spc_ewma — SPC change op

• データ種: signal → table

• 呼び出し: import fullseye as fs; fs.ledger.spc_ewma(signal, target, lam=0.2, L=3.0, sigma=None) (実装を直接呼ぶなら import spc; spc.spc_ewma(signal, target, lam=0.2, L=3.0, sigma=None)、台帳から引くなら opsspc.get("spc_ewma"))

使い方

個別計測の EWMA 管理図(Roberts 1959)—— λ で記憶の深さを調節し、CUSUM と同様に小さな持続シフトを Shewhart より早く捕らえる。

> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。

`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.

参考(サンプルデータ・文献)

• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。

• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。

• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• poc_spc — py -3.11 examples/poc_spc.py

型が繋がる次の op(table を入力に取れる)

—

同カテゴリ(change)

spc_cusum

*Provenance: spc.py — SPC operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.