Table of Contents

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 }$

Print Page