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fdars - Functional Data Analysis for Python

fdars.spm

fdars.spm¶

Statistical Process Monitoring (SPM) for functional data using FPCA-based control charts.

Functions¶

Function	Description
`spm_phase1`	Phase I estimation (in-control model)
`spm_monitor`	Phase II monitoring (new observations)
`hotelling_t2`	Hotelling T-squared statistic

`spm_phase1`¶

fdars.spm_phase1(data, argvals, ncomp=3, alpha=0.05)

Phase I: estimate the in-control model from historical data. Computes FPCA, T-squared, and SPE statistics with control limits.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		In-control functional data
`argvals`	`ndarray (m,)`		Evaluation points
`ncomp`	`int`	`3`	Number of FPC components
`alpha`	`float`	`0.05`	Significance level for control limits

Returns	Type	Description
result	`dict`	Keys: `t2` (n,), `spe` (n,), `t2_limit`, `spe_limit`, `mean` (m,), `loadings` (m, ncomp), `weights` (m,), `eigenvalues` (ncomp,)

t = np.linspace(0, 1, 100)
phase1 = fdars.spm_phase1(data, t, ncomp=3, alpha=0.05)
print(f"T2 limit: {phase1['t2_limit']:.2f}")
print(f"SPE limit: {phase1['spe_limit']:.2f}")

`spm_monitor`¶

fdars.spm_monitor(mean, loadings, weights, eigenvalues,
                  t2_limit, spe_limit, new_data, argvals)

Phase II: monitor new observations against the in-control model from Phase I.

Parameter	Type	Description
`mean`	`ndarray (m,)`	FPCA mean from Phase I
`loadings`	`ndarray (m, ncomp)`	FPCA rotation matrix from Phase I
`weights`	`ndarray (m,)`	Integration weights from Phase I
`eigenvalues`	`ndarray (ncomp,)`	Eigenvalues from Phase I
`t2_limit`	`float`	T-squared upper control limit
`spe_limit`	`float`	SPE upper control limit
`new_data`	`ndarray (n_new, m)`	New observations to monitor
`argvals`	`ndarray (m,)`	Evaluation points

Returns	Type	Description
result	`dict`	Keys: `t2` (n_new,), `spe` (n_new,), `t2_alarm` (bool array), `spe_alarm` (bool array)

monitor = fdars.spm_monitor(
    phase1["mean"], phase1["loadings"], phase1["weights"],
    phase1["eigenvalues"], phase1["t2_limit"], phase1["spe_limit"],
    new_data, t
)
if any(monitor["t2_alarm"]):
    print("T2 alarm triggered!")

`hotelling_t2`¶

fdars.hotelling_t2(scores, eigenvalues)

Compute the Hotelling T-squared statistic from FPC scores.

Parameter	Type	Description
`scores`	`ndarray (n, p)`	FPC scores
`eigenvalues`	`ndarray (p,)`	Eigenvalues

Returns	Type	Description
t2	`ndarray (n,)`	T-squared statistics

pca = fdars.fpca(data, t, n_comp=3)
t2 = fdars.hotelling_t2(pca["scores"], pca["singular_values"]**2)