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StatisticalProcessControlEvents¤

Shewhart control-chart rules (the eight Nelson tests, including the Western Electric zone rules), dynamic control limits and CUSUM shift detection. Control limits come from reference rows of one signal (tolerance_uuid); the rules are checked on the rows of another (actual_uuid).

ts_shape.events.quality.statistical_process_control · Quality guide · API reference

Example¤

import pandas as pd
import ts_shape
from ts_shape.events.quality.statistical_process_control import StatisticalProcessControlEvents

df = pd.concat([
    ts_shape.make_timeseries(["limit:temp"], n_points=200, seed=1),  # in-control reference
    ts_shape.make_timeseries(["sensor:temp"], n_points=500, drift=3.0, n_outliers=3, seed=2),
], ignore_index=True)

spc = StatisticalProcessControlEvents(df, value_column="value_double", tolerance_uuid="limit:temp",
                                      actual_uuid="sensor:temp", event_uuid="spc:temp")
violations = spc.detect_violations()
print(violations["triggered_rule"].value_counts())
shifts = spc.detect_cusum_shifts(k=0.5, h=5.0)

Methods¤

Method Returns
control_limits() individuals-chart center line and ±1σ/2σ/3σ limits from the reference rows
detect_violations(selected_rules=None, include_severity=True) one row per violating point: systime, value, triggered_rule, severity
detect_rule_violations(selected_rules=None) one row per point and rule: systime, value, rule, severity
dynamic_control_limits(method='moving_range', window_size=20, ewma_lambda=None, n_sigma=3.0) limits per systime: value, mean, 1sigma_upper … 3sigma_lower, lcl, ucl; method='ewma' adds the EWMA statistic ewma (see below)
detect_cusum_shifts(target=None, k=0.5, h=5.0) systime, value, cusum_high, cusum_low, shift_direction, severity
interpret_violations(violations_df) adds interpretation, meaning, recommendation
rule_1(df, limits) … rule_8(df, limits) the violating rows with a boolean rule column; the input is not modified

Notes¤

  • Sigma. sigma_method="moving_range" (constructor, default) is the Shewhart individuals chart: σ̂ = MR̄ / d₂ with d₂ = 1.128, where MR̄ is the mean moving range |xᵢ − xᵢ₋₁| of consecutive reference values; the center line is the reference mean (Montgomery, Introduction to Statistical Quality Control, §6.4). It measures short-term variation only, so a drift inside the reference does not widen the limits. sigma_method="std" uses the sample standard deviation, as ts-shape did before October 2026. The same σ̂ drives control_limits, the rule zones, CUSUM and the EWMA chart. Example: a reference trending 1, 2, …, 20 has MR̄ = 1, σ̂ = 0.8865 and limits 7.84 / 13.16 (the sample std gave −7.25 / 28.25).
  • Rolling chart (dynamic_control_limits(method="moving_range")): each point is tested against the window_size points before it: center = their mean, σ̂ = mean of their moving ranges / 1.128 (their sample std with sigma_method="std"). The first window_size points have no complete history and get NaN limits. Before October 2026 the window included the tested point itself and started with one point.
  • EWMA chart (method="ewma", Montgomery §9.2): zᵢ = λxᵢ + (1 − λ)zᵢ₋₁ with z₀ = μ₀, limits μ₀ ± L·σ̂·√(λ/(2 − λ)·[1 − (1 − λ)²ⁱ]). μ₀ and σ̂ come from the reference rows; λ is ewma_lambda, else 2 / (window_size + 1); lcl / ucl use L = n_sigma and the ksigma columns L = 1, 2, 3. Compare the ewma column with the limits; mean is μ₀. Before October 2026 this method returned an exponentially weighted mean ± exponentially weighted std of the actual values.
  • The rules follow Nelson (1984): rule 1 a point beyond 3σ; rule 2 nine points on one side of the center line; rule 3 six points steadily rising or falling; rule 4 fourteen points alternating up and down; rule 5 two of three beyond 2σ on one side; rule 6 four of five beyond 1σ on one side; rule 7 fifteen points within 1σ; rule 8 eight points with none within 1σ. Points beyond the next zone count for rules 5 and 6. An unchanged value breaks the runs of rules 3 and 4.
  • Severity per rule: rule 1 critical, rule 5 high, rules 2, 3, 4, 6 medium, rules 7 and 8 low. detect_violations reports a point that violates several rules once, with the first selected rule.
  • CUSUM (tabular, Montgomery §9.1): C⁺ᵢ = max(0, xᵢ − μ₀ − kσ̂ + C⁺ᵢ₋₁), C⁻ᵢ = max(0, μ₀ − kσ̂ − xᵢ + C⁻ᵢ₋₁); a shift when either exceeds hσ̂. k and h are in multiples of the reference σ̂; target (μ₀) defaults to the reference mean. It is skipped (empty result) when the reference has fewer than two rows or zero spread.
  • selected_rules takes names such as ["rule_1", "rule_5"].