Part A: Determining Control Limits (Data for these questions is given in the spreadsheet)

Among its many different criterion for quality assurance, the Burnetas Brewery measures the ph level of its beer. A ph of 7.0 is acid/base neutral, while a ph of less than 7 indicates the beer is acidic and a ph greater than 7 indicates it is basic. Burnetas strives for a beer that is slightly basic. The brewery samples each batch of beer. A sample consists of drawing 7 glasses and testing each for ph level. The last 16 samples of data are shown in the table below. Given this data, compute the upper and lower control limits and the mean for an X-bar and an R-chart.

	Observation #
Sample #	1	2	3	4	5	6	7
1	7.01	7.00	7.09	7.02	7.12	7.20	7.00
2	7.22	7.20	7.17	7.07	7.02	6.99	7.01
3	6.97	7.09	7.11	7.15	7.05	6.98	7.17
4	7.13	7.17	7.24	7.07	7.14	7.00	7.16
5	7.13	7.06	7.10	7.29	7.11	7.05	7.10
6	7.10	6.95	7.03	7.21	7.13	7.04	7.15
7	7.25	7.08	7.03	7.08	7.00	7.25	7.13
8	7.17	7.10	7.02	7.18	6.96	7.05	6.99
9	7.17	6.98	7.15	7.11	7.05	7.16	7.16
10	7.24	7.17	7.04	7.06	7.14	7.25	7.02
11	6.98	7.07	7.21	7.28	7.04	7.10	7.00
12	7.20	7.09	7.07	6.93	6.99	7.20	6.96
13	7.04	7.14	7.09	7.15	7.19	7.09	7.21
14	7.03	7.03	7.15	7.06	7.09	7.16	7.20
15	7.13	7.14	7.11	7.07	7.04	7.13	7.00
16	7.11	7.15	7.02	7.13	7.18	7.12	7.15

Part B: Interpreting Control Charts (Data for these questions is given in the spreadsheet)

1) In Part B of the spreadsheet, there are 4 data sets. Each data set represents 16 samples of size 10 observations. From each sample, X-bar and R were calculated and then plotted on the appropriate control chart. You are to evaluate each data set for out of control conditions. Specifically, you should:

• State whether the process seems to be in control or out of control
• If you believe it is out of control, you should clearly state why (e.g. x-bar chart has sample 12 below the lower control limit).
• If you believe it is out of control, you should clearly state the nature of the out of control condition (e.g. process mean has shifted lower).