Question

A company produces a product with the upper specification limit of 22 inches long and the lower specification limit of 18 inches. The process that produces the product has an average length of 19 inches with a standard deviation of 0.4 inches. What is the process capability ratio/index

Answer 1

Answer:

0.83

Explanation:

Given that ;

the upper specification limit USL = 22 inches

the  lower specification limit LSL =  18 inches.

Mean average length $\bar X$ =  19 inches

Standard deviation $\sigma$  = 0.4 inches

The process capability ratio/index $C_{pk$$= Min[\dfrac{USL - \bar X}{3(\sigma)}, \dfrac{\bar X - LSL}{3( \sigma)}]$

$C_{pk$$= Min[\dfrac{22 - 19}{3(0.4)}, \dfrac{19- 18}{3( 0.4)}]$

$C_{pk }= Min[\dfrac{3}{1.2}, \dfrac{1}{1.2}]$

$C_{pk }= Min[2.5 \ ,\ 0.83]$

The process capability ratio/index = 0.83