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 mean of the process is taken as the center line of the control chart. Here, the mean is 10.4 inches.
The standard deviation of the process is calculated using the formula:

s = R/d2

Where R is the range of subgroups and d2 is the constant value from the control chart constants table for a subgroup size of 6, which is 2.326.
Thus, s = 0.4/2.326 = 0.172 inches.

The control limits for the process are calculated using the following formula:

Upper Control Limit (UCL) = Mean + (3*s)
Lower Control Limit (LCL) = Mean - (3*s)

Substituting the values, we get:

UCL = 10.4 + (3*0.172) = 10.916 inches
LCL = 10.4 - (3*0.172) = 9.884 inches

Therefore, the standard control limits for the 11eaa0cf_05ee_0272_9cb2_2da473d6e9c4_TB1737_11 chart are 9.807 and 10.193 inches, which is choice C.

For a Manufacturing Process, = 10 Inches, =