Quality and SPC

How to find outliers, apply control-chart rules and compute process capability. The classes live in ts_shape.events.quality.

Example data

A measured shaft diameter that drifts upward and has a few spikes, an in-control reference run for the control limits, and the specification limits as two signals.

import pandas as pd
import ts_shape

reference = ts_shape.make_timeseries(["shaft:diameter_ref"], n_points=200, baseline=20.0, noise=0.01, seed=1)
measured = ts_shape.make_timeseries(
    ["shaft:diameter"], n_points=500, baseline=20.0, noise=0.01, drift=0.03, n_outliers=3, start="2025-01-02"
)
spec_limits = pd.DataFrame({
    "systime": pd.Timestamp("2025-01-01"),
    "uuid": ["shaft:usl", "shaft:lsl"],
    "value_double": [20.05, 19.95],
})
df = pd.concat([reference, measured, spec_limits], ignore_index=True)

Outliers

from ts_shape.events.quality.outlier_detection import OutlierDetectionEvents

detector = OutlierDetectionEvents(df, value_column="value_double", signal_uuids=["shaft:diameter"])
zscore = detector.detect_outliers_zscore(threshold=3.0)
mad = detector.detect_outliers_mad(threshold=3.5)
iqr = detector.detect_outliers_iqr(threshold=(1.5, 1.5))

Method	Suited for
detect_outliers_zscore	roughly normal data; mean and standard deviation are themselves affected by outliers
detect_outliers_iqr	skewed data
detect_outliers_mad	noisy or heavy-tailed data; median-based, the most robust of the three
detect_outliers_isolation_forest	multivariate or irregular patterns; needs ts-shape[ml]

Statistics are computed per signal (group_by_uuid=True). Outliers closer than time_threshold (default 5 minutes) are grouped into one event. Each row has a numeric severity score.

Control charts

StatisticalProcessControlEvents takes the center line and sigma from a reference signal (tolerance_uuid, here the in-control run) and checks the actual signal against the eight Nelson / Western Electric rules. Sigma is the individuals-chart estimate MR̄ / 1.128 of consecutive reference values (Montgomery, Introduction to Statistical Quality Control, §6.4); pass sigma_method="std" for the sample standard deviation.

from ts_shape.events.quality.statistical_process_control import StatisticalProcessControlEvents

spc = StatisticalProcessControlEvents(
    df, "value_double", tolerance_uuid="shaft:diameter_ref", actual_uuid="shaft:diameter", event_uuid="quality:spc"
)
limits = spc.control_limits()                   # mean and 1, 2, 3 sigma bands
violations = spc.detect_violations()            # one row per violating sample, with triggered_rule and severity
rules_1_2 = spc.detect_rule_violations(selected_rules=["rule_1", "rule_2"])
explained = spc.interpret_violations(rules_1_2) # adds interpretation, meaning, recommendation
shifts = spc.detect_cusum_shifts(k=0.5, h=5.0)  # small sustained shifts of the mean

dynamic_control_limits(method="moving_range", window_size=20) is a rolling individuals chart (each point against the 20 points before it), and method="ewma" an EWMA chart (column ewma against lcl / ucl). For several correlated variables use MultivariateSPCEvents (Hotelling T²), and for a change of level without reference data ChangePointEvents.

Specification limits and capability

from ts_shape.events.quality.tolerance_deviation import ToleranceDeviationEvents

tolerance = ToleranceDeviationEvents(
    df,
    tolerance_column="value_double",
    actual_column="value_double",
    actual_uuid="shaft:diameter",
    upper_tolerance_uuid="shaft:usl",
    lower_tolerance_uuid="shaft:lsl",
    event_uuid="quality:tolerance",
)
out_of_spec = tolerance.detect_deviations()                   # deviation_abs, deviation_pct, severity
capability = tolerance.capability_indices(target_value=20.0)  # Cp, Cpk, Pp, Ppk, Cpm in one row

The limits are signals, so they may change over time; each measurement is compared with the limit in force at its timestamp. Give only one of the two limits for a one-sided specification. Cp and Cpk use the within (short-term) sigma MR̄ / 1.128 of consecutive measurements, Pp and Ppk the overall sample standard deviation (AIAG SPC manual); sigma_method="std" makes Cp/Cpk equal Pp/Ppk.

Other quality detectors

Question	Class	Page
Which kind of anomaly is it (spike, drift, oscillation, flatline)?	AnomalyClassificationEvents	Anomaly classification
Is the sensor data usable (gaps, sampling, stuck values)?	SignalQualityEvents, DataGapAnalysisEvents	Signal quality, Data gaps
Is a sensor drifting or out of calibration?	SensorDriftEvents, CalibrationValidationEvents	Sensor drift, Calibration
Do redundant sensors agree?	MultiSensorValidationEvents	Multi-sensor validation
Is the gauge capable (Gauge R&R)?	GaugeRepeatabilityEvents	Gauge R&R
How does Cpk develop over time?	CapabilityTrendingEvents	Capability trending
When did the process level change?	ChangePointEvents	Change points
Several correlated variables at once?	MultivariateSPCEvents	Multivariate SPC
Measurement uncertainty (GUM)?	MeasurementUncertaintyEvents	Measurement uncertainty
Distribution shape, bimodality?	ValueDistributionEvents	Value distribution
Is the sampling rate or resolution sufficient?	SamplingResolutionEvents	Sampling and resolution
Correct a measurement for ambient conditions?	EnvironmentalCompensationEvents	Environmental compensation