Suppose that you're the Quality Manager for the Emerson D. Meritz Machine Tool Company. Your model IE566 grinding machine is afflicted by three types of defects classified as major (type A), serious (type B) and minor (type C). You wish to set up a demerit system for this product using the following weighting scheme:

D=100 xa +50 xb +xc

where xa, xb, and xc are the number of the corresponding defect types observed on a single grinding machine. Based on past history xa, xb, and xc are known to be poisson distributed with means ca=5, cb=10 and cc=20.

I. Determine the center line and upper and lower control limits for the weighted number of demerits D observed on a single machine.

II. Using Minitab or other statistical software of your choosing, simulate 30 sets of observations of xa, xb, and xc and compute D for each set. Plot the D values on the control chart determined above.

III. Use the moving range of the D values found in item II to estimate the standard deviation of D. Compare it to the theoretical value of the standard deviation of D you computed in item I above.

IV. Using the approximate normality of D compute b and the ARL if the poisson means change to ca=10, cb=15 and cc=4