# Statistics – Process Sigma

Process sigma can be defined using following four steps:

1.     Measure opportunities,

2.     Measure defects,

3.     Calculate yield,

4.     Look-up process sigma.

## Formulae Used

DPMO=Total defectTotal Opportunities×1000000DPMO=Total defectTotal Opportunities×1000000

Defect(%)=Total defectTotal Opportunities×100Defect(%)=Total defectTotal Opportunities×100

Yield(%)=100−Defect(%)Yield(%)=100−Defect(%)

ProcessSigma=0.8406+29.37−−−−√−2.221×(log(DPMO))ProcessSigma=0.8406+29.37−2.221×(log(DPMO))

Where −

·        OpportunitiesOpportunities = Lowest defect noticeable by customer.

·        DPMODPMO = Defects per Million Opportunities.

### Example

Problem Statement:

In equipment organization hard plate produced is 10000 and the defects is 5. Discover the process sigma.

Solution:

Given: Opportunities = 10000 and Defects = 5. Substitute the given qualities in the recipe,

#### STEP 1: COMPUTE DPMO

DPMO=Total defectTotal Opportunities×1000000=(10000/5)×1000000,=500DPMO=Total defectTotal Opportunities×1000000=(10000/5)×1000000,=500

#### STEP 2: COMPUTE DEFECT(%)

Defect(%)=Total defectTotal Opportunities×100=100005×100,=0.05Defect(%)=Total defectTotal Opportunities×100=100005×100,=0.05

#### STEP 3: COMPUTE YIELD(%)

Yield(%)=100−Defect(%)=100−0.05,=99.95Yield(%)=100−Defect(%)=100−0.05,=99.95

#### STEP 3: COMPUTE PROCESS SIGMA

ProcessSigma=0.8406+29.37−−−−√−2.221×(log(DPMO))=0.8406+29.37−−−−√−2.221×(log(DPMO)),=0.8406+(√29.37)−2.221∗(log(500)),=4.79