Solution:
Calculate mean of the sample data as shown below :
x (bar) = [tex]\frac{6 + 11 + 15 + 10+ 4+ 9 +3+ 20}{8}[/tex]
= 60.5
Calculate the upper and lower control limits as below :
UCL = x (bar) + z[tex]\sqrt{x(bar)}[/tex]
= 60.5 + 3 [tex]\sqrt{60.5}[/tex]
= 60.5 + 3 ( 7.778 )
= 83.834
LCL = x (bar) - z[tex]\sqrt{x(bar)}[/tex]
= 60.5 - 3 ( 7.778 )
= -37.166
The three-sigma control units for complaints that are being received every day employing data would be as follows:
Mean - [tex]60.5[/tex]
Upper Control Limit - [tex]83.834[/tex]
Lower Control Limit - [tex]-37.166[/tex]
To determine the three-sigma control units,,
We will find out the mean,
Mean = (Sum of all the observations)/(No. of observations)
= 60.5
Upper Control Limit = Mean + [tex]z\sqrt{xbar}[/tex]
[tex]= 60.5 +[/tex] [tex]3\sqrt{60.5}[/tex]
[tex]= 60.5 + 3(7.778)[/tex]
[tex]= 83.834[/tex]
Lower Control Limit = [tex]Mean -[/tex] [tex]z\sqrt{xbar}[/tex]
= [tex]60.5 - 3(7.778)[/tex]
= [tex]-37.166[/tex]
Learn more about 'Mean' here:
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