An ad agency tracks the complaints, by week received, about the billboards in its city:

Week No. of Complaints
1 7
2 7
3 5
4 7
5 4
6 19

a. What type of control chart would you use to monitor this process? Why?
b. What are the 3-sigma control limits for this process? Assume that the historical complaint rate is unknown.
c. Is the process mean in control, according to the control limits? Why or why not?
d. Assume now that the historical complaint rate has been four calls a week. What would the 3-sigma control limits for this process be now? Is the process in control according to the control limits?

Explanation:

A) The type of control chart that is best to monitor this process is C chart. Because here the number of defects on in a unit is given an we have to monitor the number of defects in the process

B) Number of weeks = 6

Sum of complaints = 7+7+5+7+4+19 = 49

Value of C-bar = Complaints per week = Sum of complaints / Number of weeks = 49/6 = 8.17

Using Z = 3,

UCL = C-bar + [3(Sqrt of C-bar)]

= 8.17 + [3(Sqrt of 8.17)]

= 8.17 + (3X2.86)

= 8.17 + 8.58

= 16.75

LCL = C-bar - [3(Sqrt of C-bar)]

= 8.17 - [3(Sqrt of 8.17)]

= 8.17 - (3X2.86)

= 8.17 - 8.58

= - 0.41 or 0 (as when the LCL is less than zero, it is considered as zero)

d) According to the control limits, this process has been out of control. Because the number of defects in week 6 is more than the Upper specification limit. When the number of defects go beyond the upper and lower specification limit the process is out of control and a process is within control if the number of defects falls within the lower and upper specification limit.

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