For a manufacturing process, = 10 inches, = .4 inches,and the subgroup sample size is 6 units.Calculate the standard control limits for the chart.
A)9.526 and 10.474
B)9.769 and 10.231
C)9.807 and 10.193
D)9.484 and 10.516
E)8.80 and 11.20

Question

For a manufacturing process,  = 10 inches,  = .4 inches,and the subgroup sample size is 6 units.Calculate the standard control limits for the  chart.
A)9.526 and 10.474 
B)9.769 and 10.231 
C)9.807 and 10.193 
D)9.484 and 10.516 
E)8.80 and 11.20

Quizplus · Accepted Answer

The formula for calculating standard control limits for an X-bar chart is:

Upper Control Limit (UCL) = X-double bar + A2*R
Lower Control Limit (LCL) = X-double bar - A2*R

Where,
X-double bar = Grand mean
A2 = Constant based on sample size (A2 = 0.577 for n=6)
R = Range of subgroups (R = Maximum value - Minimum value within subgroup)

Here, 
X-double bar = (10 + 0.4)/2 = 5.2
A2 = 0.577
R = Maximum value - Minimum value within subgroup

For finding the maximum and minimum value within the subgroup, we need to know the actual values for the subgroup. Without that information, we cannot calculate the R. So, we cannot calculate the standard control limits for the given chart without additional information. Therefore, the answer is C) Not enough information provided.

For a Manufacturing Process, = 10 Inches, =