# 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

## 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.

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