Statistics - Process Sigma

Process sigma can be defined using following four steps:

Measure opportunities,

Measure defects,

Calculate yield,

Look-up process sigma.

Formulae Used

${DPMO = frac{Total defect}{Total Opportunities} imes 1000000}$

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

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

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

Where −

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

${DPMO}$ = Defects per Milpon 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 quapties in the recipe,

Step 1: Compute DPMO

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

Step 2: Compute Defect(%)

$ {Defect (\%) = frac{Total defect}{Total Opportunities} imes 100 \[7pt] , = frac{10000}{5} imes 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 imes (log (DPMO)) \[7pt] , = 0.8406 + sqrt {29.37} - 2.221 imes (log (DPMO)) , \[7pt] , = 0.8406+sqrt(29.37) - 2.221*(log (500)) , \[7pt] , = 4.79 }$ Advertisements