In: Mechanical Engineering
A large bank established X-Bar and R charts for the time
required to process applications for its charge cards. A sample of
five applications is taken each day. The first four weeks (20 days)
of data give:
X bar bar = 16 min s bar = 3 min R bar = 7
min
Based on the values given, calculate the centerline and
control limits for the X bar and R charts.
For the given problem sample size is 5 tht is less than 10 .For n<10 we estimate the standard deviation by mean range .for greater sample size we take in account s mean .
So x bar bar and R bar limits can be calculated by general formula and using control limit factor for given sample size
X bar chart
Center line= x_bar_bar=16min
UCL=Xbar_bar+A2 R_bar
LCL=Xbar_bar-A2 R_bar
Where A2 is contol limit factor
For n=5 A2=0.577
So UCL=20.039
LCL=11.961
Please give feedback and comment any doubt
R_bar Chart
Centerline = R_bar=7 min
UCL=D4R_bar
LCL=D3R_bar
For sampla size 5 D4=2.114
D3=0
UCL=14.798
LCL=0