Pareto analysis
The Pareto principle states that roughly 80% of effects come from 20% of causes — the "vital few" vs. the "trivial many." A Pareto chart is a bar chart sorted by frequency (or cost or impact), with a cumulative percentage line, that makes this pattern visible. It is a primary tool for prioritizing which problems or causes to investigate first, used in Measure and Analyze.
Pareto chart structure
- X-axis: Categories (defect types, failure modes, suppliers, operators) sorted highest to lowest frequency
- Left Y-axis: Count or frequency for each category
- Right Y-axis: Cumulative percentage (0% to 100%)
- Bars: One per category, sorted descending
- Line: Cumulative % plotted at the top-right corner of each bar
The "vital few" are the bars on the left that together account for approximately 80% of the total — where the cumulative line crosses 80%.
Worked example: Examplorphine packaging rejects
| Defect type | Count | % of total | Cumulative % |
|---|---|---|---|
| Fill weight out of spec | 189 | 45.0% | 45.0% |
| Cap torque below spec | 105 | 25.0% | 70.0% |
| Label misaligned | 63 | 15.0% | 85.0% |
| Bottle cosmetic defect | 37 | 8.8% | 93.8% |
| Other | 26 | 6.2% | 100.0% |
Conclusion: Fill weight and cap torque together account for 70% of all rejects. The CSSGB project should focus on these two defect types first. Label misalignment brings cumulative % to 85% and may be a secondary target.
How to build a Pareto chart
- Define your unit of measure: count, cost, or some other impact measure. Cost-based Pareto charts can change priorities significantly vs. count-based ones.
- Collect data using a check sheet. Stratify by product, line, shift, or time period so you can create secondary Pareto charts.
- Sort categories from highest to lowest count.
- Calculate cumulative %: after each bar, add its % to all previous ones.
- Plot bars and overlay the cumulative line.
- Draw a reference line at 80% and note which bars are to its left — those are the vital few.
Stratification: second-level Pareto
Once you identify the vital few defect types, build a second Pareto chart within the dominant category. For example, if "fill weight out of spec" is #1:
- Stratify by shift: Does the problem concentrate on night shift?
- Stratify by day of week: Does it spike on Mondays (changeovers)?
- Stratify by operator: Is one operator responsible for more events?
Each level of stratification narrows the likely root cause and guides where to look in the fishbone diagram.
Pareto vs. histogram
| Tool | Use for | X-axis |
|---|---|---|
| Pareto chart | Categorical data; prioritizing defect types, failure modes | Categories (nominal data) |
| Histogram | Continuous data; showing distribution shape | Bins of a continuous measurement |
Common exam traps
- The 80/20 rule is a guideline, not a law. Your data may show 70/30 or 90/10. The principle is that a few categories dominate — the specific numbers vary.
- Sort by frequency, not alphabetically. An alphabetically sorted bar chart is just a bar chart, not a Pareto chart.
- Cost-based Pareto often changes the ranking. A low-frequency defect that causes a very expensive recall may outrank a high-frequency cosmetic defect when sorted by cost impact.
- Pareto does not confirm root cause. It shows which categories to investigate. Fishbone and 5 Whys suggest causes within those categories; data (stratification, tests, experiments) confirms them.
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