Assume that you are 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 historyxa, xb, and xc are known to be poissondistributed 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 chartdetermined above.
III. Use the moving rangeof the D values found in item II to estimate the standard deviationof 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
II. Note the 30 values for xa,xb and xc are generated in excel. To do this : go to “tools > data analysis> random number generator> select Poisson …
The expert examines the control limits for quality managers. Three types of defects classified as major, serious and minor are determined.