Answer:
0.83
Explanation:
Given that ;
the upper specification limit USL = 22 inches
the lower specification limit LSL = 18 inches.
Mean average length [tex]\bar X[/tex] = 19 inches
Standard deviation [tex]\sigma[/tex] = 0.4 inches
The process capability ratio/index [tex]C_{pk[/tex][tex]= Min[\dfrac{USL - \bar X}{3(\sigma)}, \dfrac{\bar X - LSL}{3( \sigma)}][/tex]
[tex]C_{pk[/tex][tex]= Min[\dfrac{22 - 19}{3(0.4)}, \dfrac{19- 18}{3( 0.4)}]\\[/tex]
[tex]C_{pk }= Min[\dfrac{3}{1.2}, \dfrac{1}{1.2}]\\[/tex]
[tex]C_{pk }= Min[2.5 \ ,\ 0.83]\\[/tex]
The process capability ratio/index = 0.83
