Western Electric Rules

UCL ─────────────────────── +3σ
      Zone A (upper)
      ─────────────────────── +2σ
      Zone B (upper)
      ─────────────────────── +1σ
      Zone C (upper)
CL  ═════════════════════════ 0
      Zone C (lower)
      ─────────────────────── -1σ
      Zone B (lower)
      ─────────────────────── -2σ
      Zone A (lower)
LCL ─────────────────────── -3σ

# Always included in any rule set
signals = result.detect_signals(rules='standard')

from processbehavior.signals import RuleSet

rules = RuleSet().zone_a(consecutive=2)```

### Rule 3: Zone B (4 of 5)

**Pattern**: 4 of 5 consecutive points in Zone B or beyond (same side).

**Detection**: In a window of 5 consecutive points, 4 or more are beyond 1σ on the same side.

**False Alarm Rate**: ~0.28% per point

**Interpretation**: Process is likely shifting, but shift is smaller than Rule 2.

**Example Causes**:
- Small sustained shift
- Calibration drift
- Slow process change

```python
rules = RuleSet().zone_b(consecutive=4)```

### Rule 4: Run

**Pattern**: 8 or more consecutive points on the same side of the centerline.

**Detection**: 8+ points all above CL or all below CL.

**False Alarm Rate**: 0.39% per 8-point sequence

**Interpretation**: Process has shifted. Even small shifts (< 1σ) will eventually produce runs.

**Example Causes**:
- Process adjustment
- Tool change
- New material lot
- Seasonal effect

```python
rules = RuleSet().run(length=8)
# More sensitive (shorter run)
rules = RuleSet().run(length=7)```

### Rule 5: Trend

**Pattern**: 6 or more consecutive points continuously increasing or decreasing.

**Detection**: 6+ points where each is higher (or lower) than the previous.

**False Alarm Rate**: 0.28% per 6-point sequence

**Interpretation**: Process is drifting. Identify and address the cause.

**Example Causes**:
- Tool wear
- Chemical degradation
- Temperature change
- Fatigue effects

```python
rules = RuleSet().trend(length=6)
# More sensitive
rules = RuleSet().trend(length=5)```

### Rule 6: Oscillation

**Pattern**: 14 or more consecutive points alternating up and down.

**Detection**: 14+ points where each alternates direction from the previous.

**False Alarm Rate**: 0.006% per 14-point sequence

**Interpretation**: Process is being over-controlled. Each adjustment causes the next deviation.

**Example Causes**:
- Over-adjustment (tampering)
- Two alternating streams
- Measurement round-off
- Systematic sampling issue

```python
rules = RuleSet().oscillation(length=14)```

### Rule 7: Hugging Center

**Pattern**: 15 or more consecutive points in Zone C (within 1σ of centerline).

**Detection**: 15+ points all within ±1σ of the centerline.

**False Alarm Rate**: 0.003% per 15-point sequence

**Interpretation**: Variation has been reduced. Could be good (process improvement) or suspicious (data manipulation, stratification).

**Example Causes**:
- Process improvement
- Incorrect subgrouping
- Mixed product/operators
- Data averaging or smoothing

```python
rules = RuleSet().reduced_variation(length=15)```

### Rule 8: Avoiding Center

**Pattern**: 8 or more consecutive points avoiding Zone C (all beyond 1σ).

**Detection**: 8+ points all outside ±1σ from centerline.

**False Alarm Rate**: 0.41% per 8-point sequence

**Interpretation**: Distribution is bimodal or has excessive variation.

**Example Causes**:
- Mixture of two processes
- Systematic over-adjustment
- Two distinct populations
- Subgroup selection issue

```python
rules = RuleSet().avoiding_center(length=8)```

## Rule Sets

### Standard Rules (1-4)

The most commonly used rules with lower false alarm rates.

```python
signals = result.detect_signals(rules='standard')

signals = result.detect_signals(rules='extended')

from processbehavior.signals import RuleSet

# Just limits and trends
rules = RuleSet().beyond_limits().trend()
# Limits and runs with custom length
rules = RuleSet().beyond_limits().run(length=7)
# Full configuration
rules = (
    RuleSet()
    .beyond_limits()
    .zone_a(consecutive=2)
    .run(length=8)
    .trend(length=5)
    )

signals = result.detect_signals(rules=rules)

signals = result.detect_signals(chart='X')
signals.is_partial          # True
signals.evaluation_status   # 'partial'
signals.rules_evaluated     # ['rule_1', 'rule_2']
signals.rules_skipped       # {'rule_3': 'needs 5 observations, have 4', ...}
signals.evaluation_note     # '2 of 8 rules applicable at n=4 (below min_observations=20); skipped: ...'

✓ No signals detected in X

⚠ Partial evaluation in X: 2 of 8 rules applicable at n=4 (below min_observations=20);
skipped: rule_3 (needs 5), rule_4 (needs 8), rule_5 (needs 6), rule_6 (needs 14),
rule_7 (needs 15), rule_8 (needs 8). No signals from the rules evaluated.

import warnings
from processbehavior import ProcessBehaviorWarning
warnings.simplefilter('ignore', ProcessBehaviorWarning)

signals = result.detect_signals(rules='extended')

# Check if any signals
if signals.has_signals:
    print(f"Found {signals.count} signals")

    # View all violations
    print(signals.violations)

    # Summary by rule
    print(signals.summary)

    # Violations for specific rule
    rule_1 = signals.by_rule.get('rule_1', [])
    print(f"Beyond limits: {len(rule_1)} violations")

# Show all rule violations on chart
fig = result.plot(
    show_zones=True,   # Zone shading helps see violations
    show_rules=True    # All WECO rule violations
)
fig.show()