Question

The Money Pit Mortgage Company is interested in monitoring the performance of the mortgage process. Fifteen samples of five completed mortgage transactions each were taken during a period when the process was believed to be in control. The times to complete the transactions were measured. The means and ranges of the mortgage process transaction times, measured in days, are as follows: 

Sample	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Mean	20	16	10	19	14	15	17	18	15	16	18	11	13	11	14
Range	6	10	3	7	8	12	11	14	9	9	11	5	8	10	12

Subsequently, samples of size 5 were taken from the process every week for the next 10 weeks. The times were measured and the following results obtained: 

Sample	16	17	18	19	20	21	22	23	24	25
Mean	13	16	11	17	19	20	15	24	22	20
Range	7	10	5	3	11	14	10	9	7	5

Click the icon to view the table of factors for calculating three-sigma limits for thex-chart and R-chart. 

a. Construct the control charts for the mean and the range, using the original 15 samples 

Set up the R-chart by specifying the center line and three-sigma control limits below. (Enter your responses rounded to two decimal places.,)

R-chart
UCL_(R)=19.026
bar(R)=9
LCL_(R)=0

Set up the x-chart by specifying the center line and three-sigma control limits below. (Enter your responses rounded to two decimal places.)

b. On the control charts developed in part (a), plot the values from samples 16 through 25 and comment on whether the process is in control Choose the correct R-chart for the data below

c. In part (b), if you concluded that the process was out of control, would you attribute it to a drift in the mean, or an increase in the variability, or both?

The process variability is _______  statistical control and the process average is _______  statistical control. Therefore, the entire process is _______  control.

Answer 1

(a) Control limits of Xbar and R-chart

(b)

(c)

We see that R chart is in control, but Xbar chart is out of control. Therefore,

The process variability is __In__ statistical control, and the process average is __Out of__ statistical control. Therefore, the entire process is __Out of__ control.