spc_ewma — SPC `change` op

• Datenarten: signal → table

• Aufruf: import fullseye as fs; fs.ledger.spc_ewma(signal, target, lam=0.2, L=3.0, sigma=None) (die Implementierung direkt: import spc; spc.spc_ewma(signal, target, lam=0.2, L=3.0, sigma=None); aus dem Register: opsspc.get("spc_ewma"))

Verwendung

> Für diesen Operator gibt es noch keine Übersetzung. Es folgt der Originaltext unverändert.

EWMA control chart for individual measurements (Roberts 1959).

`signal` is a 1-D series of individual measurements. With a reference value

`target (the in-control mean), a smoothing constant lam in (0, 1]` and

a control-limit width `L` (in sigmas), the exponentially weighted moving

average and its time-varying limits are::

z_i = lam * x_i + (1 - lam) * z_{i-1}, z_0 = target

var_i = sigma^2 * (lam / (2 - lam)) * (1 - (1 - lam) ** (2 (i + 1)))

UCL_i / LCL_i = target +/- L * sqrt(var_i)

`sigma is the process standard deviation; if None` it is estimated from the

series as the sample std (`ddof=1`). The limits widen from the first sample to

the asymptote `target +/- L * sigma * sqrt(lam / (2 - lam))`. EWMA, like CUSUM,

catches small sustained shifts that a single-point Shewhart chart misses; `lam`

trades memory (small = long memory, sensitive to small shifts) against speed.

Returns a dict with the `z / ucl / lcl arrays, the integer alarms`

indices (`z_i outside its limits), the first alarm index (or -1`), the

asymptotic `ucl_inf / lcl_inf, and the echoed target / lam / L`

/ `sigma / in_control`.

Ground truth (pinned in the tests): a series constant at `target` keeps

`z == target with no alarm; z is exactly the recursion above; ucl`

increases monotonically toward `ucl_inf; with lam = 1` the chart reduces to

a Shewhart individuals chart (`z == x, limits constant at `target +/- L

sigma``).

Raises `ValueError`: a non-1-D / empty *signal*, a non-finite

*target* / *lam* / *L*, `lam outside (0, 1]`, a non-positive *L*, a

non-finite or non-positive *sigma*, or (when estimating) a constant series whose

sample std is zero.

Referenzen (Beispieldaten, Literatur)

• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).

• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.

• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.

Ausführbare Beispiele (verifizierte Samples, die diesen Operator wirklich aufrufen)

• poc_spc — py -3.11 examples/poc_spc.py

Typkompatible Folge-Operatoren (nehmen `table` als Eingabe)

—

Gleiche Kategorie (`change`)

spc_cusum

*Provenance: spc.py — SPC Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*

spc_ewma — SPC change op