Chapter 13.4, Problem 13.18ACI

Cereal box manufacturing. A machine at K-Company fills boxes with bran flakes cereal. The target weight for the filled boxes is 24 ounces. The company would like to use an x-chart to monitor the performance of the machine. To develop the control chart, the company decides to sample and weigh five boxes of cereal each day (at 8:00 and 11:00 A.M. and 2:00, 5:00, and 8:00 P.M. ) for 20 consecutive days. The data are summarized in the SPSS printout below.

1. a. Construct an $\bar{x}$-chart from the summary statistics.
2. b. What does the chart suggest about the stability of the filling process (whether the process is in or out of statistical control)? Justify your answer.
3. c. Should the control limits be used to monitor future process output? Explain.
4. d. Two shifts of workers run the filling operation. Each day the second shift takes over at 3:00 P.M. Will the rational subgrouping strategy used by K- Company facilitate or hinder the identification of process variation caused by differences in the two shifts? Explain.