In: Operations Management
A finishing process packages assemblies into boxes. You have noticed variability in the boxes and desire to improve the process to fix the problem because some products fit too tightly into the boxes and others fit too closely. Following are width measurements of the box. Using x and R charts, plot and interpret the process.
MEAN | CI x-bar (Grand Mean) |
LCL x-bar (CI-A2*R-bar) |
UCL x-bar (CI+A2*R-bar) |
Sample Range (Max-Min) |
R-bar (Mean) |
UCL R (R-bar*D4) |
Spring 2020 | |||||||||
1 | 68.51 | 68.46 | 68.54 | 68.34 | 68.46 | 68.46 | ||||||||||
2 | 68.94 | 68.2 | 68.54 | 68.56 | 68.7 | 68.7 | ||||||||||
3 | 68.66 | 68.44 | 68.55 | 68.77 | 68.7 | 68.64 | ||||||||||
4 | 68.49 | 68.94 | 68.56 | 68.62 | 68.69 | 68.56 | ||||||||||
5 | 68.64 | 68.63 | 68.62 | 68.32 | 68.34 | 68.24 | ||||||||||
6 | 68.34 | 68.42 | 68.99 | 68.02 | 68.03 | 68.47 | ||||||||||
7 | 68.99 | 68.94 | 68.95 | 68.95 | 68.94 | 68.97 | ||||||||||
8 | 68.92 | 68.91 | 68.97 | 68.93 | 68.96 | 68.95 | ||||||||||
GRAND MEAN | ||||||||||||||||
n= | ||||||||||||||||
A2= | ||||||||||||||||
D4= | ||||||||||||||||
info from chart |
n= 6
A2= 0.483
D4=2.004
D3 = 0
Formula
R-chart
CL (Center line) = R-bar = 0.4
UCL = D4*R-bar = 2.004*0.4 = 0.8016
LCL = D3*R-bar = 0
We can see the process is not in control for R chart
Graph Data
Sample Range | Center line | UCL | LCL |
0.2 | 0.4 | 0.8016 | 0 |
0.74 | 0.4 | 0.8016 | 0 |
0.33 | 0.4 | 0.8016 | 0 |
0.45 | 0.4 | 0.8016 | 0 |
0.4 | 0.4 | 0.8016 | 0 |
0.97 | 0.4 | 0.8016 | 0 |
0.05 | 0.4 | 0.8016 | 0 |
0.06 | 0.4 | 0.8016 | 0 |
x-bar chart,
CL (Center line) = x-bar-bar = Grand mean = 68.63479167
UCL = x-bar-bar + A2*R-bar = 68.63479167+0.483*0.4 =
68.82799167
LCL = x-bar-bar - A2*R-bar = 68.63479167-0.483*0.4 = 68.44159167
We can see the process is not in control for x-bar chart
Graph Data
Sample | Sample mean | Center line | UCL | LCL |
1 | 68.461667 | 68.635 | 68.828 | 68.442 |
2 | 68.606667 | 68.635 | 68.828 | 68.442 |
3 | 68.626667 | 68.635 | 68.828 | 68.442 |
4 | 68.643333 | 68.635 | 68.828 | 68.442 |
5 | 68.465 | 68.635 | 68.828 | 68.442 |
6 | 68.378333 | 68.635 | 68.828 | 68.442 |
7 | 68.956667 | 68.635 | 68.828 | 68.442 |
8 | 68.94 | 68.635 | 68.828 | 68.442 |