1) A machine at the Dream Mix Company fills boxes with cereals. The labeled weight of the boxes is 9.4 ounces, with +/- 0.9 ounce. The company wants to construct 3-sigma control charts to monitor the filling process and make sure the box weights are in control. The quality control department for the company sampled five boxes every 2 hours for six cycles. The sample observations are as follows.
Sample Box Weights
1 9.06 9.13 8.97 8.85 8.46
2 8.52 8.61 9.09 9.21 8.95
3 9.35 8.95 9.2 9.03 8.42
4 9.17 9.21 9.05 9.01 9.53
5 9.21 8.87 8.71 9.05 9.35
6 8.74 8.35 8.5 9.06 8.89
a) Construct 3sigma control charts.
b) The quality control department collected observation for another six cycles. Plot the corresponding values on control charts.
Sample Box Weights
1 9.00 9.21 9.05 9.23 8.78
2 9.15 9.20 9.23 9.15 9.06
3 8.98 8.90 8.81 9.05 9.13
4 9.03 9.10 9.26 9.46 8.47
5 9.53 9.02 9.11 8.88 8.92
6 8.95 9.10 9.00 9.06 8.95
c) What do the charts suggest about the process?
d) Based on the facts and information given in problem (1) above, what is the process capability index? Considering the old and new samples in problem (1), what are your remarks and suggestions?