Checkout time in minutes at the Starkville Kroger is monitored using a mean and

Question

Checkout time in minutes at the Starkville Kroger is monitored using a mean and range chart. Six samples of n = 20 observations have been obtained and the sample means and ranges computed:

Sample Mean Range

1 3.03 0.25

2 3.15 0.30

3 3.11 0.33

4 3.13 0.28

5 3.06 0.34

6 3.09 0.27

Is the process in control?

S

A. No: Because one or more of the means are outside of the upper and lower control limits.

B. No: Because the ranges are within the upper and lower control limits.

C. Yes: Because all means are within the upper and lower control limits.

D. Yes: Because the ranges meet or exceed the upper and lower control limts.

Explanation / Answer

for above sample mean Xbar =3.095

and average range Rbar=0.295

for n=20 ; constant A2 =0.18

therfore for mean chart: UCL =xbar+A2*Rbar =3.148

and LCL =3.042

for range chart ; for n=20 ; D3 =0.415 and D4 =1.585

hence UCL =D4*Rbar =0.4678

and LCL =D3*Rbar =0.1224

for 2nd sample has mean value higher then upper control limit: therefore

option A is correct

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