Find the control limits for the -chart with = 0.08, = 0.01,and sample size of 10.
A)The R is too small to determine control limits.
B)LCL = 0.077 and UCL = 0.083
C)LCL = 0.769 and UCL = 0.831
D)LCL = 0.797 and UCL = 0.803

Question

Find the control limits for the  -chart with  = 0.08,  = 0.01,and sample size of 10.
A)The R is too small to determine control limits. 
B)LCL = 0.077 and UCL = 0.083 
C)LCL = 0.769 and UCL = 0.831 
D)LCL = 0.797 and UCL = 0.803

Quizplus · Accepted Answer

To find the control limits for an R-chart, the following formula is used:
UCL_R = R-bar * D4
LCL_R = R-bar * D3
where D4 and D3 are constants from the R-chart factors table based on the sample size. For sample size 10, D4 = 2.113 and D3 = 0.0.
The range of the data is:
R = (0.08-0.01) = 0.07
Therefore, R-bar = R/n = 0.07/10 = 0.007
Using the formula above:
UCL_R = 0.007 * 2.113 = 0.015
LCL_R = 0.007 * 0 = 0
The control limits for the original data (not the range) are:
UCL = 0.08 + 3*0.015 = 0.125
LCL = 0.08 - 3*0.015 = 0.035
Therefore, the control limits for the given data are LCL = 0.077 and UCL = 0.083, which is option B.

Find the Control Limits for the -Chart with