Question

A quality engineer is assessing the capability of a process. He took a sample of the production line for the inner tubes, which yileded an average of 61 psi with a satndard deviation of 2 psi. The specification calls for the acceptance range to be from 55 psi to 65 psi. What is the Cpk of this line?

Answer 1

The Cpk of this line is 0.6667.

Explanation:

Cpk:

In a process with mean
`\mu`, standard deviation
`\sigma`, upper limit U and lower limit M, the CPK is of:

`C_(pk) = \text{min}((U-\mu)/(3\sigma), (\mu-L)/(3\sigma))`

Average of 61 psi with a standard deviation of 2 psi.

This means that
`\mu = 61, \sigma = 2`

The specification calls for the acceptance range to be from 55 psi to 65 psi.

This means that
`L = 55, U = 65`.

Cpk

`(U-\mu)/(3\sigma) = (65-61)/(3(2)) = 0.6667`

`(\mu-L)/(3\sigma) = (61-55)/(3(2)) = 1`

The minimum of these values is 0.6667, so the Cpk of this line is 0.6667.