Question

the deployment time of an airbag should be between 21 and 27 milliseconds and their current average is 22 milliseconds with a standard deviation of 0.25 milliseconds. Determine the process capability index if they were to center the mean.

Answer 1

Answer:

4.00

Explanation:

Given:

Upper Specification Limit, USL = 27

Lower Specification Limit, LSL = 21

Mean = 22

Standard deviation, $\sigma$ = 0.25

Required:

Find the process capability index

First center the mean by taking the average of the LSL and USL.

$X = \frac{21 + 27}{2}$

$\frac{48}{2} = 24$

$X = 24$

Use formula below to find process capability index:

$C_p_i = min [(\frac{USL - X}{3*\sigma}), (\frac{X - LSL}{3*\sigma})]$

$C_p_i = min [(\frac{27 - 24}{3*0.25}), (\frac{24 - 21}{3*0.25})]$

$= min [(\frac{3}{0.75}), (\frac{3}{0.75})]$

$min [ (4.00), (4.00)]$

We are sullosed to take the minimum value, but since both values are equal, our process capability index will be 4.00

Therefore, the process capability index = 4.00