When to use IQCC: exact and corrected control charts

Purpose

IQCC implements Improved Quality Control Charts: control charts with exact, corrected, or standardized limits for situations where classical Shewhart-type approximations may be poorly calibrated.

The package is not intended to replace general-purpose statistical process control packages. Instead, it is useful when the monitoring statistic is bounded, discrete, skewed, non-normal, or based on small samples. In those settings, the usual three-sigma limits can produce a false alarm probability that is meaningfully different from the nominal value.

Positioning in the R ecosystem

A practical way to position IQCC is:

IQCC is a specialized package for exact and corrected control-chart limits, especially for small samples, rare defects, asymmetric statistics, and selected multivariate monitoring problems.

Use a general SPC package when the goal is a broad control-chart workflow. Use IQCC when the main concern is whether the classical limits are statistically well calibrated for the distribution and sample size at hand.

When IQCC is especially useful

Monitoring problem	Classical difficulty	IQCC direction
Range-based dispersion monitoring	Normal approximations can inflate the actual false alarm risk, especially for small subgroups.	Use exact range-chart limits based on the relative range distribution.
Standard deviation monitoring	The distribution of the sample standard deviation is asymmetric for small samples.	Use exact limits derived from the chi-square distribution of the sample variance.
Nonconforming proportion in high-quality processes	The binomial distribution is discrete, bounded, and strongly skewed when the nonconforming proportion is very small.	Use Cornish-Fisher corrected limits or the double-sampling np chart.
Multivariate process mean monitoring	Hotelling T² requires phase-specific calibration.	Use the implemented Phase I and Phase II Hotelling T² functions.
Multivariate process variability	A single normal approximation for generalized variance may be poorly calibrated.	Candidate future extensions include generalized variance and auxiliary trace charts.

Current implemented methods

The current package includes several families of functions:

cchart.R() for range charts, including exact Tukey-based limits.
cchart.S() for standard deviation charts, including exact chi-square-based limits.
cchart.p() for nonconforming proportion charts, including Cornish-Fisher corrected limits.
cchart.u() for nonconformities per unit.
T2.1(), T2.2(), cchart.T2.1(), and cchart.T2.2() for Hotelling T² monitoring.
alpha.risk() for studying the actual false alarm risk of classical range charts.
dsnp_prob_accept(), dsnp_arl(), dsnp_ass(), dsnp_limits(), and cchart.DSnp() for double-sampling np charts.

Example: using a corrected p chart

The example below uses the package’s binomial data and constructs a p chart with Cornish-Fisher corrected limits. It is intentionally short; the purpose is to show where IQCC fits into the usual control-chart workflow.

library(IQCC)

data(binomdata)

cchart.p(
  x1 = binomdata$Di[1:12],
  n1 = binomdata$ni[1:12],
  type = "CF",
  x2 = binomdata$Di[13:25],
  n2 = binomdata$ni[13:25]
)

Example: DS-np chart with automatic limit search

The double-sampling np chart uses two sampling stages to monitor the nonconforming proportion in high-quality processes. dsnp_limits() searches for feasible fractional control limits, and cchart.DSnp() builds and plots the chart.

library(IQCC)

# Find limits for a given in-control proportion
lim <- dsnp_limits(p0 = 0.005, n1 = 34, n2 = 162, alpha = 0.0027,
                   p1 = 0.0075)
lim$best[, c("wl", "ucl1", "ucl2", "arl0", "arl1", "ass0")]

# Build the chart from observed data
x1 <- c(0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0)
x2 <- c(NA, NA, NA, NA, NA, NA, NA, NA, NA, 1, NA, NA, NA, NA, NA)

chart <- cchart.DSnp(x1, n1 = 34, n2 = 162, p0 = 0.005,
                     x2 = x2, limits = lim)
chart$performance

Development principles

Future extensions should follow three principles.

First, numerical calculations should be separated from plotting functions. A limit, probability, average run length, or false alarm risk shown in a chart should be reproducible by a small numerical function.

Second, new methods should be validated against published tables or examples when possible. This is particularly important for charts based on exact or corrected distributional calculations.

Third, IQCC should remain complementary to the broader R SPC ecosystem. Its strongest role is to provide statistically calibrated alternatives for cases where classical approximations are simple but inaccurate.

The main planned extensions are:

generalized variance charts for multivariate process variability;
Cornish-Fisher corrected generalized variance limits;
auxiliary trace charts for complementary multivariate variability monitoring;
validation fixtures reproducing numerical values from the underlying papers.

These items are tracked in the GitHub issue roadmap and should be implemented in small, reviewable pull requests.