fullseye

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

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.

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)

msa_anova_table · msa_gauge_rr · msa_bias_linearity · msa_attribute_agreement · gum_standard_uncertainty · gum_propagate · gum_expanded · gum_monte_carlo

同カテゴリ(change)

spc_cusum

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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.

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