Question

An airline operates a call center to handle customer questions and complaints. the airline monitors a sample of calls to help ensure that the service being offered is of high quality. The random samples of 100 calls each were monitored under normal conditions. The center can be thought of as being in control when these 10 samples were taken. The number of calls in each sample not resulting in a satisfactory resolution for the customer is as follows:

4 5 3 2 3 3 4 6 4 7

a. What is an estimate of the proportion of calls not resulting in a satisfactory outcome for the customer when the center is in control?

b. Construct the upper and lower limits for a p chart for the process.

c. With the results in part b. what is your conclusion if a sample of 100 calls has 12 calls not resulting in a satisfactory outcome for the customer?

d. Compute the upper and lower limit for the np chart

Answer 1

a) estimate of the proportion of calls center lin in control

=[(4 + 5 + 3 + 2 + 3 + 3 + 4 + 6 + 4 + 7)/10]/100

=0.041

p=0.041

b) Compute upper control limit for p chart

UCL=p+3*sqrt(p*(1-p)/n)

=0.041+3*sqrt(0.041*(1-0.041)/100)

=0.1005

lower control limit can not go below zero so set it as zero. so LCL=0

LCL=p-3*sqrt(p*(1-p)/n)

=0.041-3*sqrt(0.041*(1-0.041)/100)

=-0.0185

c) Given if sample of 100 calls has 12 calls not resulting in a satisfactory outcome for the customer

p^=12/100
=0.12

so it lies out of control limit region so process is out of control

d) Between 3-sigma control limits so the process is in control.

If 12 calls are not resulting in a satisfactory resolution for the customer then result may not be

changed that is the result is same as d) part.