Question

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

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. 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. 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. 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 above. 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. Use Excel to answer the question.

b. Is the process in statistical control? Identify out-of-control points.

Answer 1

(a) The calculations are:

Sample size	4
Number of samples	10
	Mean	Range
Upper Control Limit, UCL	98.767	0.844
Center	98.498	0.370
Lower Control Limit, LCL	98.228	0.000

The control charts are:

(b) The process is not in statistical control.

The out-of-control points are 97.675, 99.25, 98, 98.875, 97.675 & 99.3.