# 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

${DPMO = \frac{Total\ defect}{Total\ Opportunities} \times 1000000}$

${Defect (\%) = \frac{Total\ defect}{Total\ Opportunities} \times 100}$

${Yield (\%) = 100 - Defect (\%) }$

${Process Sigma = 0.8406+\sqrt{29.37}-2.221 \times (log (DPMO)) }$

Where −

• ${Opportunities}$ = Lowest defect noticeable by customer.

• ${DPMO}$ = 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

${DPMO = \frac{Total\ defect}{Total\ Opportunities} \times 1000000 \\[7pt] \, = (10000/5) \times 1000000 , \\[7pt] \, = 500}$

#### Step 2: Compute Defect(%)

${Defect (\%) = \frac{Total\ defect}{Total\ Opportunities} \times 100 \\[7pt] \, = \frac{10000}{5} \times 100 , \\[7pt] \, = 0.05}$

#### Step 3: Compute Yield(%)

${Yield (\%) = 100 - Defect (\%) \\[7pt] \, = 100 - 0.05 , \\[7pt] \, = 99.95}$

#### Step 3: Compute Process Sigma

${Process Sigma = 0.8406+\sqrt{29.37}-2.221 \times (log (DPMO)) \\[7pt] \, = 0.8406 + \sqrt {29.37} - 2.221 \times (log (DPMO)) , \\[7pt] \, = 0.8406+\sqrt(29.37) - 2.221*(log (500)) , \\[7pt] \, = 4.79 }$