Question

Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) LOADING... for this problem. Eagletrons are​ all-electric automobiles produced by Mogul​ Motors, Inc. One of the concerns of Mogul Motors is that the Eagletrons be capable of achieving appropriate maximum speeds. To monitor​ this, Mogul executives take samples of 8 Eagletrons at a time.

For each​ sample, they determine the average maximum speed and the range of the maximum speeds within the sample.

They repeat this with 35 samples to obtain 35 sample means and 35 ranges. They find that the average sample mean is 98.50 miles per​ hour, and the average range is 3.50 miles per hour. Using these​ results, the executives decide to establish an​ R-chart. They would like this chart to be established so that when it shows that the range of a sample is not within the control​ limits, there is only approximately a 0.0027 probability that this is due to natural variation.

The control limits for the chart based on the above requirement for the given information​ are:

UCLR ​=    miles per hour ​(round the reponse to three decimal​ places).

LCLr

Answer 1

UCL_R and LCL_R are given by below formula

LCL_R = D₃*(Average Range)

UCL_R = D₄*(Average Range)

where D₃ and D₄ are R chart constants which are dependent on sample size. For the given sample size of 8, D₃=0.136 and D₄=1.864. Hence we have the control limits as below

LCL_R = 0.136*(3.5) = 0.476 miles per hour

UCL_R = 1.864*(3.5) = 6.524 miles per hour