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 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 and​three-sigma control limits below. ​(Enter your responses rounded to two decimal​ places.)

Answer 1

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