2. Below are the X-bar and R values for five samples. If the lower control limit for the X-bar chart is 8.34, what is the sample size?
Sample
X-bar
R
1
8.51
0.44
2
8.37
0.58
3
8.42
0.66
4
8.61
0.47
5
8.54
0.60
Expert Answer
Sample
X-bar
R
1
8.51
0.44
2
8.37
0.58
3
8.42
0.66
4
8.61
0.47
5
8.54
0.6
mean
8.49
0.55
LCL
8.34
X bar chart
UCL = X double bar + A2 * R bar
LCL = X double bar – A2 * R bar
where A2 is obtained from the Table of Control Chart Constants, for sample size m.
LCL = X double bar – A2 * R bar
8.34=8.49-A2*0.55
Solving for A2:
0.55*A2=8.49-8.34
0.55*A2=0.15
A2=0.15/0.55
A2=
0.27
Looking for A2 in Table of Control Chart constants:
A2=0.266 for m=12
A2=0.285 for m =11
Choosing m=12 as 0.266 is closer to required A2 value of 0.27
Hence,
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