Question

22. A) Use the following data to construct a Control Chart with the UCL, LCL and Central Line for the X Bar and R Chart. n- 5 Group 1: 2.1, 2.3, 2.5, 2.1, 2.0 Group 2: 2.2, 2.1, 2.0, 2.0, 2.1 Group 3: 2.0, 2.3, 2.1, 2.5, 2.2 Group 4: 2.0, 2.1, 2.1, 2.0, 2.1 Group 5: 2.3, 2.0, 2.3, 2.1, 2.2 Group 6: 2.2, 2.5, 2.1, 2.0, 2.0 Group 7: 2.1, 2.3, 2.5, 2.0, 2.1 Group 8: 2.0, 2.1, 2.3, 2.5, 2.0 2.2, 2.1, 2.0, 2.5, 2.4 Group 9: Group 10: 2.4, 2.3, 2.1, 2.0, 2.0 B) After you construct the Control Charts, plot the following data: n 5 Group 1: 2.2, 2.0, 2.1, 2.0, 2.1 Group 2: 2.2, 2.3, 2.5, 2.1, 2.0 Group 3: 2.3, 2.1, 2.0, 1.9, 2.3 Group 4: 2.0, 2.1, 2.3, 2.0, 2.4 Group 5: 2.4, 2.3, 2.1, 2.5, 2.0 Group 6: 2.0, 1.9, 2.3, 2.5, 2.0 Group 7: 2.4, 2.0, 2.1, 2.0, 2.3 Group 8: 2.0, 2.1, 2.2, 2.0, 1.9 Group 9: 2.2, 2.3, 2.0, 2.0 , 2.4 Group 10: 2.3, 2.5, 2.0, 2.1, 2.0

Answer 1

A) Here we have given group wise data set and have to construct a control chart with the UCL, LCL and Central Line for the X Bar and R chart where n = 5 (size of the group).

Using MINITAB we can easily construct a control chart. (Because if we have statistical software like- MINITAB then there is no need to find the UCL, LCL & CL manually.

Steps using which you can construct the above control chart is-

First enter the data in this way-

СЗ C1 C2 C4 C5 2.1 2.3 2.5 2.1 2.0 1 2.2 2.1 2.0 2.0 2.1 2 2.0 2.3 2.1 2.5 2.2 3 2.0 2.0 2.1 2.1 2.1 4 2.3 2.0 2.3 2.1 2.2 5 2.0 2.2 2.5 2.1 2.0 2.1 2.3 2.5 2.0 2.1 7 2.0 2.1 2.3 2.5 2.0 8 2.2 2.1 2.0 2.5 2.4 2.0 2.4 2.3 2.1 2.0 10 Ln

Now, you have to follow this steps-

  

Stat ControlCharts V ariablesChartsforsubgroups R.

After that a dialog box will be displayed on the screen like-

Xbar-R Chart C1 Observations for a subgroup are in one row of columns: C2 C3 C1 C2 C3 C4C5 C4 C5 Scale... Labels... Multiple Graphs... Xbar-R Options.. Data Options... Select Cancel OK Help

In this box first you have to choose observations for a subgroup are in one row of columns then in 2nd box we have to enter all the variables and then click OK. You will get-

X-Bar Chart UCL 2.3987 2,4 2.3 2.2 X-2.168 2.1 2.0 LCL 1.9373 4 1 2 3 5 6 7 10 Group No. CO O Sample Mean

R Chart UCL-0.8458 0.8 0.6 R-0.4 0.4 0.2 LCL 0 0.0 4 7 1 2 3 6 8 10 Group No. Sample Range et

In the above chart we see that each points are falling between UCL and LCL. Hence we may conclude that the process is under control.

B) In this part it has not mentioned that what kind of control chart are you looking for so i have simply construct the same control chart which i have drawn in the first part of this question.

Hence we can similarly construct the control chart for the another given data set-

Here we have also given n = 5.

Since in first part i have already discussed the steps to construct the X-Bar and R control chart then there is no need to repeat the steps again. Please follow the same steps then - we get that

X-Bar Chart 2.4 UCL-2.3963 2.2 X-2.154 2.0 LCL 1.9117 7 1 2 8 9 10 Group No. Group Mean O

R Chart UCL 0.8881 0.8 0.6 R=0.42 0.4 0.2 0.0 LCL 0 4 1 2 3 5 7 8 9 10 Group No. Group Range et

In the above chart we can see that each points are in between UCL and LCL. Hence we may conclude that the process is under control.

Note: In both part of the problem you can also construct the control chart manually. But when we find UCL, LCL and CL manually then we will face many complexity because in that case we need to find the many estimate so it's better to construct & find the limits using MINITAB or some other statistical software.