Question

Eagletrons are all electric cars produced by Mogul motors. One of the concernsof Mogul is that the Eagletrons be capable of achieving appropriate maximumspeeds. To monitor this, Mogul executives take samples of 8 Eagletrons at atime. For each sample, they determine the average maximum speed and the rangeof the maximum speeds within the sample. They repeat this with 35 samples toobtain 35 sample means and 35 ranges. They find that the average sample mean is88.50 mph and the average range is 3.25 mph. Using these results, theexecutives decide to establish an R chart. They would like this chart to beestablished so that when it shows that the range of a sample is not within thecontrol limits, there is only approximately a .0027 probability that this is dueto natural variation. What will the upper control limit (UCL) and the lowercontrol limit (LCL) in this chart?

Trying to confirm that what I came up with is correct.

Answer 1

upper control limit = 6.058

lower control limit = 0.442

Explanation:

Given that:

The numbers of sample n Mogul executives took = 8 Eagletrons at a time.

They find out that the average sample mean is 88.50 mph and;

the average range
`\overline r` is 3.25 mph.

From the tables:

`\text {Table values for n = 8 } \left \{ {{D_4=1.864} \atop {D_3=0.136}} \right.`

Control Limit =
`\overline r` = 3.25

Therefore; the upper control limit and the lower control limit can be computed as follows:

upper control limit =
`D_4 \overline r`

upper control limit = 1.864(3.25)

upper control limit = 6.058

lower control limit =
`D_3 \overline r`

lower control limit = 0.136(3.25)

lower control limit = 0.442