process-improve

Multivariate analysis, designed experiments, and process monitoring for Python. Built for the chemometrics, manufacturing, and pharma workflows where you need to know not just what fits, but is this observation normal, which variable moved, and how sure am I?

New here? The architecture overview (source) is the map of the codebase - package layout, the estimator stack, and the MCP tool layer.

What's new

The last few releases extend process-improve from offline model-building into end-to-end, on-line workflows. Highlights (full history in CHANGELOG.md):

• Design, rather than predict. PLS.invert() (v1.61) solves for the inputs that reach a target quality, and returns the null space of equally valid recipes. OPLS reaches the same designs by separating that freedom while fitting. See the user guide or the longer book chapter.
• Models that keep up with a drifting process. AdaptivePCA and AdaptivePLS (v1.55) fit once, then stream one observation at a time, re-learning the correlation structure and reporting how far the process has drifted, in units of components.
• A DOE engine that goes past textbook designs. OMARS designs, D-/I-/A-optimal designs, fractional-cube CCDs, design augmentation (fixed_runs=), and an evaluate_design suite scoring any design on efficiency, aliasing, and prediction variance.
• Sensory & descriptive panel analysis (process_improve.sensory): validate a panel, flag inconsistent assessors with the Mixed Assessor Model, and relate attributes to product covariates.
• Robust regression (process_improve.regression): repeated-median and Theil-Sen estimators for data with outliers, plus OLS and fit_robust_lm.

What it does

process-improve provides production-grade implementations of the methods practitioners actually use on real plant and lab data:

• PCA with SVD and NIPALS, plus native missing-value handling via Trimmed Score Regression
• PLS regression with a fully sklearn-compatible API, VIP scores, and cross-validated diagnostics
• TPLS - PLS for T-shaped (multi-block) data structures
• Model inversion - PLS.invert() and OPLS solve for the inputs that reach a target quality, return the null space of equally valid designs, and report how far each design sits from the data that support it
• Adaptive PCA / PLS - recursive, self-updating models for on-line process monitoring and soft sensing; they follow a drifting process one observation at a time and report how far it has moved
• Outlier detection combining Hotelling's T² and SPE with an ESD-based test
• Designed experiments - full-factorial, fractional-factorial, and response-surface designs; OMARS and D-/I-/A-optimal designs; a design-quality scorer (evaluate_design); and a multi-stage DOE strategy recommender
• Process monitoring - Shewhart, CUSUM, and Holt-Winters control charts
• Batch data analysis - alignment, feature extraction, and multivariate batch monitoring (MBPCA / MBPLS)
• Sensory & descriptive panel analysis - panel validation, the Mixed Assessor Model, and attribute-to-product relations with a genuine-vs-proxy separation
• Robust regression - repeated-median and Theil-Sen estimators for data with outliers
• Interactive Plotly diagnostics bound directly to every fitted model

Outputs are pandas-native: scores, loadings, and predictions keep your row and column labels.

It is the companion package to the online textbook Process Improvement using Data.

Works alongside scikit-learn

process-improve is designed to sit next to scikit-learn, not replace it. It follows the same conventions (fit, predict, score, the _ suffix on fitted attributes), so its estimators drop straight into Pipeline, GridSearchCV, and cross_val_score. What it adds is the process-analytics layer on top: the diagnostics that tell you whether a new observation is normal, which variable moved, and how confident the prediction is.

Installation

pip install process-improve                    # core (numpy, pandas, sklearn, statsmodels, patsy, pydantic, pyyaml, tqdm)
pip install 'process-improve[plotting]'        # adds matplotlib, plotly, seaborn, ridgeplot
pip install 'process-improve[expt]'            # adds pyDOE3 (designed experiments / DOE)
pip install 'process-improve[batch]'           # adds openpyxl, scikit-image (batch process data IO)
pip install 'process-improve[mcp]'             # adds the MCP server runtime
pip install 'process-improve[fast]'            # adds numba (JIT speedups for batch alignment)
pip install 'process-improve[all]'             # everything above (the pre-1.24.11 closure)

Requires Python 3.10 or newer. The core install pulls in numpy, pandas, scikit-learn, statsmodels, patsy, pydantic, pyyaml, and tqdm (scipy arrives transitively via scikit-learn and statsmodels). Heavier optional surfaces (plotting, designed experiments, batch IO, MCP server, numba JIT) live in extras so a caller who only needs, say, detect_multivariate_outliers does not have to install Plotly or numba.

Use it from Claude

The designed-experiments tooling ships as a Claude Skill, so you can plan, generate, verify and analyse experiments in your own Claude account with no server involved:

/plugin marketplace add kgdunn/process-improve
/plugin install doe-designer@process-improve

The skill's first rule is that a design matrix is never written out by the model: it is generated from a catalogue and then verified, because a language model asked to produce a fractional factorial will often return one that looks right and is a lower resolution than it claims. See skills/README.md for the other install routes (local folder, claude.ai upload) and for the MCP server, which exposes the same tool registry without the workflow guidance.

Quick start

PCA - Principal Component Analysis

import pandas as pd
from process_improve.multivariate.methods import PCA, MCUVScaler

X = pd.read_csv("your_data.csv", index_col=0)
X_scaled = MCUVScaler().fit_transform(X)

pca = PCA(n_components=3).fit(X_scaled)
print(pca.r2_cumulative_)         # cumulative R² per component
pca.score_plot()                  # interactive Plotly figure

# Flag outliers using combined T² and SPE limits at 95% confidence
outliers = pca.detect_outliers(conf_level=0.95)

# Which variables drove the first observation off?
contrib = pca.score_contributions(pca.scores_.iloc[0].values)

PLS - Projection to Latent Structures

from process_improve.multivariate.methods import PLS, MCUVScaler

# Scale X and Y separately
scaler_x = MCUVScaler().fit(X)
scaler_y = MCUVScaler().fit(Y)
X_s, Y_s = scaler_x.transform(X), scaler_y.transform(Y)

pls = PLS(n_components=3).fit(X_s, Y_s)
print(pls.beta_coefficients_)     # regression coefficients (K x M)
print(pls.r2_cumulative_)         # cumulative R² for Y
print(pls.vip())                  # VIP scores per X variable

# Predict new observations (sklearn-compatible: returns just y_hat)
y_pred = pls.predict(scaler_x.transform(X_new))

# Predict with full per-row diagnostics (scores, T², SPE, plus y_hat)
result = pls.diagnose(scaler_x.transform(X_new))
result.y_hat                      # point predictions
result.spe                        # squared prediction error
result.hotellings_t2              # Hotelling's T² for new observations

# Cross-validated component selection
cv_select = PLS.select_n_components(X_s, Y_s, max_components=6)
print(cv_select.n_components)     # recommended number of components
print(cv_select.rmsecv)           # RMSECV per component count

# Cross-validation with beta-coefficient confidence intervals
cv = pls.cross_validate(X_s, Y_s, cv="loo")
print(cv.beta_ci_lower, cv.beta_ci_upper)   # 95% CI for each beta
print(cv.significant)                       # betas significantly != 0
print(cv.q_squared)                         # cross-validated R² (Q²)

Model inversion - design the inputs for a quality you choose

from process_improve.multivariate.methods import PLS, OPLS

# X: acetic acid, H2S and lactic acid in 26 cheddar cheeses; y: their taste score
pls = PLS(n_components=2).fit(X, y)

design = pls.invert(y_desired=20.9)
print(design.x_new.round(2).to_list())   # [5.52, 5.56, 1.4], in the original units
print(design.hotellings_t2.round(2))     # 0.06: well inside the calibration data
print(design.null_space_dimension)       # 1: a line of designs, not a single recipe

# Walk that line. The recipe changes; the predicted taste does not.
for step in (-1.0, 0.0, 1.0):
    print(pls.invert(20.9, null_space_coordinates=[step]).x_new.round(2).to_list())
# [4.95, 6.1, 1.33]
# [5.52, 5.56, 1.4]
# [6.09, 5.02, 1.46]

# O-PLS separates that freedom while fitting, so inversion becomes one division.
opls = OPLS(n_orthogonal_components=1).fit(X, y)
print(opls.invert(y_desired=20.9).x_new.round(2).to_list())   # [5.46, 5.62, 1.39]

Both routes describe the same set of designs, and differ only in which point on it they report. The freedom is what you spend on cost, supply, or a regulatory window; the hotellings_t2 is what tells you when a design has walked past the evidence.

DOE - multi-stage experimental strategy

from process_improve.experiments.factor import Factor, Response
from process_improve.experiments.strategy import recommend_strategy

factors = [
    Factor(name="Temperature", low=25, high=40, units="degC"),
    Factor(name="pH", low=5.0, high=7.5),
    Factor(name="Glucose", low=10, high=50, units="g/L"),
]
strategy = recommend_strategy(
    factors=factors,
    responses=[Response(name="Yield", goal="maximize", units="g/L")],
    budget=40,
    domain="fermentation",
)
for s in strategy["stages"]:
    print(s["stage_number"], s["design_type"], s["estimated_runs"])

One-shot optimal & OMARS designs

Ask for a ready-to-run design table and score it, in two lines:

from process_improve.experiments import Factor, generate_design, evaluate_design

factors = [
    Factor(name="A", low=-1, high=1),
    Factor(name="B", low=-1, high=1),
    Factor(name="C", low=-1, high=1),
]

# An OMARS design: main effects clear of every second-order term
design = generate_design(factors, design_type="omars")

# Or a run-budgeted D-optimal design, then grade its quality
d_opt = generate_design(factors, design_type="d_optimal", budget=14)
print(evaluate_design(d_opt, metric="all"))   # D/I/G-efficiency, aliasing, prediction variance

On-line monitoring with Adaptive PCA

A static model goes stale the moment the process drifts. AdaptivePCA starts from an initial fit, then keeps learning as data streams in - flagging faults and reporting exactly how far the process has moved from where it was trained:

from process_improve.multivariate import AdaptivePCA

# Seed on a block of known-good ("common cause") data
monitor = AdaptivePCA(n_components=3).fit(X_reference)

# Feed live observations one row at a time
for _, row in X_stream.iterrows():
    result = monitor.update(row.to_numpy())
    if not result.in_control:
        print(f"Out-of-control point: SPE={result.spe:.2f}, T²={result.hotellings_t2:.2f}")

# How far has the model drifted from its training subspace? (in units of components)
print(monitor.distance_.tail())
print(monitor.center_shift_.tail())   # operating-point migration, in training-SD units

AdaptivePLS does the same for regression and soft sensing, and handles infrequently-sampled responses: the X-space model adapts every step while the regression part waits for the next lab result.

Longer, fully-worked versions of each example live in the Quickstart guide and the examples/ folder.

New to designed experiments? The Applied DoE tutorial is an eight-module worked-solution series.

API design

PCA and PLS follow scikit-learn conventions: fit() returns self, fitted attributes end with a trailing underscore (scores_, loadings_, spe_, hotellings_t2_, r2_cumulative_, ...), and predict() returns an sklearn.utils.Bunch with named fields (y_hat, spe, hotellings_t2, ...). Inputs are accepted as pandas.DataFrame, and index/column labels are preserved through fit and transform.

Documentation & learning resources

• API reference & user guide: https://kgdunn.github.io/process-improve/
• Applied DoE tutorial (8 modules): https://kgdunn.github.io/process-improve/applied_doe/index.html
• Model inversion, end to end: the user-guide page, and the book chapter it is drawn from, Using a PLS model backwards
• Companion textbook: Process Improvement using Data
• Local docs build: cd docs && make html

Citing process-improve

If you use this package in academic work, please cite it. The CITATION.cff file carries the current version and release date, and GitHub renders a "Cite this repository" button in the sidebar with ready-made BibTeX and APA entries:

@software{dunn_process_improve,
  author  = {Dunn, Kevin G.},
  title   = {{process-improve: Multivariate Analysis for Process Improvement}},
  year    = {2026},
  url     = {https://github.com/kgdunn/process-improve}
}

Add the version field from CITATION.cff (or the release tag you installed) when citing a specific version.

Contributing

Bug reports, feature requests, and pull requests are welcome. See CONTRIBUTING.md for development setup, testing, and code style. Bugs and feature requests can be filed on the issue tracker.

License

MIT - see LICENSE for details.