Control Limit Charts

Question

Samples
1 2 3 4 5 6 7 8 9 10 11 12
20.2 19.9 19.8 20.1 19.8 19.7 20.2 20.1 20 19.9 20.1 19.9
20.1 19.9 19.9 19.9 20.1 19.6 20.1 20.1 19.9 19.8 20.1 19.4
19.8 19.7 20 19.9 20.1 19.7 19.9 19.8 20.1 20.1 19.9 19.7
19.9 20.1 20.1 19.8 19.9 19.4 19.9 19.7 19.8 19.9 19.9 19.8

A) What are the control limits for the mean chart?
B) What are the control limits for the range data?
C) Is the process in control?

Answer 1

Arrange your data into subgroups.  The subgroups are sample data that are categorized by a common integer. Since you have numbers that have integers from 1 to 20, you will have these subgroups:

 

1 , 2 , 3 , 4 ,  , 6 , 7 , 8 , 9 , 10 , 19 , and 20.

 

 

The measurements are represented the digits after the decimal point. So you will organize your measurements based on subgroups.

 

Subgroup     |    Measurement

1                            .00

2                            .00

3                            .00

4                            .00

5                            .00

6                            .00

7                            .00

8                            .00

9                            .00

10                          .00

11                          .00

12                          .00

19                       

20                      

 

 

Notice the measurements for subgroups 1 to 12 is 0.00.  This is because the actual measurements for these samples are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

 

You have a lot of samples that measure in the 19, 20, and 21 subgroups.  Complete the chart that I have started for you for those remaining groups.  Then, you are going to find the maximum number of samples possible for any subgroup.  This will be the number of samples you will use to calculate the control limits.  You have a total of 15 subgroups. 

 

Use these values to calculate the control limit:

 

N = number of measurements possible for any subgroup in the data collection

g = 14

 

 

x(bar) = sum of the measures from each subgroup / N 

 

x(double bar) = sum of the means / g

 

R(bar) = sum of the ranges / g 

 

 

 

The formula for the control limits for mean are:

 

Upper limit = x(double bar) + R(bar)A₂

Lower limit = x(double bar) - R(bar)A₂

 

 

The formula for control limits for range are:

 

Upper limit = R(bar)D₄

Lower limit = R(bar)D₃

 

Use any references your instructor provided you or what your textbook has to obtain the A and D values.

 

 

The limits will be indicated by straight horizontal line.  If the mean values are below the mean lower limit or above the mean upper limit, then the process is out of control.  The same concept goes for the range limits.

 

 

I advise you use an excel spreadsheet to complete the chart and calculations.  Then use the data to create the charts in excel.