The Money Pit Mortgage Company is interested in monitoring the performance of the mortgage process. Fifteen samples of five comp
leted 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 13 11 5 14 9 10 12 13 10 11 14 6 8 6 9
range 9 13 6 10 11 17 14 17 12 12 13 8 11 13 15
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 9 11 6 12 14 15 10 19 17 15
range 9 13 8 6 14 15 13 12 10 8
Factors for calculating three-sigma limits for the
x overbarx-chart and R-chart
Size of Sample (n)
Factor for UCL and LCL for
x overbarx-chart
(Upper A 2A2)
Factor for LCL for R-Chart
(Upper D 3D3)
Factor for UCL for R-Chart
(Upper D 4D4)
2 1.8801.880 00 3.2673.267
3 1.0231.023 00 2.5752.575
4 0.7290.729 00 2.2822.282
5 0.5770.577 00 2.1152.115
6 0.4830.483 00 2.0042.004
7 0.4190.419 0.0760.076 1.9241.924
8 0.3730.373 0.1360.136 1.8641.864
9 0.3370.337 0.1840.184 1.8161.816
10 0.3080.308 0.2230.223 1.7771.777
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 andthree-sigma control limits below. (Enter your responses rounded to two decimal places.)
sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
mean 13 11 5 14 9 10 12 13 10 11 14 6 8 6 9
range 9 13 6 10 11 17 14 17 12 12 13 8 11 13 15
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 9 11 6 12 14 15 10 19 17 15
range 9 13 8 6 14 15 13 12 10 8
Factors for calculating three-sigma limits for the
x overbarx-chart and R-chart
Size of Sample (n)
Factor for UCL and LCL for
x overbarx-chart
(Upper A 2A2)
Factor for LCL for R-Chart
(Upper D 3D3)
Factor for UCL for R-Chart
(Upper D 4D4)
2 1.8801.880 00 3.2673.267
3 1.0231.023 00 2.5752.575
4 0.7290.729 00 2.2822.282
5 0.5770.577 00 2.1152.115
6 0.4830.483 00 2.0042.004
7 0.4190.419 0.0760.076 1.9241.924
8 0.3730.373 0.1360.136 1.8641.864
9 0.3370.337 0.1840.184 1.8161.816
10 0.3080.308 0.2230.223 1.7771.777
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 andthree-sigma control limits below. (Enter your responses rounded to two decimal places.)
1 answer:
Answer and Explanation:
As per the data given in the question,
Sum of the all mean value = 151
Average of the mean value = 151 ÷ 15 = 10.067
Similarly, Sum of the all given range = 151
Average of given range value = 151÷ 15 = 10.067
Control charts for the mean and the range, using the original 15 samples :
Upper control limit(UCL) - Lower control limit(LCL) for X bar is
= 10.067 + A2 × R bar
= 10.067 + (0.223 × 10.067)
= 12.31
LCL - UCL for X bar is
= 10.067 - A2 × R bar
= 10.067 -(0.223 × 10.067)
= 7.82
Set up the R-chart by specifying the center line and three-sigma control limits below :
UCLr = D4 × r
= 1.653 × 10.07
= 16.65
r = 10.067
= 10.07
LCLr = D3 × r
= 0.347 ×10.07
= 3.49
You might be interested in