pls_monitoring — PLS monitoring (T² + Q with control limits)

Group: Diagnostic · Registry tolerance: 10.0

Description

PLS process monitoring (T²/Q thresholds + alarms) (§19)

Registry note — R mdatools::pls reused for monitoring T². SIMPLS convention differences inflate the divergence; widened tolerance flags external-ref presence.

Parameters

Name

Type

Default

Notes

n_components

int

4

registry benchmark cell value

alpha

float

0.05

registry benchmark cell value

Explanations

Bibliographic source

Kourti, T. & MacGregor, J. F. (1996). Multivariate SPC methods for process and product monitoring and control. Journal of Quality Technology 28(4), 409–428.

Mathematical principle

Combine T² and Q with parametric control limits to obtain a 2-D monitoring chart for online process control. Samples are classified as in-control if both statistics fall below their respective limits; otherwise an alarm is raised. The two statistics are statistically nearly independent (T² lives in the latent space, Q in its orthogonal complement), so joint alarms reflect compound failures.

pls4all’s monitoring routine returns, for each sample, the T² and Q values, their control-limit ratios, and a boolean alarm flag. Limits are derived from the calibration distribution: F-quantile for T², Jackson–Mudholkar normal approximation for Q.

Used as the back-end of a process SPC dashboard or as a test-set sanity check before deploying a PLS model in production.

Implementation

n4m_pls_monitoring_run — returns a dict with alarm vectors.

Usage

Every pls4all binding tab dispatches into the same C kernel; the external libraries listed at the bottom of the page are the parity references registered in benchmarks.parity_timing.registry. Switch tabs to read the same fit in your language. The R package now ships drop-in-compatible facades for the CRAN pls package (plsr, pcr, mvr) and for the mdatools::pls(x, y, ...) matrix idiom — those tabs appear only on the methods that have a meaningful equivalence.

pls4all bindings

/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_pls_monitoring_run(ctx, cfg, &x_view, &y_view, /* hyperparams */, &res);
/* … read coefficients / mask / scores via */
/* n4m_method_result_get_double_matrix / vector / scalar … */
n4m_method_result_destroy(res);
n4m_config_destroy(cfg);
n4m_context_destroy(ctx);
import pls4all
from pls4all._methods import pls_monitoring_run
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = pls_monitoring_run(ctx, cfg, X, y, n_components=4)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …
from pls4all.sklearn import pls_monitoring
result = pls_monitoring(X, y, n_components=4)
library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("pls_monitoring", X, y,
                      n_components = 4L, params = list(alpha = 0.05))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.
res  = pls4all.fit("pls_monitoring", X, y, "NumComponents", 4);
yhat = predict(res, Xtest);

No idiomatic classdef wrapper — invoke pls4all.fit("pls_monitoring", X, y, …) directly from the unified MEX factory.

Registry parity references 📐

  • 📐 ref.r_mdatools (R · r) — mdatools 0.15.0 · qualitative (rmse_rel ≤ 1e+01) — R mdatools::pls returning T² for monitoring rows. SIMPLS-convention differences with pls4all inflate divergence; qualitative parity.

Benchmarks

Adaptive wall-clock per cell measured against full_matrix.csv. Only backends that implement this method are listed; libraries without the method are omitted.

Verdict  ·  ✓ ref / ≈ ref / ~ shape mark a reference-gate pass at strict / relaxed / qualitative tolerance  ·  ✓ bind = pls4all binding agrees with the C++ baseline  ·  ⇄ cross-check = documented by-design selector/RNG/model, noncanonical API/facade convention, or secondary oracle  ·  ✗ divergent  ·  ⚠ error  ·  — not run. The fastest backend per column is marked 🏆.

Reference gate: strict — numeric equivalence (rmse_rel_tol 1e-08).

Rows tagged with 📐 are the canonical parity references for this method (declared in parity_timing.registry). C++ and external rows show reference parity; pls4all language bindings show binding parity against the C++ backend. Hover the icon for role and tolerance band.

BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 5e-151.23 ms
Python · pls4all
pls4all.python✓ bind1.18 ms🏆
pls4all.sklearn✓ bind1.32 ms
R · pls4all
pls4all.R✓ 1e-132.90 ms
pls4all.R.formula✓ 1e-133.54 ms
pls4all.R.mdatools✓ 1e-133.81 ms
pls4all.R.pls✓ 1e-133.74 ms
R · external
📐ref.r_mdatoolssource14.2 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 5e-151.19 ms🏆
Python · pls4all
pls4all.python✓ bind2.29 ms
pls4all.sklearn✓ bind1.41 ms
R · pls4all
pls4all.R✓ 1e-133.19 ms
pls4all.R.formula✓ 1e-134.18 ms
pls4all.R.mdatools✓ 1e-134.00 ms
pls4all.R.pls✓ 1e-134.17 ms
R · external
📐ref.r_mdatoolssource14.3 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 5e-151.26 ms🏆
Python · pls4all
pls4all.python✓ bind1.61 ms
pls4all.sklearn✓ bind1.34 ms
R · pls4all
pls4all.R✓ 1e-135.85 ms
pls4all.R.formula✓ 1e-139.79 ms
pls4all.R.mdatools✓ 1e-137.99 ms
pls4all.R.pls✓ 1e-133.84 ms
R · external
📐ref.r_mdatoolssource14.4 ms

See also: benchmark overview · methods index · interactive dashboard