Consider the observations in Table 12E.2. The target value for this process is 50.

(a) Set up an integral controller for this process. Assume that the gain for the adjustment variable is g = 1.6 and assume that  = 0.2 in the EWMA forecasting procedure will provide adequate one-step-ahead predictions.
(b) How much reduction in variability around the target does the integral controller achieve?
Based on the reduction in variance, there is significant reduction in variability with use of integral control scheme.
(c) Rework parts (a) and (b) assuming that  = 0.4. What change does this make in the variability around the target in comparison to that achieved with  = 0.2?

TABLE 12E. 2 Process Data for Exercise 12.9 Ohservation, Observation. 26 15 16 58 27 35 37 42 18 19 56 30 32 21 69 43 35 23 20 63 54 34 12 37