# X AND R CHART EXAMPLE IN-CLASS EXERCISE

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```					  X AND R CHART EXAMPLE
IN-CLASS EXERCISE
The following collection of data represents
samples of the amount of force applied in
a gluing process:

Determine if the process is in control
by calculating the appropriate upper and
lower
control limits of the X-bar and R charts.
X AND R CHART EXAMPLE
IN-CLASS EXERCISE
Sample   Obs 1    Obs 2    Obs 3    Obs 4    Obs 5
1      10.68   10.689   10.776   10.798   10.714
2      10.79    10.86   10.601   10.746   10.779
3      10.78   10.667   10.838   10.785   10.723
4      10.59   10.727   10.812   10.775    10.73
5      10.69   10.708    10.79   10.758   10.671
6      10.75   10.714   10.738   10.719   10.606
7      10.79   10.713   10.689   10.877   10.603
8      10.74   10.779    10.11   10.737    10.75
9      10.77   10.773   10.641   10.644   10.725
10     10.72   10.671   10.708    10.85   10.712
11     10.79   10.821   10.764   10.658   10.708
12     10.62   10.802   10.818   10.872   10.727
13     10.66   10.822   10.893   10.544    10.75
14     10.81   10.749   10.859   10.801   10.701
15     10.66   10.681   10.644   10.747   10.728
1. Calculate sample means, sample
ranges, mean of means, and mean of
ranges.
Sample   Obs 1    Obs 2    Obs 3    Obs 4       Obs 5      Avg   Range
1      10.68   10.689   10.776   10.798      10.714   10.732    0.116
2      10.79    10.86   10.601   10.746      10.779   10.755    0.259
3      10.78   10.667   10.838   10.785      10.723   10.759    0.171
4      10.59   10.727   10.812   10.775       10.73   10.727    0.221
5      10.69   10.708    10.79   10.758      10.671   10.724    0.119
6      10.75   10.714   10.738   10.719      10.606   10.705    0.143
7      10.79   10.713   10.689   10.877      10.603   10.735    0.274
8      10.74   10.779    10.11   10.737       10.75   10.624    0.669
9      10.77   10.773   10.641   10.644      10.725   10.710    0.132
10     10.72   10.671   10.708    10.85      10.712   10.732    0.179
11     10.79   10.821   10.764   10.658      10.708   10.748    0.163
12     10.62   10.802   10.818   10.872      10.727   10.768    0.250
13     10.66   10.822   10.893   10.544       10.75   10.733    0.349
14     10.81   10.749   10.859   10.801      10.701   10.783    0.158
15     10.66   10.681   10.644   10.747      10.728   10.692    0.103

Averages    10.728 0.220400
Example of x-bar and R charts: Step 2.
Determine Control Limit Formulas and
Necessary Tabled Values
x Chart Control Limits
n     A2    D3     D4
UCL = x + A 2 R           2   1.88      0   3.27
3   1.02      0   2.57
LCL = x - A 2 R           4   0.73      0   2.28
5   0.58      0   2.11
6   0.48      0   2.00
R Chart Control Limits    7   0.42   0.08   1.92
8   0.37   0.14   1.86
UCL = D 4 R               9   0.34   0.18   1.82
10   0.31   0.22   1.78
LCL = D 3 R              11   0.29   0.26   1.74
Steps 3&4. Calculate x-bar Chart
and Plot Values
UCL = x + A R  10.728  .58( 0.2204 )= .856
2                           10
LCL = x - A R  10.728-.58( 0.2204 )= .601
2                         10
10.900

10.850

10.800

10.750
Means

Sample
10.700                                                                     mean
UCL

10.650                                                                     LCL

grand
10.600
mean of x

10.550
1   2   3   4   5   6   7     8      9   10   11   12   13   14   15
Sample
Steps 5&6: Calculate R-chart and
Plot Values
UCL = D 4 R  ( 2.11)( 0.2204 )  0.46504
LCL = D 3 R  ( 0)( 0.2204 )  0

0.800
0.700
0.600
0.500                                                           Range
UCL
R 0.400
LCL
0.300                                                           R-bar

0.200
0.100
0.000
1   2   3   4   5   6   7   8   9   10 11 12 13 14 15
Sample

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