Question

In: Operations Management

A finishing process packages assemblies into boxes. You have noticed variability in the boxes and desire...

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

Solutions

Expert Solution

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

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