[Solved] An ad agency tracks the complaints, by week received, about the billboards in its…..

Answer to question a :

Choice of C hart will be the appropriate control chart to monitor this process.

C chart is used when counting total count of defects ( here that is ‘complaints’) per unit ( here that is ‘week)and is appropriate when the sample size is uniform . Here sample size for each case is “Week” and hence has an uniform sample size.

In case sample size was not uniform , c chart could not have been used and instead u chart would have been used.

Answer to question b :

Let , Cbar = Average number of complaints per week

Therefore, Cbar = ( 4 + 5 + 4 + 11 + 3 + 9) / 6 = 6

Thus 3 sigma control limits are :

Upper Control Limit ( UCL )

= Cbar + 3 x square root ( Cbar)

= 6 + 3x square root ( 6)

= 6 + 3 x 2.45

UPP

= 13.35

Centerline ( CL) =Cbar = 6

Lower control Limit ( LCL)

= Cbar – 3 x square root ( Cbar)

= 6 – 3 x 2.45

= 6 – 7.35

= – 1.35

However since derived result for CL is negative number, we must consider LCL = 0

Answer to question c:

The data on number of complaints are : 4. 5, 4 , 11, 3 and 9 . It can be seen that all these data are within UCL of 13.35 and LCL of 0 . Therefore, it can be concluded that the process is in control.

Answer to question 4 :

Now the historical complaint rate = 4 calls a week

Therefore ,

C bar = Average of all historical complaint rates each of which is 4 = 4

Therefore,

3 Sigma Upper Control Limit ( UCL )

= Cbar + 3x Square root ( Cbar)

= 4 + 3 x Square root( 4)

= 4 + 6

= 10

Centerline = Cbar = 4

3 sigma Lower control Limit

= Cbar – 3 x Square root ( Cbar )

= 4 – 3 x 2

= 4 – 6

= – 2

However since LCL cannot be a negative number, we shall consider LCL = 0

Thus :

It is to be noted that there is complaint data e.g 11 which is > UCL . Therefore it can be concluded that the process is out of control.