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IQCC

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IQCC implements Improved Quality Control Charts: statistical process control charts with exact, corrected, standardized, or simulation-based 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, usual normal-based three-sigma limits can be badly misplaced. In those cases, the nominal false-alarm risk may differ substantially from the actual one. IQCC keeps the familiar control-chart workflow while exposing numerical functions that make limits, risk, ARL, and sample-size calculations reproducible and testable.

Main features

  • Univariate control charts: X-bar, R, S, p, and u charts.
  • Improved probability limits: exact, Cornish-Fisher corrected, standardized, and simulation-based limits.
  • High-quality processes: corrected p charts and double-sampling np charts for rare nonconformities.
  • Multivariate monitoring: Hotelling T² charts, generalized variance charts, and auxiliary tr(V) variability charts.
  • False-alarm diagnostics: exact binomial, Poisson, range-chart, and generalized variance risk calculations where available.
  • Phase I and Phase II support: retrospective estimation and prospective monitoring.
  • Research-oriented numerical layer: pure functions separated from plotting interfaces for validation and simulation studies.

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 X-bar/R workflows.
Range / process dispersion cchart.R() Shewhart R chart; exact Tukey-based R chart Exact limits use the relative range distribution.
Standard deviation cchart.S() Normalized S chart; exact chi-square-based S chart Exact limits use the sample-variance distribution.
Nonconforming proportion pchart_limits(), pchart_alpha_risk(), cchart.p() Normal, CF1, CF2, and standardized p charts Includes exact binomial false-alarm evaluation and pooled estimation.
Double-sampling np chart dsnp_prob_accept(), dsnp_arl(), dsnp_ass(), dsnp_limits(), cchart.DSnp() Exact-binomial DS-np performance, limit search, and chart Two-stage sampling for high-quality processes with small samples.
Nonconformities per unit uchart_limits(), uchart_alpha_risk(), cchart.u() Normal, CF1, CF2, and standardized u charts Includes exact Poisson risk and pooled rate estimation.
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.
Multivariate variability gv_stat(), gv_limits(), gv_alpha_risk(), cchart.GV() Normal, Cornish-Fisher, selected exact, and simulation-based generalized variance charts Exact dimension-two limits and selected published dimension-three quantiles.
Multivariate variability structure trv_stat(), trv_limits(), trv_alpha_risk(), cchart.trV() Exact chi-square and simulation-based trace-statistic charts Complements |S| by detecting standardized trace changes that may preserve determinant.
Relative range constants d2(), d3() Numerical integration using Tukey distribution functions Used by exact R-chart calculations.
False-alarm risk for R charts alpha.risk() Exact false-alarm probability for the classical three-sigma R chart Diagnoses inflated false-alarm risk.

Installation

Install the CRAN version:

install.packages("IQCC", dependencies = TRUE)

Install the development version from GitHub:

remotes::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 limits and exact false-alarm risk
p_limits <- pchart_limits(p = 0.015, n = 20, type = "cf2")
pchart_alpha_risk(
  p = 0.015,
  n = 20,
  lcl = p_limits$lcl,
  ucl = p_limits$ucl
)

# u-chart with pooled Phase I rate and CF2 limits
data(moonroof)
cchart.u(
  x1 = moonroof$yi[1:17],
  n1 = moonroof$ni[1:17],
  type = "cf2",
  x2 = moonroof$yi[18:34],
  n2 = moonroof$ni[18:34]
)

# DS-np performance for a published high-quality-process design
dsnp_arl(
  p = c(0.005, 0.0075),
  n1 = 34,
  n2 = 162,
  wl = 1.5,
  ucl1 = 2.5,
  ucl2 = 4.5
)

# Generalized variance limits for dimension two
gv_limits(
  n = 10,
  p = 2,
  det_sigma = 0.5320,
  type = "exact"
)

# Auxiliary trace chart for covariance-structure changes
set.seed(123)
phase1 <- array(rnorm(6 * 8 * 2), dim = c(6, 8, 2))
cchart.trV(phase1, Sigma0 = diag(2), plot = FALSE)

Learning more

The package includes three vignettes:

vignette("iqcc-positioning", package = "IQCC")
vignette("high-quality-processes", package = "IQCC")
vignette("statistical-foundations", package = "IQCC")
  • iqcc-positioning explains where IQCC fits in the R/SPC ecosystem.
  • high-quality-processes focuses on rare nonconformities, Cornish-Fisher p charts, and DS-np monitoring.
  • statistical-foundations records the probability models, derivations, and validation strategy behind the audited methods.

A longer article-oriented technical document is available at paper/statistical-foundations.md.

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 highly skewed attribute statistics;
  • exact discrete false-alarm evaluation for binomial and Poisson charts;
  • exact range-chart limits through the relative range distribution;
  • double-sampling designs for rare nonconformities;
  • Hotelling T² monitoring for multivariate process means;
  • generalized variance monitoring through products of chi-square variables and Bartlett decomposition;
  • auxiliary tr(V) monitoring through the trace of a standardized Wishart matrix.

Development roadmap

Candidate extension Statistical target Possible function names Status
Double-sampling np chart Nonconforming proportion in high-quality processes dsnp_limits(), cchart.DSnp() Implemented and validated
Generalized variance chart Multivariate process variability using |S| gv_limits(), cchart.GV() Implemented and validated
Cornish-Fisher generalized variance limits Corrected limits for skewed |S| distribution gv_limits(type = "cf") Implemented
Auxiliary trace chart Complementary monitoring using tr(V) trv_limits(), cchart.trV() Implemented
Full DS-np sample-size optimization Joint design over sample sizes and limits future API Planned
Generic exact generalized variance quantiles Meijer-G or another validated numerical approach future API Research stage
Numerical validation catalogue Centralized published fixtures and metadata tests/testthat/ and documentation In progress

References

  • Montgomery, D. C. (2008). Introduction to Statistical Quality Control. 6th ed. Wiley.
  • 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.