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

Group: Diagnostic · Registry tolerance: 1e-08

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. Verified primary link: https://doi.org/10.1080/00224065.1996.11979699.

Mathematical principle

The routine computes T-squared and Q statistics for the reference observations, sorts each empirical distribution, and chooses its \((1-\alpha)\) sample quantile as the corresponding control limit. New observations are flagged when either statistic exceeds that stored limit.

Appropriate uses

Process or instrument monitoring with paired score-leverage and X-residual alarms.

Limits and validation

Current control limits are empirical reference quantiles, so alpha is resolution-limited in small reference sets and no F/Jackson–Mudholkar model is fitted.

Implementation

No parametric F approximation for T-squared and no Jackson–Mudholkar Q approximation is evaluated in this path. Reference-set size and representativeness directly determine the empirical limits.

Sources and provenance

Current implementation: cpp/src/core/pls_monitoring.cpp.

API and bindings

C ABI (ABI 2): n4m_metrics_pls_monitoring_run. Use the linked public header for the exact signature, configuration, and result handles.

Python: no current AST-verified public n4m re-export was found for this method. The linked C ABI above is the documented surface in this checkout.

R (source-verified): pls_monitoring(model, X_reference, X_monitor, alpha = 0.95).

The source signature has additional required inputs, so no example call is fabricated.

MATLAB / Octave (source-verified): pls_monitoring(X_reference, Y_reference, X_monitor, ... n_components, alpha).

The source signature has additional required inputs, so no example call is fabricated.

Registry parity references 📐

• 📐 ref.r_mdatools (R · r) — mdatools 0.15.0 · strict (rmse_rel ≤ 1e-08) — R mdatools::pls returning T² for monitoring rows. SIMPLS-convention differences with pls4all inflate divergence; qualitative parity.

Benchmarks

Archived measurement identity. Backend labels in this table are the raw IDs recorded when the benchmark ran (including historical pls4all.* IDs). They preserve measurement provenance and do not describe a current public Python, R, or MATLAB binding; use the source-verified API and bindings section above for current entry points.

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 = archived binding-harness result 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; archived language-harness rows show binding parity against the C++ backend. Hover the icon for role and tolerance band.

1 thread

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 5e-15	1.23 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.18 ms🏆
pls4all.sklearn	✓ bind	1.32 ms
R · archived pls4all benchmark
pls4all.R	✓ 1e-13	2.90 ms
pls4all.R.formula	✓ 1e-13	3.54 ms
pls4all.R.mdatools	✓ 1e-13	3.81 ms
pls4all.R.pls	✓ 1e-13	3.74 ms
R · external
📐ref.r_mdatools	source	14.2 ms

3 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 5e-15	1.19 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	2.29 ms
pls4all.sklearn	✓ bind	1.41 ms
R · archived pls4all benchmark
pls4all.R	✓ 1e-13	3.19 ms
pls4all.R.formula	✓ 1e-13	4.18 ms
pls4all.R.mdatools	✓ 1e-13	4.00 ms
pls4all.R.pls	✓ 1e-13	4.17 ms
R · external
📐ref.r_mdatools	source	14.3 ms

10 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 5e-15	1.26 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.61 ms
pls4all.sklearn	✓ bind	1.34 ms
R · archived pls4all benchmark
pls4all.R	✓ 1e-13	5.85 ms
pls4all.R.formula	✓ 1e-13	9.79 ms
pls4all.R.mdatools	✓ 1e-13	7.99 ms
pls4all.R.pls	✓ 1e-13	3.84 ms
R · external
📐ref.r_mdatools	source	14.4 ms

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See also: benchmark overview · methods index · interactive dashboard