| Type: | Package |
| Title: | Risk-Based Control Charts |
| Version: | 0.2.0 |
| Description: | 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) <doi:10.1016/j.eswa.2016.06.019>, Kosztyan and Katona (2018) <doi:10.1016/j.cie.2018.04.052>, Katona et al. (2023) <doi:10.1109/ACCESS.2023.3312226>, Saghir et al. (2025) <doi:10.1016/j.rineng.2025.107278>, and Saghir et al. (2026) <doi:10.1016/j.rico.2026.100661>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| Language: | en-US |
| LazyData: | true |
| Depends: | R (≥ 4.1.0) |
| Imports: | ggplot2 (≥ 3.4.0), parallel, PearsonDS, qcc, stats, utils |
| RoxygenNote: | 7.3.3 |
| ByteCompile: | true |
| NeedsCompilation: | no |
| URL: | https://github.com/kzst/rbcc |
| BugReports: | https://github.com/kzst/rbcc/issues |
| Packaged: | 2026-10-26 08:49:36 UTC; kzst |
| Author: | Aamir Saghir [aut], Attila Imre Katona [aut], Zsolt Tibor Kosztyan [aut, cre] |
| Maintainer: | Zsolt Tibor Kosztyan <kosztyan.zsolt@gtk.uni-pannon.hu> |
| Repository: | CRAN |
| Date/Publication: | 2026-10-26 13:00:14 UTC |
Risk-Based Control Charts
Description
Tools for risk-based statistical process control in the presence of measurement uncertainty. The package evaluates four decision outcomes and optimizes chart parameters by minimizing total decision cost.
Details
Available charts include X-bar, R, S, moving-average, EWMA, CUSUM, and
multivariate T-squared charts. See citation("rbcc") for references.
Author(s)
Aamir Saghir, Attila Imre Katona, and Zsolt Tibor Kosztyan.
Generate Data from the Pearson Distribution System
Description
Generate Data from the Pearson Distribution System
Usage
data_gen(
obs,
mu,
va,
sk,
ku,
seed = NULL,
engine = c("auto", "pearson"),
validate = TRUE
)
Arguments
obs |
Positive number of observations per variable. |
mu |
Numeric vector of means. |
va |
Numeric vector of variances. |
sk |
Numeric vector of skewness coefficients. |
ku |
Numeric vector of kurtosis coefficients. |
seed |
Optional integer seed. The caller's random-number state is restored after generation. |
engine |
Either |
validate |
Logical; validate inputs. |
Value
A numeric matrix with one column per variable.
Plot Risk-Based Control Charts
Description
Plot Risk-Based Control Charts
Usage
## S3 method for class 'rbcc'
plot(x, title = NULL, xlab = "Group", ylab = "Chart statistic", ...)
## S3 method for class 'rbcusumcc'
plot(x, title = NULL, xlab = "Group", ylab = "Cumulative sum", ...)
## S3 method for class 'rbmcc'
plot(x, title = NULL, xlab = "Group", ylab = "T-squared statistic", ...)
Arguments
x |
A fitted risk-based chart object. |
title |
Optional title. |
xlab, ylab |
Axis labels. |
... |
Reserved for future use. |
Value
A visible ggplot object.
Print Risk-Based Control-Chart Objects
Description
Print Risk-Based Control-Chart Objects
Usage
## S3 method for class 'rbcc'
print(x, digits = getOption("digits"), ...)
## S3 method for class 'rbcusumcc'
print(x, digits = getOption("digits"), ...)
## S3 method for class 'rbmcc'
print(x, digits = getOption("digits"), ...)
## S3 method for class 'summary.rbcc'
print(x, digits = getOption("digits"), ...)
## S3 method for class 'summary.rbcusumcc'
print(x, digits = getOption("digits"), ...)
## S3 method for class 'summary.rbmcc'
print(x, digits = getOption("digits"), ...)
Arguments
x |
A fitted or summarized chart object. |
digits |
Number of significant digits. |
... |
Additional print arguments. |
Value
The input object, invisibly.
Risk-Based Shewhart Control Chart
Description
Risk-Based Shewhart Control Chart
Usage
rbcc(
X,
UC,
C,
n,
type = c("xbar", "R", "S"),
confidence_level = 0.9973,
K = 3,
validate = TRUE
)
Arguments
X |
Numeric process observations. |
UC |
Numeric additive measurement errors. |
C |
Four decision costs ordered as |
n |
Subgroup size. Defaults to one when omitted. |
type |
Chart type: |
confidence_level |
Traditional-chart confidence level. |
K |
Nonnegative risk-based limit coefficient. |
validate |
Logical; validate inputs. |
Value
An object of class rbcc.
Construct Optimization Controls
Description
Construct Optimization Controls
Usage
rbcc_control(grid_size = 201L, tol = .Machine$double.eps^0.25)
Arguments
grid_size |
Number of points used by the grid optimizer. |
tol |
Positive numerical tolerance. |
Value
A list suitable for the control argument.
Optimize a Risk-Based Shewhart Control Chart
Description
Optimize a Risk-Based Shewhart Control Chart
Usage
rbcc_opt(
X,
UC,
C,
n,
type = c("xbar", "R", "S"),
confidence_level = 0.9973,
K_init = 0,
LKL = 0,
UKL = 5,
optimizer = c("exact", "optimize", "grid"),
parallel = FALSE,
workers = NULL,
control = list(),
validate = TRUE
)
Arguments
X |
Numeric process observations. |
UC |
Numeric additive measurement errors. |
C |
Four decision costs ordered as |
n |
Subgroup size. Defaults to one when omitted. |
type |
Chart type: |
confidence_level |
Traditional-chart confidence level. |
K_init |
Initial or tie-breaking coefficient. |
LKL, UKL |
Lower and upper search bounds. |
optimizer |
One of |
parallel |
Logical; parallelize the grid optimizer. |
workers |
Optional worker count. |
control |
A list created by |
validate |
Logical; validate inputs. |
Value
An optimized rbcc object.
Risk-Based CUSUM Control Chart
Description
Risk-Based CUSUM Control Chart
Usage
rbcusumcc(X, UC, C, n = 1, T = 5, se.shift = 1, K = 5, validate = TRUE)
Arguments
X |
Numeric process observations. |
UC |
Numeric additive measurement errors. |
C |
Four decision costs ordered as |
n |
Subgroup size. Defaults to one when omitted. |
T |
Positive traditional decision-interval coefficient. |
se.shift |
Positive standardized reference shift. |
K |
Nonnegative risk-based limit coefficient. |
validate |
Logical; validate inputs. |
Optimize a Risk-Based CUSUM Control Chart
Description
Optimize a Risk-Based CUSUM Control Chart
Usage
rbcusumcc_opt(
X,
UC,
C,
n = 1,
T = 5,
se.shift = 1,
K_init = 0,
LKL = 0,
UKL = 6,
optimizer = c("exact", "optimize", "grid"),
parallel = FALSE,
workers = NULL,
control = list(),
validate = TRUE
)
Arguments
X |
Numeric process observations. |
UC |
Numeric additive measurement errors. |
C |
Four decision costs ordered as |
n |
Subgroup size. Defaults to one when omitted. |
T |
Positive traditional decision-interval coefficient. |
se.shift |
Positive standardized reference shift. |
K_init |
Initial or tie-breaking coefficient. |
LKL, UKL |
Lower and upper search bounds. |
optimizer |
One of |
parallel |
Logical; parallelize the grid optimizer. |
workers |
Optional worker count. |
control |
A list created by |
validate |
Logical; validate inputs. |
Risk-Based EWMA Control Chart
Description
Risk-Based EWMA Control Chart
Usage
rbewmacc(
X,
UC,
C,
n = 1,
lambada = 0.2,
nsigmas = 3,
K = 3,
lambda = NULL,
validate = TRUE
)
Arguments
X |
Numeric process observations. |
UC |
Numeric additive measurement errors. |
C |
Four decision costs ordered as |
n |
Subgroup size. Defaults to one when omitted. |
lambada |
EWMA smoothing parameter; retained for compatibility. |
nsigmas |
Traditional EWMA limit coefficient. |
K |
Nonnegative risk-based limit coefficient. |
lambda |
Correctly spelled alias for |
validate |
Logical; validate inputs. |
Optimize a Risk-Based EWMA Control Chart
Description
Optimize a Risk-Based EWMA Control Chart
Usage
rbewmacc_opt(
X,
UC,
C,
n = 1,
lambada = 0.2,
nsigmas = 3,
K_init = 0,
LKL = 0,
UKL = 5,
lambda = NULL,
optimizer = c("exact", "optimize", "grid"),
parallel = FALSE,
workers = NULL,
control = list(),
validate = TRUE
)
Arguments
X |
Numeric process observations. |
UC |
Numeric additive measurement errors. |
C |
Four decision costs ordered as |
n |
Subgroup size. Defaults to one when omitted. |
lambada |
EWMA smoothing parameter; retained for compatibility. |
nsigmas |
Traditional EWMA limit coefficient. |
K_init |
Initial or tie-breaking coefficient. |
LKL, UKL |
Lower and upper search bounds. |
lambda |
Correctly spelled alias for |
optimizer |
One of |
parallel |
Logical; parallelize the grid optimizer. |
workers |
Optional worker count. |
control |
A list created by |
validate |
Logical; validate inputs. |
Risk-Based Moving-Average Control Chart
Description
Risk-Based Moving-Average Control Chart
Usage
rbmacc(X, UC, C, n = 1, w = 2, K = 3, validate = TRUE)
Arguments
X |
Numeric process observations. |
UC |
Numeric additive measurement errors. |
C |
Four decision costs ordered as |
n |
Subgroup size. Defaults to one when omitted. |
w |
Positive moving-average span. |
K |
Nonnegative risk-based limit coefficient. |
validate |
Logical; validate inputs. |
Optimize a Risk-Based Moving-Average Control Chart
Description
Optimize a Risk-Based Moving-Average Control Chart
Usage
rbmacc_opt(
X,
UC,
C,
n = 1,
w = 2,
K_init = 0,
LKL = 0,
UKL = 5,
optimizer = c("exact", "optimize", "grid"),
parallel = FALSE,
workers = NULL,
control = list(),
validate = TRUE
)
Arguments
X |
Numeric process observations. |
UC |
Numeric additive measurement errors. |
C |
Four decision costs ordered as |
n |
Subgroup size. Defaults to one when omitted. |
w |
Positive moving-average span. |
K_init |
Initial or tie-breaking coefficient. |
LKL, UKL |
Lower and upper search bounds. |
optimizer |
One of |
parallel |
Logical; parallelize the grid optimizer. |
workers |
Optional worker count. |
control |
A list created by |
validate |
Logical; validate inputs. |
Risk-Based Multivariate T-Squared Control Chart
Description
Constructs a risk-based Hotelling T-squared control chart in the presence of additive measurement uncertainty.
Usage
rbmcc(
X,
UC,
C,
n = 1,
confidence_level = 0.99,
K = 0,
validate = TRUE
)
Arguments
X |
Numeric matrix of true process characteristics. |
UC |
Numeric matrix of additive measurement errors. |
C |
Four decision costs ordered as |
n |
Subgroup size. |
confidence_level |
Traditional-chart confidence level. |
K |
Correction subtracted from the traditional upper control limit. |
validate |
Logical; validate inputs. |
Value
An object of class rbmcc.
References
Kosztyan, Z. T. and Katona, A. I. (2016). Risk-Based Multivariate Control Chart. Expert Systems with Applications, 62, 250–262. doi: 10.1016/j.eswa.2016.06.019
Examples
data("t2uc")
X <- as.matrix(t2uc[, 1:2])
UC <- as.matrix(t2uc[, 5:6])
C <- c(1, 20, 160, 5)
fit <- rbmcc(X, UC, C)
fit$cost0
Optimize a Risk-Based Multivariate T-Squared Control Chart
Description
Optimize a Risk-Based Multivariate T-Squared Control Chart
Usage
rbmcc_opt(
X,
UC,
C,
n = 1,
confidence_level = 0.99,
K_init = 0,
LKL = -5,
UKL = 5,
optimizer = c("exact", "optimize", "grid"),
parallel = FALSE,
workers = NULL,
control = list(),
validate = TRUE
)
Arguments
X |
Numeric matrix of true process characteristics. |
UC |
Numeric matrix of additive measurement errors. |
C |
Four decision costs ordered as |
n |
Subgroup size. |
confidence_level |
Traditional-chart confidence level. |
K_init |
Initial or tie-breaking correction. |
LKL, UKL |
Lower and upper correction bounds. |
optimizer |
One of |
parallel |
Logical; parallelize the grid optimizer. |
workers |
Optional worker count. |
control |
A list created by |
validate |
Logical; validate inputs. |
Value
An optimized rbmcc object.
Summarize Risk-Based Control-Chart Objects
Description
Summarize Risk-Based Control-Chart Objects
Usage
## S3 method for class 'rbcc'
summary(object, ...)
## S3 method for class 'rbcusumcc'
summary(object, ...)
## S3 method for class 'rbmcc'
summary(object, ...)
Arguments
object |
A fitted risk-based chart object. |
... |
Reserved for future use. |
Value
A structured summary object retaining all original components.
Brake-Cylinder Measurement Data
Description
Measurements of two brake-cylinder characteristics obtained with a high-precision optical system and production measurement devices. Measurement errors are the differences between production and optical measurements.
Usage
data("t2uc")Format
A data frame with 50 observations and six numeric variables:
- length_optical
Optical cutting-length measurement in millimeters.
- diameter_optical
Optical main-diameter measurement in millimeters.
- length_manual
Manual cutting-length measurement in millimeters.
- diameter_manual
Manual main-diameter measurement in millimeters.
- length_error
Manual minus optical cutting-length measurement.
- diameter_error
Manual minus optical main-diameter measurement.
Source
Automotive-industry measurement study.
References
Katona, A. I. (2021). Validation of Risk-Based Quality Control Techniques: A Case Study from the Automotive Industry. Journal of Applied Statistics.
Examples
data("t2uc")
X <- as.matrix(t2uc[, 1:2])
UC <- as.matrix(t2uc[, 5:6])
fit <- rbmcc_opt(X, UC, c(1, 20, 160, 5))
fit$cost0