The height of the stack is the sum of the thicknesses of the individual plates, each of which has the same nominal value. Because each plate thickness is a random variable, the height of a stack of four plates is a random variable,too.
There is a specified tolerance of ±0.004 inch for the stack. the inner two plates must have less variation in thickness for better functioning during field use. Suppose the inner plates should have a standard deviation in thickness that is 50% of that of the outer plates. Design for a Cpk of 1.333 for both individual plates and the stack height. Determine the required maximum standard deviation for the outer plates and for the inner plates.