Answer:
Step-by-step explanation:
Given that :
sample mean = 4.001 inches
sample standard deviation = 0.002 inch
a.
[tex]C_{pk} = min [\dfrac{(USL- \bar X)}{(3*std \ dev)} \ ; \ \dfrac{ (\bar X- LSL)}{(3*std \ dev)}][/tex]
specification = [tex]4 \pm 0.003[/tex]
Upper specification limit USL = 4 + 0.003 = 4.003
Lower specification limit LSL = 4 - 0.003 = 3.997
[tex]\dfrac{ (\bar X- LSL)}{(3*std \ dev)} = \dfrac{ (4.001-3.997)}{(3*0.002)}[/tex] [tex]= 0.667[/tex]
[tex]\dfrac{(USL- \bar X)}{(3*std \ dev)} =\dfrac{(4.003-4.001)}{(3*0.002)}[/tex][tex]= 0.333[/tex]
Thus ;
[tex]C_{pk} =[/tex][tex]min (0.333 , 0.667)[/tex] = 0.333
[tex]C_{pk}[/tex] is a measure of closeness to one's target and the consistency around the average performance.
b) No, C - spec should not use this machine to produce this part because [tex]C_{pk}[/tex] < 1.33 which typical means that the part is not fully capable of hitting the target specification on a consistent basis .
