10.29. The viscosity of a chemical product is read every two minutes. Some data from this process are shown in Table 10E.11 (read down, then across from left to right). (a) Is there a serious problem with autocorrelation in these data? (b) Set up a control chart for individuals with a moving range used to estimate process variability. What conclusion can you draw from this chart? (c) Design a cusum control scheme for this process, assuming that the observations are uncorrelated. How does the cusum perform? (d) Set up an EWMA control chart with l = 0.15 for the process. How does this chart perform? (e) Set up a moving center line EWMA scheme for these data. (f) Suppose that a reasonable model for the viscosity data is an AR (2) model. How could this model be used to assist in the development of a statistical process-control procedure for viscosity? Set up an appropriate control chart and use it to assess the current state of statistical control.

TABLE 10E.11 Chemical Product Viscosity \begin{tabular}{llll} \hline 29.330 & 33.220 & 27.990 & 24.280 \\ 19.980 & 30.150 & 24.130 & 22.690 \\ 25.760 & 27.080 & 29.200 & 26.600 \\ 29.000 & 33.660 & 34.300 & 28.860 \\ 31.030 & 36.580 & 26.410 & 28.270 \\ 32.680 & 29.040 & 28.780 & 28.170 \\ 33.560 & 28.080 & 21.280 & 28.580 \\ 27.500 & 30.280 & 21.710 & 30.760 \\ 26.750 & 29.350 & 21.470 & 30.620 \\ 30.550 & 33.600 & 24.710 & 20.840 \\ 28.940 & 30.290 & 33.610 & 16.560 \\ 28.500 & 20.110 & 36.540 & 25.230 \\ 28.190 & 17.510 & 35.700 & 31.790 \\ 26.130 & 23.710 & 33.680 & 32.520 \\ 27.790 & 24.220 & 29.290 & 30.280 \\ 27.630 & 32.430 & 25.120 & 26.140 \\ 29.890 & 32.440 & 27.230 & 19.030 \\ 28.180 & 29.390 & 30.610 & 24.340 \\ 26.650 & 23.450 & 29.060 & 31.530 \\ 30.010 & 23.620 & 28.480 & 31.950 \\ 30.800 & 28.120 & 32.010 & 31.680 \\ 30.450 & 29.940 & 31.890 & 29.100 \\ 36.610 & 30.560 & 31.720 & 23.150 \\ 31.400 & 32.300 & 29.090 & 26.740 \\ 30.830 & 31.580 & 31.920 & 32.440 \\ \hline \end{tabular} TABLE 10E.11 Chemical Product Viscosity \begin{tabular}{llll} \hline 29.330 & 33.220 & 27.990 & 24.280 \\ 19.980 & 30.150 & 24.130 & 22.690 \\ 25.760 & 27.080 & 29.200 & 26.600 \\ 29.000 & 33.660 & 34.300 & 28.860 \\ 31.030 & 36.580 & 26.410 & 28.270 \\ 32.680 & 29.040 & 28.780 & 28.170 \\ 33.560 & 28.080 & 21.280 & 28.580 \\ 27.500 & 30.280 & 21.710 & 30.760 \\ 26.750 & 29.350 & 21.470 & 30.620 \\ 30.550 & 33.600 & 24.710 & 20.840 \\ 28.940 & 30.290 & 33.610 & 16.560 \\ 28.500 & 20.110 & 36.540 & 25.230 \\ 28.190 & 17.510 & 35.700 & 31.790 \\ 26.130 & 23.710 & 33.680 & 32.520 \\ 27.790 & 24.220 & 29.290 & 30.280 \\ 27.630 & 32.430 & 25.120 & 26.140 \\ 29.890 & 32.440 & 27.230 & 19.030 \\ 28.180 & 29.390 & 30.610 & 24.340 \\ 26.650 & 23.450 & 29.060 & 31.530 \\ 30.010 & 23.620 & 28.480 & 31.950 \\ 30.800 & 28.120 & 32.010 & 31.680 \\ 30.450 & 29.940 & 31.890 & 29.100 \\ 36.610 & 30.560 & 31.720 & 23.150 \\ 31.400 & 32.300 & 29.090 & 26.740 \\ 30.830 & 31.580 & 31.920 & 32.440 \\ \hline \end{tabular}