The following data represent individual observations on molecular weight ($x_i$) taken hourly ($i$) from a chemical process. The target value of the molecular weight is 1050 and process standard deviation is known to be $\sigma = 25$.
i $x_i$ i $x_i$
1 1054 11 1064
2 1046 12 1167
3 1075 13 1146
4 1052 14 1103
5 1016 15 1119
6 1051 16 1154
7 1057 17 1150
8 1037 18 1146
9 1090 19 1178
10 1032 20 1120
a) Construct the two-sided tabular form of the CUSUM chart using $k = 0.4$.
b) Based on this tabular CUSUM, please conclude whether the process has a mean shift using $h = 6$. If the process has a mean shift, please indicate which sample is the last sample in control and estimate the magnitude of this mean shift.
c) When an EWMA chart is used with $\lambda = 0.4$ based on all data points, what are the steady-state control limits in the control chart given sample size $n = 4$? Assume $L = 5$ is used, and $\sigma = 25$.