Statistics - Process Sigma
Process sigma can be defined using following four steps:
Measure opportunities,
Measure defects,
Calculate yield,
Look-up process sigma.
Formulae Used
${DPMO = \frac{Total\ defect}{Total\ Opportunities} \times 1000000}$
${Defect (\%) = \frac{Total\ defect}{Total\ Opportunities} \times 100}$
${Yield (\%) = 100 - Defect (\%) }$
${Process Sigma = 0.8406+\sqrt{29.37}-2.221 \times (log (DPMO)) }$
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 }$
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