Calculator
Quick tips
- Use consistent defect definitions across suppliers.
- Opportunities per unit should reflect your inspection plan.
- For small samples, watch the confidence interval width.
- Trend sigma and DPMO over time, not once.
Example data table
| Supplier | Units | Opp/Unit | Defects | Notes |
|---|---|---|---|---|
| Apex Components | 1000 | 5 | 12 | Routine incoming inspection |
| Northline Metals | 450 | 8 | 9 | Process change validation lot |
| Orchid Plastics | 2000 | 3 | 7 | Stable supplier; quarterly audit sample |
Formula used
- Total Opportunities = Units × Opportunities per Unit
- DPO = Defects ÷ Total Opportunities
- DPMO = DPO × 1,000,000
- Yield = 1 − DPO
- Sigma(ST) = Φ⁻¹(Yield)
- Sigma(LT) = Sigma(ST) + Shift
How to use this calculator
- Collect inspection results: units checked, opportunities per unit, and defects found.
- Enter values in the calculator fields.
- Set a confidence level if you want uncertainty bounds.
- Adjust sigma shift if your program uses a different convention.
- Press Submit to view sigma, DPMO, yield, and intervals.
- Export the report using the CSV or PDF buttons.
Why sigma level matters in supplier management
Sigma level converts inspection outcomes into a comparable capability score. When suppliers ship mixed lots, defect counts alone mislead. Sigma normalizes performance to opportunities, letting you rank vendors, set entry criteria, and monitor drift across months. Many teams also report DPMO as PPM for dashboards and supplier reviews.
Choosing opportunities per unit with CTQs
Opportunities per unit should mirror your critical-to-quality checks. For a machined housing you might track diameter, flatness, burrs, coating, and packaging, giving five opportunities. Keep the definition stable, or trends will be false. Document CTQs in the control plan. If one unit has two independent issues, record two defects. Match counting rules to your inspection worksheet.
Reading DPMO, yield, and sigma together
The calculator first finds DPO and then DPMO. Example: 1,000 units, 5 opportunities each, and 12 defects gives 5,000 opportunities. DPO is 0.0024, DPMO is 2,400, and yield is 99.76%. The corresponding short-term sigma is about 2.81, and long-term sigma with a 1.5 shift is about 4.31. Use yield for communication, and sigma for benchmarking. Sigma uses inverse normal of yield; very high yields are bounded.
Using confidence intervals for audit decisions
Sampling uncertainty matters, especially with small lots. The calculator uses a Wilson interval on defect probability, then converts bounds into sigma. With 12 defects in 5,000 opportunities at 95% confidence, the defect-rate interval can shift sigma by tenths. If a supplier shows 0 defects in 200 opportunities, the point estimate looks perfect, but the interval may still allow risk. When the interval is wide, increase sample size or tighten containment.
Turning results into corrective action plans
Translate capability into actions. For sigma below 4.0, require root-cause analysis, verified corrective actions, and increased inspection frequency. For sigma between 4.0 and 5.0, target process controls, operator training, and preventive maintenance. Above 5.0, focus on sustaining controls and reducing inspection cost through supplier certification and periodic audits. Set escalation triggers, for example two consecutive months below target sigma, or any critical defect, and track closure dates to prevent recurrence.
FAQs
What is an opportunity per unit?
An opportunity is one measurable chance for a defect, often a CTQ check. Opportunities per unit equals the number of checks applied to each unit in the inspection plan.
Why can defects be higher than units?
A single unit can contain multiple independent defects across different checks. The calculator treats each defect as a failure within the total opportunity count, not a unit-level reject rate.
What does the sigma shift mean?
Shift adjusts short-term capability to a long-term view that accounts for drift over time. Many programs use 1.5, but you can set 0 if your reporting standard avoids shifts.
Which confidence level should I choose?
Use 90% for quicker directional decisions and 95% for typical quality reporting. Higher confidence widens the interval, so pair it with enough sample size to keep the bounds actionable.
How do I compare two suppliers fairly?
Use the same CTQs, counting rules, and sampling approach for both suppliers. Then compare long-term sigma and the confidence intervals, not just the point estimates, before changing sourcing decisions.
What if I observe zero defects?
Zero defects improves yield, but it does not prove zero risk. Use the confidence interval to see an upper defect-rate bound, and increase opportunities or sampling time if you need tighter assurance.