For a manufacturing process, $\overline { \overline X }$
= 10 inches, $\overline { \mathrm { R } }$
= )4 inches,and the subgroup sample size is 6 units.Calculate the standard control limits for the $\bar { X }$
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, $\overline { \overline  X }$ 
= 10 inches, $\overline { \mathrm { R } }$
= )4 inches,and the subgroup sample size is 6 units.Calculate the standard control limits for the $\bar { X }$
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 to calculate the control limits for an X̄ chart is:

Upper control limit (UCL) = ̅X + A2R̅
Lower control limit (LCL) = ̅X - A2R̅

Where A2 is a constant from the standard normal distribution table, which depends on the subgroup size. For a subgroup size of 6, A2 = 0.576.

Substituting the given values in the formula, we get:

UCL = 10 + (0.576)(4/√6) = 10.193
LCL = 10 - (0.576)(4/√6) = 9.807

Therefore, the answer is C, 9.807 and 10.193.

For a Manufacturing Process X‾‾\overline { \overline X }X = 10 Inches

For a Manufacturing Process $\overline { \overline X }$ = 10 Inches