision outcomes. The methodology is described by Kosztyan and Katona (2016) , Kosztyan and Katona (2018) , Katona et al. (2023) , Saghir et al. (2025) , and Saghir et al. (2026) .

rbcc 0.2.0

rbcc implements risk-based statistical process control charts in the presence of measurement uncertainty. The package evaluates all four possible decision outcomes—correct acceptance, false control, missed control, and correct control—and can optimize chart limits by minimizing their total cost.

Available charts

• Shewhart X-bar, R, and S charts: rbcc() and rbcc_opt()
• Moving-average charts: rbmacc() and rbmacc_opt()
• EWMA charts: rbewmacc() and rbewmacc_opt()
• CUSUM charts: rbcusumcc() and rbcusumcc_opt()
• Multivariate Hotelling T-squared charts: rbmcc() and rbmcc_opt()

Version 0.2.0 substantially refactors the computational core. Optimization no longer rebuilds a complete chart for every trial value. The default exact threshold optimizer exploits the piecewise-constant structure of the decision cost and is deterministic. Bounded numerical optimization and optional parallel grid search remain available.

Example

library(rbcc)

set.seed(42)
X <- rnorm(80, mean = 10, sd = 0.5)
UC <- rnorm(80, mean = 0, sd = 0.05)
C <- c(1, 5, 60, 5)

fit <- rbcc_opt(X, UC, C, n = 1, type = "xbar")
print(fit)

s <- summary(fit)  # no console output
s$cost0

p <- plot(fit)     # no drawing during assignment
p                  # draws the ggplot object

Optional parallel grid optimization

fit_grid <- rbcc_opt(
  X, UC, C,
  optimizer = "grid",
  parallel = TRUE,
  workers = 2,
  control = rbcc_control(grid_size = 401)
)

See citation("rbcc") for the methodological publications.