Question

1. The table below contains the widths of a product, showing 10 samples of size 5 measurements each.

1	2	3	4	5	6	7	8	9	10
40 42 43 41 40	39 45 41 34 42	38 44 46 43 48	48 45 43 43 47	41 40 44 44 43	37 39 40 42 44	43 41 42 43 40	44 46 48 41 42	42 44 40 41 42	39 40 41 42 43

1. Construct a sample means, X control chart and R chart for the above data.
2. Identify those subgroup means which are outside the control limits.
3. Comment on the process.

Answer 1

(i)

We make a table :

Sub-group Number	Measurements	Total	Mean	Range
1	40	42	43	41	40	206	41.2	3
2	39	45	41	34	42	201	40.2	11
3	38	44	46	43	48	219	43.8	10
4	48	45	43	43	47	226	45.2	5
5	41	40	44	44	43	212	42.4	4
6	37	39	40	42	44	202	40.4	7
7	43	41	42	43	40	209	41.8	3
8	44	46	48	41	42	221	44.2	7
9	42	44	40	41	42	209	41.8	4
10	39	40	41	42	43	205	41	4
Total	N/A	N/A	422	58

Hence the mean of the subgroup means and that of the subgroup ranges are given by

Here the subgroup size(n)=5, and therefore from the table of SQC, we have A2=0.577 . Thus,

Then, for the mean chart we have,

Again for the range chart, the values are obtained from the table of SQC for n=5 as

D2	0
D3	2.115

Hence for the range chart,

(ii)

From the control limits of the mean chart, it can be seen that all the subgroup means are within the control limits. Hence there are no subgroup means which are outside the control limits.

Similarly, from the control limits of the range chart, it can be seen that all the subgroup ranges are within the control limits. Hence there are no subgroup ranges which are outside the control limits.

(iii)

As all the subgroup means are within the control limits, it can be concluded that the process is in control. The variations which may still be present in the data are due to chance causes or random causes and cannit be controlled.

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