change op• Data kinds: signal → table
• Call: import fullseye as fs; fs.ledger.spc_ewma(signal, target, lam=0.2, L=3.0, sigma=None) (to call the implementation directly, import spc; spc.spc_ewma(signal, target, lam=0.2, L=3.0, sigma=None); from the registry, opsspc.get("spc_ewma"))
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.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• poc_spc — py -3.11 examples/poc_spc.py
table as input)msa_anova_table · msa_gauge_rr · msa_bias_linearity · msa_attribute_agreement · gum_standard_uncertainty · gum_propagate · gum_expanded · gum_monte_carlo
change)*Provenance: spc.py — SPC operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.