# `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.
### 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_metrics_pls_monitoring_run` — returns a dict with alarm vectors.
R roxygen note (`diagnostics.R::pls_monitoring`):
> PLS process monitoring (Hotelling T² + Q with alarms).
### 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**
::::{tab-set}
:class: pls4all-bindings
:::{tab-item} C ABI · libn4m
:sync: c
:class-label: lang-c
```c
/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t* cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_metrics_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);
```
:::
:::{tab-item} Python · pls4all (raw)
:sync: python-raw
:class-label: lang-python
```python
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"), …
```
:::
:::{tab-item} Python · pls4all.sklearn
:sync: python-sklearn
:class-label: lang-python
```python
from pls4all.sklearn import pls_monitoring
result = pls_monitoring(X, y, n_components=4)
```
:::
:::{tab-item} R · pls4all_method()
:sync: r-dispatcher
:class-label: lang-r
```r
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.
```
:::
:::{tab-item} R · pls4all (raw fn)
:sync: r-raw
:class-label: lang-r
```r
library(pls4all)
res <- pls_monitoring(model, X_reference, X_monitor, alpha = 0.95)
yhat <- pls4all_predict(res, X_test)
```
:::
:::{tab-item} MATLAB · pls4all (MEX)
:sync: matlab-mex
:class-label: lang-matlab
```matlab
res = pls4all.fit("pls_monitoring", X, y, "NumComponents", 4);
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("pls_monitoring", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`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
Adaptive wall-clock per cell measured against [`full_matrix.csv`](../benchmarks/overview.md). 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`](../benchmarks/methodology.md)). 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.
::::{tab-set}
:class: parity-tabs
:::{tab-item} 1 thread
:sync: threads-1
| Backend | Parity | 200×30 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas+omp | ✓ ref 5e-15 | 1.23 ms |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 1.18 ms🏆 |
pls4all.sklearn | ✓ bind | 1.32 ms |
| R · pls4all |
|---|
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 |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 200×30 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas+omp | ✓ ref 5e-15 | 1.19 ms🏆 |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 2.29 ms |
pls4all.sklearn | ✓ bind | 1.41 ms |
| R · pls4all |
|---|
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 |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 200×30 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas+omp | ✓ ref 5e-15 | 1.26 ms🏆 |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 1.61 ms |
pls4all.sklearn | ✓ bind | 1.34 ms |
| R · pls4all |
|---|
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 |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)