(a) Construct the normal probability plot and note that the hypothesis of normality is rejected if we use α = .05 since the p-value for the test that MINITAB uses is .018. Would you suggest that an X-chart be constructed for these data? Why or why not?

(b) Even though doing so might be highly questionable in view of the normal probability plot, construct an X-chart for American League earned run averages (ERAs), using the data from 1901 to 1972. (Note that “averages” are being treated as individual observations since the averages are computed over teams and there is no interest in the individual teams.) Use the moving range approach to estimate sigma.

(c) Would you have constructed the control limits using a different approach? Explain. If you would have constructed the control limits differently, do so. Are any points outside the control limits now?

(d) Now plot the earned run averages starting in 1973, one at a time in simulating real time. Construct an X-chart with 3-sigma limits, and a CUSUM chart using k = 0.5 and h = 5. Is there a sufficient number of observations to enable the parameters to be estimated for the X-chart and have the chart perform in a reliable manner? Similarly, would you expect the CUSUM procedure to be reliable (i.e., have a small performance variance)?

(e) Do the two chart methods give different signals after 1972? Since the designated hitter rule was started in 1973, which method gives the correct signal?

Exercise 1.1

Assume that a practitioner decides to use a control chart with 2.5-sigma limits. If normality can be assumed (as well as known parameter values), what is the numerical value of the in-control ARL?