- Six Sigma Tutorial
- Six Sigma DMAIC process
- Six Sigma Acceptance Sampling
- Sampling Plan Variation vs Lot Size Variation in Acceptance Sampling
- AQL Based Sampling Plans
- Decision Tree for Selecting Type of Variables in Sampling Plan
- FMEA – Failure Mode and Effects Analysis
- Types Of FMEA: Design FMEA (DFMEA), Process FMEA (PFMEA)
- The FMEA Quality Lever – Where To Put The Effort
- FMEA Quiz
- Six Sigma Confidence Intervals
- Confidence Limits
- Confidence Interval Formulas
- Z Confidence Interval for Means – Example
- t Confidence Interval for a Variance – Example
- Six Sigma Defect Metrics – DPO, DPMO, PPM, DPU Conversion table
- Fishbone Diagram – Fishbone Analysis
- Cost of Quality Defects and Hidden Factory in Six Sigma
- Pareto Analysis using Pareto Chart
- Six Sigma Calculators – DPMO, DPM, Sample Size
- How to select a Six Sigma project? Download selection grid template.
- How to create Six Sigma Histograms? Download MS Excel template
- Scatter Plots – Free Six Sigma Scatter Plot template
- How to create, use Six Sigma SIPOC tool? Download SIPOC Template
- Quality Function Deployment (QFD) – Download free templates
- What is Decision Matrix or Decision Making Matrix ?
- The nature of Process Variation
- What is RACI or RASCI Matrix/Chart/Diagram? Download free templates
Six Sigma Defect Metrics – DPO, DPMO, PPM, DPU Conversion table
What Is DPO? What Is DPMO?
A unit of product can be defective if it contains one or more defects. A unit of product can have more than one opportunity to have a defect.
- Determine all the possible opportunities for problems
- Pare the list down by excluding rare events, grouping similar defect types, and avoiding the trivial
- Define opportunities consistently between different locations
Proportion Defective (p):
p = Number Of Defective Units / Total Number of Product Units
Yield (Y1st-pass or Yfinal or RTY)
Y = 1 – p The Yield proportion can converted to a sigma value using the Z tables
Defects Per Unit – DPU, or u in SPC
DPU = Number Of Defects / Total Number Of Product Units The probability of getting ‘r’ defects in a sample having a given dpu rate can be predicted with the Poisson Distribution.
Defects Per Opportunity – DPO
DPO = no. of defects / (no. of units X no. of defect opportunities per unit)
Defects Per Million Opportunities (DPMO, or PPM)
DPMO = dpo x 1,000,000 Defects Per Million Opportunities or DPMO can be then converted to sigma & equivalent Cp values in the next page. The DPMO, DPM, Sample Size, CI Calculator will help you calculate the metrics.
If there are 9 defects among 150 invoices, and there are 8 opportunities for errors for every invoice, what is the dpmo? dpu = no. of defects / total no. of product units = 9/150 = .06 dpu dpo = no. of defects / (no. of units X no. of defect opportunities per unit) = 9/(150 X 8) = .0075 dpo dmpo = dpo x 1,000,000 = .0075 X 1,000,000 = 7,500 dpmo What are the equivalent Sigma and CP values? See Sigma Table.
Converting Yield to sigma & Cp Metrics – Example
Given: a proportion defective of 1%
- Yield = 1 – p = .990
- Z Table value for .990 = 2.32σ
- Estimate process capability by adding 1.5 σ to reflect the ‘real-world’ shift in the process mean 2.32σ + 1.5σ = 3.82σ
- This σ value can be converted to an equivalent CP by dividing it by 3σ : CP = 3.82σ/3σ = 1.27 Note: Cpk cannot be estimated by this method
Six Sigma Capability Improvement
Sigma conversion table
This six sigma conversion table converts yield to dpmo, sigma, copq etc.
| Yield | dpmo | Sigma (σ) | Cp Equiv. | COPQ (Cost of Poor Quality) |
| .840 | 160,000 | 2.50 | 0.83 | 40% |
| .870 | 130,000 | 2.63 | 0.88 | |
| .900 | 100,000 | 2.78 | 0.93 | |
| .930 | 70,000 | 2.97 | 0.99 | |
| .935 | 65,000 | 3.01 | 1.00 | |
| .940 | 60,000 | 3.05 | 1.02 | |
| .945 | 55,000 | 3.10 | 1.03 | 30% |
| .950 | 50,000 | 3.14 | 1.05 | |
| .955 | 45,000 | 3.20 | 1.06 | |
| .960 | 40,000 | 3.25 | 1.08 | |
| .965 | 35,000 | 3.31 | 1.10 | |
| .970 | 30,000 | 3.38 | 1.13 | |
| .975 | 25,000 | 3.46 | 1.15 | |
| .980 | 20,000 | 3.55 | 1.18 | 20% |
| .985 | 15,000 | 3.67 | 1.22 | |
| .990 | 10,000 | 3.82 | 1.27 | |
| .995 | 5,000 | 4.07 | 1.36 | |
| .998 | 2,000 | 4.37 | 1.46 | |
| .999 | 1,000 | 4.60 | 1.53 | 10% |
| .9995 | 500 | 4.79 | 1.60 | |
| .99975 | 250 | 4.98 | 1.66 | 5% |
| .9999 | 100 | 5.22 | 1.74 | |
| .99998 | 20 | 5.61 | 1.87 | |
| .9999966 | 3.4 | 6.00 | 2.00 |
DPMO, DPM, Sample Size, CI Calculator will help you calculate the metrics.