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# Control Chart with LCL and UCL Control limits

In OPS571, Week 5, DQ

Ch. 13, 14, & 16 of Operations Management for Competitive Advantage.
In preparation for this week's paper, let's step back to Technical Note 8 - Process Capability and Statistical Quality Control
1. Start by walking through Example TN8.3
2. Using data in Technical Note 8, Problem 6:

What are the controls limits for a X-bar chart? (upper and lower limit (UCL & LCL) - be sure to show your calculations. What are control limits uses?

Problem 6
Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows:

Develop an _X chart and an R chart and plot the values. From the charts, what comments can you make about the process?

1 1010 991 985 986
2 995 996 1009 994
3 990 1003 1015 1008
4 1015 1020 1009 998
5 1013 1019 1005 993
6 994 1001 994 1005
7 989 992 982 1020
8 1001 986 996 996
9 1006 989 1005 1007
10 992 1007 1006 979
11 996 1006 997 989
12 1019 996 991 1011
13 92 991 989 1003
14 999 993 988 984
15 1013 1002 1005 992

#### Solution Preview

The solution is in the attached spreadsheet.

Examine it for these important things:

1] The textbox in the upper right with comments on calculating control limits, the interpretation of the ...

#### Solution Summary

The solution is in an attached spreadsheet.

It contains these important things:

1] A textbox in the upper right with comments on calculating control limits, the interpretation of the control limits of this data set.

2] Note how the pasted in data on the top right and how each sample contributes to the average (x-bar), range and control limit columns to the left. Look at the Excel formulas in each cell.

3] Note the use in the formulas of "\$"-notation to use the same A_2, D_3, and D_4 values for each sample and produces a column of identical control limit values.

4] Graphs are set up to read the appopriate columns on the top middle of the spreadsheet.

\$2.19