For a given item the upper specification limit is 63 and the

For a given item, the upper specification limit is 63 and the lower specification limit is 47. We can assume that the process mean is centered within this interval. If this process, to be considered capable, must have a Cp of at least 1.4, what is the maximum value for the process standard deviation that would be acceptable?

Solution

USL=63

LSL =47

Mean ,U=(63+47)/2=55

Std Dev = 4.4

Cpk=min (CpU,CpL)

CpU= (USL-Mean)/(3*std dev)

CpL= (Mean-LSL)/(3*Std Dev)

Since the process mean is centered, CpU=CpL=Cpk

Now for Cpk= 1.4

We can consider CpU= 1.4 =(63-55)/(3*Std dev)

Hence max Std dev= 8/(3*1.4)=1.9048