A component used as a part of a power transmission unit is manufactured using a lathe.

Twenty samples, each of five components, are taken at half-hourly intervals. Within the flow of the day a number of (non-)technical incidents appear. These include taking a lunch break, and adjusting or resetting the machine.

For the most critical dimension, the process mean () is found to be 3.500 cm, with a normal distribution of the results about the mean, and a mean sample range () of 0.0007 cm.

With the above scenario in mind, complete the following tasks considering the data in this table Download data in this table.

1. Use this information to set up suitable control charts.
2. If the specified tolerance is 3.498 cm to 3.502 cm, what is your reaction? Would you consider any action necessary?
3. The following table shows the operator's results over the day. The measurements were taken using a comparator set to 3.500 cm and are shown in units of 0.001 cm. What is your interpretation of these results? Do you have any comments on the process and / or the operator?

Table

Time	Component 1	Component 2	Component 3	Component 4	Component 5
7.30	0.2	0.5	0.4	0.3	0.2
7.35	0.2	0.1	0.3	0.2	0.2
8.00	0.2	-0.2	-0.3	-0.1	0.1
8.30	-0.2	0.3	0.4	-0.2	-0.2
9.00	-0.3	0.1	-0.4	-0.6	-0.1
9.05	-0.1	-0.5	-0.5	-0.2	-0.5
Machine stopped -tool clamp readjusted
10.30	-0.2	-0.2	0.4	-0.6	-0.2
11.00	0.6	0.2	-0.2	0.0	0.1
11.30	0.4	0.1	-0.2	0.5	0.3
12.00	0.3	-0.1	-0.3	0.2	0.0
Lunch
12.45	-0.5	-0.1	0.6	0.2	0.3
13.15	0.3	0.4	-0.1	-0.2	0.0
Reset tool by 0.15 cm
13.20	-0.6	0.2	-0.2	0.1	-0.2
13.50	0.4	-0.1	-0.5	-0.1	-0.2
14.20	0.0	-0.3	0.2	0.2	0.4
Batch finished - machine reset
16.15	1.3	1.7	201	1.4	1.6