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)


D: # of defects

O: # of opportunities for a defect

U: # of units

TOP: Total number of opportunities = U * O


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.

You could have 1,000,000 defects on one part and the DPMO could be 1,000,000 and the PPM is 1.0 if that part is the only part out of the million that has any defects (in other words the other 999,999 parts have 0 defects). This is an exaggeration to try and illustrate the difference between DPMO and PPM.

Also keep in mind that it's possible that each widget being measured (or assessed) has a different amount of potential defects. So theoretically you could have just a few widgets (very complex widgets) that have thousands of opportunities for defects or a lot of simple widgets that only have a few total opportunities for defects. 

DPMO Example

Examine the table shown below:

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

DPMO Example


D = 19 total defects

O = 5 opportunities (categories of defect types)

U = 10 nails

TOP = U * O = 50 total opportunities for defects

DPU = D / U = 19/10 = 1.9 defects per unit

DPO = D / TOP = 19/50 = 0.38

DPMO = 380,000

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

Notice that only Nail #3 and Nail #9 had zero defects. Therefore 8 out of 10 nails had at least one defect. That represents a PPM of 800,000. 

Using Excel to calculate Sigma and DPMO

There are a couple commonly used Microsoft Excel functions that converts Defects per Million Opportunities (DPMO) to a process sigma (z-score) and vice versa.

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 ))


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.

DPMO Calculator (Six Sigma Calculator)

Enter your values in the white cells and everything else is calculated. Notes are in the actual template that offer more guidance and information on each row.

DPMO, Z-score, TOP, DPU, and more

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