Defects Per Million Opportunities (DPMO)

Defects per Million Opportunities factors in the total opportunities for defect occurrence existing in a process. DPMO is considered long-term measurement of a process and this can be directly converted into a long-term Z-statistic (sigma value)

Given:

D: # of defects

O: # of opportunities for a defect

U: # of units

TOP: Total number of opportunities = U * O

Formula:

DPMO = DPO * 1,000,000

DPMO is NOT the same as PPM since it is possible that each unit (part) being appraised may be found to have multiple defects of the same type or may have multiple types of defects. A part is defective if it has one or more defects. The number of defectives can never exceed the number of defects.

IF each part only has one characteristic that can be a defect, then DPMO and PPM will be the same.

DPMO will always exceed or equal PPM for a given yield or sigma level of performance.

Example

Nail #1 it has two types of defects. Therefore it is ONE defective nail that contains TWO defects.

D = 19 total defects

O = 5 opportunities (categories of defect types)

U = 10 nails

TOP = U * O = 50 total opportunities

DPU = D / TOP = 1.9 defects per unit

DPO = 0.38

DPMO = 380,000

Out of a million opportunities, the long term performance of the process would create 380,000 defects

Using Excel to calculate Sigma and DPMO

To convert from DPMO to process sigma:

Process Sigma = NORMSINV * ( 1 -( DPMO / 1,000,000))+ 1.5

To convert from process sigma to DPMO:

DPMO = 1,000,000 * ( 1 - ( NORMSDIST * (process sigma - 1.5 ))

NOTE:

A Six Sigma quality process refers to the process short-term performance or how it is performing currently when there are 3.4 DPMO. Over the long term, this six sigma process is estimated to shift -1.5 sigma (lower) and will perform at a 4.5 sigma level, which produces 1,350 DPMO.