Chapter 13.5, Problem 13.34ACI

Cola bottle filling process. A soft-drink bottling company is interested in monitoring the amount of cola injected into 16-ounce bottles by a particular filling head. The process is entirely automated and operates 24 hours a day. At 6:00 a.m. and 6:00 p.m. each day, a new dispenser of carbon dioxide capable of producing 20,000 gallons of cola is hooked up to the filling machine. To monitor the process using control charts, the company decided to sample five consecutive bottles of cola each hour beginning at 6:15 a.m. (i.e.. 6:15 a.m., 7:15 a.m., 8:15 a.m., etc.). The data for the first day are saved in the file. An SPSS descriptive statistics printout for the data is shown above.

1. a. Will the rational subgrouping strategy that was used enable the company to detect variation in fill caused by differences in the carbon dioxide dispensers? Explain.
2. b. Construct an R-chart from the data.
3. c. What does the R-chart indicate about the stability of the filling process during the time when the data were collected? Justify your answer.
4. d. Should the control limit(s) be used to monitor future process output? Explain.
5. e. Given your answer to part c, should an $\bar{x}$-chart be constructed from tie given data? Explain.

Descriptive Statistics for 25 Cola Samples