Question

2.a. You are running a batch reactor. Each batch takes about four hours to run. You measure the purity of the batch four times in the last hour to ensure that it has stabilized. You want to monitor the results using an X-R chart. The data you have collected for the first 10 batches are given the table below. X1, X2, X3 and X4 are the four samples you pull from the batch in the last hour. Using all the data, find trial control limits for and R charts, construct the chart, and plot the data. (30 pts)

2.b. Is the process in statistical control? Identify out-of-control points. (30 pts)

Subgroup	X1	X2	X3	X4	X	R
1	98.4	98.6	98.3	98.7	98.5	0.4
2	97.5	97.6	98.0	97.6	97.7	0.5
3	98.8	98.9	98.4	98.7	98.7	0.5
4	99.1	99.3	99.4	99.2	99.3	0.3
5	97.8	98.0	98.2	98.0	98.0	0.4
6	98.3	98.5	98.5	98.5	98.5	0.2
7	98.9	99.0	98.6	99.0	98.9	0.4
8	97.5	97.7	97.6	97.9	97.7	0.4
9	99.3	99.3	99.2	99.4	99.3	0.2
10	98.5	98.7	98.7	98.3	98.6	0.4

Answer 1

2a) From the given data

Subgroup	X1	X2	X3	X4	X-Bar	R
1	98.4	98.6	98.3	98.7	98.50	0.4
2	97.5	97.6	98	97.6	97.68	0.5
3	98.8	98.9	98.4	98.7	98.70	0.5
4	99.1	99.3	99.4	99.2	99.25	0.3
5	97.8	98	98.2	98	98.00	0.4
6	98.3	98.5	98.5	98.5	98.45	0.2
7	98.9	99	98.6	99	98.88	0.4
8	97.5	97.7	97.6	97.9	97.68	0.4
9	99.3	99.3	99.2	99.4	99.30	0.2
10	98.5	98.7	98.7	98.3	98.55	0.4
			Total:		984.98	3.7

b) Control chart:

The process mean may not be stable. 6(60%) subgroups are out of control on the xbar chart.

Unusually small mean 2,5,8 sub groups and unusually large mean 4,7,8 sub groups in xbar chart