## DPO, DPMO, PPM, DPU Definitions – Six Sigma Defect Metrics

### 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 ( Y_{1st-pass} or Y_{final} 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 oppurtunities 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 C_{P} values? See Sigma Table.

## Converting Yield to sigma & C_{p} 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 C
_{P}by dividing it by 3σ : C_{P}= 3.82σ/3σ = 1.27 Note: C_{pk }cannot be estimated by this method

## Six Sigma Capability Improvement

## Sigma Table

Yield | dpmo | Sigma (σ) | C_{p} 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 |

Our free DPMO, DPM, Sample Size, CI Calculator will help you calculate the metrics.