IQCC in the R SPC Ecosystem: A Comparison

Introduction

The R environment hosts a mature collection of statistical process control (SPC) packages, each with distinct design goals, methodological coverage, and target audiences. General-purpose packages such as qcc and qcr provide broad charting workflows for Shewhart variables and attribute data, while specialized packages address areas like average run length computation, healthcare charting, or Six Sigma project frameworks. Choosing among them depends on the monitoring statistic, the distributional assumptions one is willing to make, and whether the primary concern is producing a chart or evaluating whether the chart’s limits are statistically well calibrated.

IQCC enters this landscape with a focused mandate: provide exact or distributionally corrected control chart limits where classical three-sigma or normal approximations are known to be poor. The package does not attempt to replicate every chart type available elsewhere. Instead, it targets specific pain points – bounded statistics, discrete counts with small denominators, rare nonconformities, asymmetric dispersion measures, and multivariate variability – where conventional SPC software either does not offer an alternative to the normal approximation or buries the numerical design behind a plotting function.

This vignette surveys the major R SPC packages, compares their features across a common set of dimensions, and identifies the conditions under which IQCC adds value beyond what the broader ecosystem provides. The goal is to help practitioners decide when IQCC is the right tool and when a general-purpose package is sufficient.

Comparable Packages

qcc (v2.7, last CRAN update 2017) is the most widely known SPC package in R. It implements Shewhart variables charts (xbar, R, S), attribute charts (p, np, c, u), CUSUM, EWMA, and a basic form of Hotelling T-squared. The package offers an integrated plotting system based on stats::qcc objects and has served as the foundation for several downstream packages. Its limits are exclusively three-sigma normal approximations.

shewhartr (v1.3.0, last CRAN update 2026) is a more recent and methodologically ambitious package that covers Shewhart variables charts, EWMA, CUSUM, Hotelling T-squared, MCUSUM, MEWMA, and regression-adjusted charts. It provides both three-sigma and exact Poisson limits for count data and explicitly separates Phase I calibration via calibrate() and Phase II monitoring via monitor(). The package ships seven vignettes.

qcr (v1.4, last CRAN update 2022) extends the SPC ecosystem beyond parametric charts by including Shewhart, EWMA, CUSUM, Hotelling T-squared, nonparametric depth-based control charts, and functional data monitoring. Its breadth is notable, but the package has no vignettes to guide users through its extensive functionality.

spc (v0.7.2, last CRAN update 2025) is a pure numerical package that computes average run lengths (ARL) for a wide range of control charts using integral equations. It does not draw charts, does not provide limit-finding functions for practitioners, and ships no vignettes. Its value lies in the research community that studies chart performance rather than in routine monitoring.

qicharts2 (v0.8.1, last CRAN update 2025) focuses on healthcare quality improvement and provides I, MR, Xbar, S, T, C, U, P, and G charts. It uses three-sigma limits alongside Anhoej decision rules and includes one vignette oriented toward clinical settings.

SixSigma (v0.11.1, last CRAN update 2023) provides a DMAIC (Define, Measure, Analyze, Improve, Control) project framework with basic control charting through ss.cc(). The package is oriented toward Six Sigma practitioners rather than methodological comparison or limit calibration.

IQCC (v0.7, active development 2026) provides Xbar, R, and S charts with exact distributional limits; p, np, c, and u charts with Cornish-Fisher corrected limits; Hotelling T-squared with asymptotically robust limits; generalized variance |S| limits; trace tr(V) limits; and the DS-np double-sampling plan, which is unique among R SPC packages. It separates pure numerical kernels from plotting wrappers, ships six vignettes and a full pkgdown site, and remains under active development.

Feature Comparison

Feature	qcc	shewhartr	qcr	spc	qicharts2	SixSigma	IQCC
Shewhart variables (R, S, xbar)	Yes	Yes	Yes	No	Yes	Yes	Yes
Attribute charts (p, np, c, u)	Yes	Yes	Yes	No	Yes	Yes	Yes
EWMA / CUSUM	Yes	Yes	Yes	ARL only	No	No	No
Exact distributional limits	No	Poisson only	No	No	No	No	Yes
CF-corrected limits	No	No	No	No	No	No	Yes
Phase I / Phase II separation	No	Yes	No	No	No	No	T² only
DS-np double-sampling	No	No	No	No	No	No	Yes
Rare defects charts	No	No	No	No	G chart	No	Yes
Multivariate T-squared	Basic	Yes	Yes	No	No	No	Yes
Multivariate	S	, tr(V)	No	No	No	No	No
ARL evaluation	No	No	No	Yes	No	No	Yes
Pure numerical kernels	No	Partial	No	Yes	No	No	Yes
Number of vignettes	1	7	0	0	1	0	6
Last CRAN update	2017	2026	2022	2025	2025	2023	active

Limit Methodology

The most important distinction among SPC packages is how each computes its control limits. Every package listed above can produce a control chart, but the statistical properties of those limits differ dramatically. qcc and qcr use three-sigma normal limits throughout: the upper and lower control limits are placed at three standard deviations above and below the center line, regardless of the underlying distribution. For large subgroup sizes and approximately normal data, this approach is adequate. For small subgroups, bounded proportions, rare counts, or skewed distributions, the actual false-alarm probability can deviate substantially from the nominal 0.0027.

shewhartr improves on this by offering exact Poisson limits for c and u charts. IQCC goes further by providing exact limits for R and S charts (based on the relative range distribution and the chi-square distribution, respectively), exact generalized variance limits in dimension two, and Cornish-Fisher corrected limits for p, np, c, and u charts. The Cornish-Fisher expansion adjusts the normal quantile using the skewness and kurtosis of the binomial or Poisson distribution, producing asymmetric limits that reflect the true shape of the monitoring statistic. IQCC also reports the actual false-alarm probability of any set of limits via pchart_alpha_risk() and uchart_alpha_risk(), enabling the practitioner to evaluate the calibration of either IQCC or third-party limits.

High-Quality Processes and Rare Defects

Conventional attribute charts perform poorly when the process proportion of nonconforming items is very small. A p chart with p = 0.001 and n = 100 has a lower control limit that is negative under the normal approximation, and the actual false-alarm probability of the three-sigma upper limit may be an order of magnitude smaller than intended. IQCC addresses this regime in two ways. First, the Cornish-Fisher correction produces asymmetric limits that remain non-negative and better reflect the binomial tail. Second, the DS-np double-sampling plan offers a specialized design for high-quality processes in which inspection is costly: a small first sample is inspected, and a second sample is drawn only when the first count falls in a warning zone. This reduces the average sample size under the in-control state while maintaining power against moderate shifts. No other R SPC package implements a double-sampling attribute plan.

qicharts2 offers a G chart for geometric monitoring of rare events, which captures a different use case (time-between-events rather than counts per sample). IQCC and qicharts2 are therefore complementary: the G chart suits continuous monitoring of interarrival times, while IQCC’s DS-np and CF-corrected p charts suit attribute sampling with fixed subgroup sizes.

Multivariate Monitoring

Multivariate SPC is an area of sharp differentiation among the packages. qcc provides a basic Hotelling T-squared chart with three-sigma limits. shewhartr provides Hotelling T-squared, MCUSUM, and MEWMA with Phase I and Phase II separation. qcr extends to nonparametric depth-based multivariate charts.

IQCC provides Hotelling T-squared with asymptotically robust limits, but its distinctive contribution is in multivariate variability monitoring. The generalized variance |S| chart detects changes in the determinant of the covariance matrix, and the trace statistic tr(V) chart detects changes in the trace of the scaled covariance matrix. These two statistics capture different aspects of covariance structure: |S| is sensitive to changes in the volume of the covariance ellipsoid, while tr(V) is sensitive to changes in the average variance across variables. Both statistics have exact or asymptotically justified limits in IQCC, and both are unavailable in the other packages surveyed. For a practitioner monitoring multivariate dispersion in addition to multivariate location, IQCC fills a gap that no other R package currently addresses.

Software Architecture

The SPC packages differ substantially in how they structure computation and plotting. qcc integrates both into a single S3 object with a unified qcc() function. qcr follows a similar monolithic design. This approach is convenient for quick use but obscures the numerical details of limit calculation and makes it difficult to reuse the statistical kernel without the plotting machinery.

IQCC adopts a deliberately separated architecture. Pure numerical functions such as pchart_limits(), gv_limits(), dsnp_arl(), and trv_limits() compute limits or operating characteristics without producing any graphical output. Chart wrappers such as cchart.p(), cchart.GV(), and cchart.DSnp() call these numerical kernels and pass the results to qcc for plotting. This separation allows the practitioner to inspect the limits and their diagnostic properties before committing to a chart, and it enables programmatic use of IQCC’s numerical methods in simulation studies or automated reporting pipelines.

shewhartr separates Phase I and Phase II monitoring through distinct calibrate() and monitor() functions, a design that parallels IQCC’s separation but at the workflow level rather than at the computation-versus-plotting level. spc operates entirely at the numerical kernel level with no charting at all, making it IQCC’s closest analogue in terms of pure computation but completely lacking any data analysis workflow.

Documentation

Documentation depth varies widely across the ecosystem. qcc ships one vignette that covers the basic chart types. qcr ships no vignettes despite its broad functionality, leaving users to navigate the help pages unaided. qicharts2 ships one vignette focused on healthcare applications. SixSigma and spc ship no vignettes.

shewhartr ships seven vignettes, making it the most thoroughly documented package among IQCC’s peers. IQCC ships six vignettes covering getting started, positioning, statistical foundations, high-quality processes, univariate dispersion monitoring, and multivariate monitoring, supplemented by a full pkgdown site with cross-referenced articles and function references.

When to Choose IQCC

IQCC is the appropriate choice when the monitoring statistic has a bounded or discrete support, when subgroup sizes are small enough to make normal approximations unreliable, when the process proportion or defect rate is very low, or when the goal is to monitor multivariate covariance structure rather than location alone. Specific scenarios include: attribute charting with p < 0.05 or small n, where the normal approximation produces negative limits or inaccurate false-alarm probabilities; R and S charting with n < 10, where the distribution of the range or standard deviation is markedly non-normal; double-sampling plans for high-quality processes where reducing inspection cost matters; and multivariate dispersion monitoring with the generalized variance or trace statistic.

IQCC is also the right choice when the practitioner needs to evaluate the actual false-alarm probability of a set of control limits rather than accepting the nominal 0.0027 value. The pchart_alpha_risk() and uchart_alpha_risk() functions compute exact binomial or Poisson probabilities for any supplied limits, making them useful as an audit tool even when the limits themselves come from another package.

Limitations of IQCC

IQCC does not implement EWMA or CUSUM charts, which are available in qcc, shewhartr, and qcr. For detecting small persistent shifts in location, these chart types are often more powerful than Shewhart charts, and the practitioner should use one of the general-purpose packages for that purpose.

IQCC does not offer nonparametric control charts of the kind provided by qcr’s depth-based methods. The package is entirely parametric in its current design. IQCC does not support functional data monitoring, regression-adjusted charts, or MCUSUM and MEWMA multivariate location schemes. Its multivariate coverage is limited to Hotelling T-squared, generalized variance, and the trace statistic.

IQCC’s exact distributional results are available only for specific combinations of statistic and dimension. Exact R chart limits are based on the relative range distribution; exact S chart limits are based on the chi-square distribution; exact generalized variance limits are available in dimension two. For higher dimensions, IQCC falls back to Cornish-Fisher corrections or simulation. The practitioner should consult the function documentation to determine whether an exact method exists for a given chart and parameter set.

IQCC remains under active development on GitHub but does not have the user base or CRAN download volume of established packages such as qcc or shewhartr. Community support, third-party extensions, and integration with other workflows are correspondingly more limited.

References

Scrucca, L. (2004). qcc: an R package for quality control charting and statistical process control. R News, 4(1), 11-17.

Cano, E. L., Moguerza, J. M., and Corcoba, M. P. (2015). Quality Control with R. Springer.

Santos-Fernandez, E. (2013). Multivariate Statistical Quality Control Using R. Springer.

Flores, M., Naya, S., Fernandez-Casal, R., Zaragoza, S., Roca-Pardinas, J., and Oviedo de la Fuente, M. (2022). qcr: quality control review. R package version 1.4.

Knoth, S. (2025). spc: statistical process control – collection of some SPC tools. R package version 0.7.2.

Jacob, A. (2025). qicharts2: quality improvement charts. R package version 0.8.1.

Canovas, L. (2023). SixSigma: Six Sigma tools for quality improvement. R package version 0.11.1.

Flores, M., Fernandez-Casal, R., and Oviedo de la Fuente, M. (2026). shewhartr: Shewhart control charts. R package version 1.3.0.