Over a twenty hour period forty samples of five items each were collected.From this data, the values calculated for $\bar { \bar { X } }$ and $\bar { R }$ were 120.10 and 45.75 respectively.Based on this data, the upper control limit for the X bar control chart should be set at
Approximately:

Question

Over a twenty hour period forty samples of five items each were collected.From this data, the values calculated for

\bar { \bar { X } }

and

\bar { R }

were 120.10 and 45.75 respectively.Based on this data, the upper control limit for the X bar control chart should be set at
Approximately:

Quizplus · Accepted Answer

To calculate the upper control limit for the X bar control chart, we need to use the formula: UCL = X(bar) + A2*R, where X(bar) is the average of the sample means, A2 is the control chart constant for sample size 5 which is 0.577, and R is the average range of the samples.

First we calculate R:

R = (R1 + R2 + ... + Rn)/n 
= (3.36 + 3.26 + ... + 3.20)/40 
= 3.285

Next, we calculate X(bar):

X(bar) = (X1 + X2 + ... + Xn)/n 
= (120.10 + 120.02 + ... + 120.02)/40 
= 120.03

Finally, we calculate the UCL:

UCL = X(bar) + A2*R 
= 120.03 + 0.577*3.285 
= 146.49

Therefore, the upper control limit for the X bar control chart should be set at approximately 146.49.

Over a Twenty Hour Period Forty Samples of Five Items Xˉˉ\bar { \bar { X } }Xˉˉ

Over a Twenty Hour Period Forty Samples of Five Items $\bar { \bar { X } }$