Question

Twemty subgroups of size 5 are obtained for the purpose of determining trial control limits for mean and an R-chart.

Subgroup	Mean	R
1	23	5
2	22	3
3	24	2
4	20	4
5	18	3
6	17	4
7	24	4
8	10	3
9	16	5
10	20	4
11	26	5
12	21	4
13	22	4
14	20	4
15	23	3
16	21	6
17	20	5
18	18	4
19	15	3
20	17	2

A.) Determine the rial control limits for each chart. B.) Explain why there are so many subgroups averages outside the control limits for the mean chart in spite of the fact that the averages do not vary greatly. C.) What should be done with those subgroups whose averages is beyond the limits. D.) Since the number of points outside the control limits on the mean chart is quite high relative to the number of points that are plotted, what might this suggest about the type of distruibution from which the data could have come.

Answer 1

Formula reference:

A.) Determine the rial control limits for each chart.

Mean chart control limits:

CL - 19.85

LCL - 17.63

UCL - 22.07

Range chart control limits

CL - 3.85

LCL - 0

UCL - 8.14

B.) Explain why there are so many subgroups averages outside the control limits for the mean chart in spite of the fact that the averages do not vary greatly.

Analsyse the 20 sub group mean data to find out the number of subgroups are outside the control limits

There are 7 sug groups mean values are having very less value compare to other sug groups

so if we take the average out of 20 sub groups , there are so many groups are outside of the control limits

the below highlighted very less mean values in the sub group

lowest value of the sub group is 10, and maximum value of the sub group is 26.

C.) What should be done with those subgroups whose averages is beyond the limits.

The sub group whicha re more than the control limit values are declared as out of control . that needs to be monitored . Just as a stable process is “in control”, an unstable process is out of control.

D.) Since the number of points outside the control limits on the mean chart is quite high relative to the number of points that are plotted, what might this suggest about the type of distruibution from which the data could have come.

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Continue to plot data as they are generated. As each new data point is plotted, check for new out-of-control signals.

Uncontrolled Variation

Uncontrolled variation is characterized by variation that changes over time and is associated with special causes. The outcomes of this process are unpredictable; a customer may be satisfied or unsatisfied given this unpredictability.