Question

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.

Answer 1

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