IQCC implements Improved Quality Control Charts: statistical process control charts with exact, corrected, or standardized limits for univariate and multivariate monitoring.
The package is motivated by a recurring practical problem in classical Shewhart-type control charts: when the statistic being monitored is discrete, skewed, bounded, or strongly non-normal, the usual normal-based three-sigma limits can be badly misplaced. In those cases, the nominal false alarm risk may be very different from the actual one. IQCC provides tools that keep the familiar control-chart workflow while using more appropriate probability limits whenever possible.
Main features
- Univariate control charts: X-bar, R, S, p, and u charts.
- Improved probability limits: exact limits, Cornish-Fisher corrected limits, and standardized variants.
- Multivariate control charts: Hotelling T² charts for Phase I and Phase II monitoring.
- False alarm diagnostics: tools for evaluating the actual false alarm risk of selected classical charts.
- Phase I and Phase II support: retrospective analysis and prospective process monitoring.
Implemented methods
| Monitoring problem | Function(s) | Implemented methods | Notes |
|---|---|---|---|
| Mean of a univariate process |
cchart.Xbar(), cchart.Xbar1(), cchart.Xbar2(), cchart.Xbar_R()
|
Shewhart-type X-bar charts | Includes support for X-bar/R workflows. |
| Range / process dispersion | cchart.R() |
Shewhart R chart; exact Tukey-based R chart | The exact chart uses the relative range distribution through the Tukey distribution. |
| Standard deviation | cchart.S() |
Normalized S chart; exact chi-square-based S chart | Exact limits are based on the chi-square distribution of the sample variance. |
| Nonconforming proportion | cchart.p() |
Shewhart p chart; Cornish-Fisher p chart; standardized p chart | The Cornish-Fisher option is designed for low nonconforming proportions where normal approximation is poor. |
| Double-sampling np chart |
dsnp_prob_accept(), dsnp_arl(), dsnp_ass(), dsnp_limits(), cchart.DSnp()
|
DS-np numerical core, limit search, and control chart | Two-stage sampling for high-quality processes with small samples. |
| Nonconformities per unit | cchart.u() |
Shewhart u chart; standardized u chart | Attribute chart for counts per inspection unit. |
| Multivariate mean vector |
T2.1(), T2.2(), cchart.T2.1(), cchart.T2.2()
|
Hotelling T² charts for Phase I and Phase II | Supports individual and subgroup observations. |
| Relative range constants |
d2(), d3()
|
Numerical integration using Tukey distribution functions | Used by exact R-chart calculations and false alarm diagnostics. |
| False alarm risk | alpha.risk() |
Exact false alarm probability for the classical three-sigma R chart | Useful for diagnosing inflated false alarm risk. |
Installation
Install the CRAN version:
install.packages("IQCC", dependencies = TRUE)Or install the development version from GitHub:
devtools::install_github("flaviobarros/IQCC")Quick start
library(IQCC)
# X-bar and R charts
data(pistonrings)
cchart.Xbar_R(pistonrings[1:25, ], 5)
# Exact R chart using Phase I data to estimate sigma
cchart.R(pistonrings[26:40, ], 5, type = "tukey", y = pistonrings[1:25, ])
# p chart with Cornish-Fisher limits
data(binomdata)
attach(binomdata)
cchart.p(
x1 = Di[1:12], n1 = ni[1:12],
type = "CF",
x2 = Di[13:25], n2 = ni[13:25]
)
# Hotelling T² chart (Phase I)
mu <- c(5.682, 88.22)
Sigma <- miscTools::symMatrix(c(3.770, -5.495, 13.53), 2)
datum <- data.1(20, 10, mu, Sigma)
estat <- stats(datum, 20, 10, 2)
T2 <- T2.1(estat, 20, 10)
cchart.T2.1(T2, 20, 10, 2)Learning more
The package includes vignettes that explain where IQCC fits and how to approach selected monitoring problems:
-
iqcc-positioningexplains when IQCC is a better fit than a classical normal-approximation chart and how it complements broader SPC packages. -
high-quality-processesfocuses on rare nonconformities, Cornish-Fisher p charts, and the DS-np numerical core.
Research background
IQCC was developed from research on improved statistical quality control charts, especially work associated with Emanuel Pimentel Barbosa and collaborators. The package emphasizes cases where classical Shewhart-type limits are simple and familiar but statistically inaccurate.
Important methodological themes include:
- Cornish-Fisher quantile correction for attribute charts in high-quality processes, where the nonconforming proportion is very small and the binomial distribution is highly skewed.
- Exact range-chart limits using the relative range distribution, implemented through the Tukey distribution, to avoid the false alarm inflation of normal-based R charts.
- Exact probability limits for S charts based on the chi-square distribution.
- Hotelling T² monitoring for multivariate process mean vectors.
Development roadmap
The package currently implements several core ideas from the research program, but some published methods are not yet implemented. Planned or candidate extensions include:
| Candidate extension | Statistical target | Possible function names | Status |
|---|---|---|---|
| Double-sampling np chart | Nonconforming proportion in high-quality processes with small samples |
dsnp_limits(), cchart.DSnp()
|
Implemented |
| Generalized variance chart | Multivariate process variability using |S|
|
gv_limits(), cchart.GV()
|
Planned |
| Cornish-Fisher corrected generalized variance chart | Corrected limits for |S| under non-normal sampling distribution |
gv_cf_limits() |
Planned |
| Auxiliary trace chart | Complementary monitoring using tr(V)
|
trv_limits(), cchart.trV()
|
Planned |
| Numerical validation tables | Reproduce selected values from the underlying papers |
tests/testthat/ fixtures |
Planned |
These extensions should be implemented incrementally, with pure numerical functions separated from plotting functions and with validation against published examples whenever possible.
References
- Montgomery, D.C. (2008). Introduction to Statistical Quality Control. 6th ed. Wiley.
- Barros, F. et al. (2017). IQCC: An R Package for Improved Quality Control Charts. Journal of Statistical Software.
- Joekes, S. and Barbosa, E.P. (2013). An improved attribute control chart for monitoring non-conforming proportion in high quality processes. Control Engineering Practice.
- Barbosa, E.P., Gneri, M.A. and Meneguetti, A. (2013). Range Control Charts Revisited: Simpler Tippett-like Formulae, Its Practical Implementation, and the Study of False Alarm. Communications in Statistics - Simulation and Computation.
- Joekes, S., Smrekar, M. and Barbosa, E.P. (2015). Extending a double sampling control chart for non-conforming proportion in high quality processes to the case of small samples. Statistical Methodology.