# Meen Chava Corp's computer chip production process yields DRAM chips with an average life of...

## Question:

Meen Chava Corp's computer chip production process yields DRAM chips with an average life of 1,800 hours and sigma = 100 hours. The tolerance upper and lower specification limits are 2,400 and 1,600 hours, respectively. Is this process capable of producing DRAM chips to specification?

## Process Capability

A process is considered capable if its process capability index is equal to or greater than 1. In this case, a portion of its output equivalent to at least six standard deviations satisfies the specifications.

We find the process capability index as

{eq}C_{pk} = \min\left\{ \frac{\text{Process Average}-\text{Lower Specification Limit}}{3*\text{Standard Deviation}}, \frac{\text{Upper Specification Limit}-\text{Process Average}}{3*\text{Standard Deviation}} \right\} \\ = \min\left\{ \frac{1{,}800-1{,}600}{3*100}, \frac{2{,}400-1{,}800}{3*100} \right\} \\ = \min\left\{ \frac{200}{300}, \frac{600}{300} \right\} \\ = \min\left\{ 0.67, 2 \right\} \\ =0.67 {/eq}

As {eq}C_{pk} <1 {/eq}, the process is not capable of producing DRAM chips to specifications.