Control charts for Green Belts
A control chart plots data in time order with a center line (mean) and control limits at ±3σ. Points or patterns outside these limits indicate special cause variation — something has changed in the process. Points within limits represent common cause variation — the natural noise of a stable process. Control charts are used in both Measure (establish baseline) and Control (sustain gains) phases.
Control chart selection guide
| Data type | Subgroup size | Chart |
|---|---|---|
| Continuous (variable) | n = 1 (individual readings) | I-MR chart (Individuals and Moving Range) |
| Continuous (variable) | Small subgroups (typically n = 2–9) | X̅-R chart (Xbar-Range) |
| Continuous (variable) | Larger subgroups (typically n ≥ 10) | X̅-S chart (Xbar-Standard deviation) |
| Attribute: proportion defective | Variable | p-chart |
| Attribute: defects per unit | Variable | u-chart |
| Attribute: # defective (constant n) | Constant | np-chart |
| Attribute: # defects (constant n) | Constant | c-chart |
I-MR chart calculations
Used when you measure individual values one at a time (e.g., one batch yield per run).
p-chart calculations
Used when each subgroup is a count of defective items vs. total inspected (proportion defective).
Note: p-chart limits vary by subgroup size — wider limits for smaller subgroups.
Nelson rules (special cause signals)
The Nelson rules are a widely used set of tests for special causes (the Western Electric rules are an older, overlapping set: 1 point beyond 3σ, 2 of 3 beyond 2σ, 4 of 5 beyond 1σ, 8 in a row on one side):
| Rule | Pattern |
|---|---|
| Rule 1 | 1 point beyond ±3σ (outside control limits) |
| Rule 2 | 9 consecutive points on one side of the center line |
| Rule 3 | 6 consecutive points all increasing or all decreasing (trend) |
| Rule 4 | 14 consecutive points alternating up and down |
| Rule 5 | 2 of 3 consecutive points beyond ±2σ (same side) |
| Rule 6 | 4 of 5 consecutive points beyond ±1σ (same side) |
| Rule 7 | 15 consecutive points within ±1σ ("hugging") |
| Rule 8 | 8 consecutive points outside ±1σ on both sides |
Software packages and textbooks number these rules differently; learn the patterns, not the rule numbers.
Control limits vs. specification limits
| Control limits (UCL/LCL) | Spec limits (USL/LSL) | |
|---|---|---|
| Set by | Process data (±3σ from mean) | Customer or engineering requirement |
| Meaning | Voice of the Process: what the process actually does | Voice of the Customer: what is acceptable |
| A point outside limits means | Special cause: the process changed | A defect was produced |
| Can be changed by | Improving the process (reducing σ) | Negotiation with customer or engineering |
Key distinction: Never use spec limits as control chart limits. Doing so makes the chart meaningless for detecting process changes.
Common exam traps
- Control charts detect process changes, not defects per se. A stable process well within spec will have no signals. A stable process outside spec will also have no signals — it has a capability problem, not a stability problem.
- I-MR, not I-R. The range chart in an individual chart is called the Moving Range (MR) chart, not a standard range chart.
- LCL can be 0. A negative LCL for counts or proportions is set to 0; negative defects are impossible.
- A point outside control limits requires investigation. Do not adjust the process without finding the assignable cause.
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