# Megasigma Corp. has a process they believe is operating near the 6-sigma level and they want to...

## Question:

Megasigma Corp. has a process they believe is operating near the 6-sigma level and they want to verify this. The specification for the process output is 7.5 mm +/- 0.5 mm. The process is centered close to the target but has a standard deviation of 0.118 mm.

What is the actual sigma level of this process?

## Process Capability

A centered process is considered capable if its process capability ratio is at least 1. If it is below 1, the process is not capable. If the process capability ratio is at least 2, the process is operating at 6-sigma level.

We need to find the company's capability ratio at 6-sigma level, which can be found as {eq}C_p=\frac{\text{Upper Tolerance Limit}-\text{Lower Tolerance Limit}}{6\sigma}= \frac{8-7}{6\cdot 0.118} \approx 1.41 {/eq}. If the process actually operated at 6-sigma level, the capability ratio would be {eq}2 {/eq}. The current process operates merely at {eq}\frac{1.41}{2}\cdot 6 \approx 4.2 {/eq}-sigma level.