Question

checkout time at a grocery store is monitored using a range and mean chart. seven samples (sample size = 5) have been collected and the sample means and sample ranges have been computed for each sample.
also, overall average checkout time and average range have been computed and are as follows:
$overline{overline{x}} = 6$
$overline{r}=1.2$
what is the value of the upper limit for the range chart?
0
7.2
2.54
2.31
0.09
6

Explanation:

Step1: Identify the formula

For the upper - control limit (UCL) of a range chart with sample size $n = 5$, the formula is $UCL_R=D_4\overline{R}$, where $D_4$ is a control - chart constant and $\overline{R}$ is the average range.

Step2: Find the value of $D_4$

For a sample size $n = 5$, from control - chart constants table, $D_4 = 2.114$.

Step3: Calculate the UCL

We know that $\overline{R}=1.2$. Substitute the values into the formula: $UCL_R = D_4\overline{R}=2.114\times1.2 = 2.5368\approx2.54$.

Answer:

2.54