If $\overline { \overline { X } }$

= 2)0144, $\bar { R }$
= )0972,and there are 25 subgroups of size 5,find the UCL and the LCL for the $\bar { x }$
Chart.
A)[1.999,2.029]
B)[1.958,2.071]
C)[1.917,2.112]
D)[1.437,2.591]

Question

If $\overline { \overline { X } }$

= 2)0144, $\bar { R }$
= )0972,and there are 25 subgroups of size 5,find the UCL and the LCL for the $\bar { x }$
Chart.
A)[1.999,2.029]
B)[1.958,2.071]
C)[1.917,2.112]
D)[1.437,2.591]

Quizplus · Accepted Answer

To calculate the UCL and LCL for the $\bar{x}$ chart, we use the following formulas:

UCL = $\overline{\overline{X}}$ + A2$\bar{R}$
LCL = $\overline{\overline{X}}$ - A2$\bar{R}$

Where A2 is a constant from the ARL table (for subgroup size of 5 and 25 subgroups, A2 = 0.577).

Substituting the given values, we get:

UCL = 2.0144 + (0.577)(0.0972) = 2.071
LCL = 2.0144 - (0.577)(0.0972) = 1.958

Therefore, the best choice is B) [1.958, 2.071].

If X‾‾\overline { \overline { X } }X = 2)0144 Rˉ\bar { R }Rˉ

If $\overline { \overline { X } }$ = 2)0144 $\bar { R }$