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?

Answer 1

a.

Estimate of the proportion of calls not resulting in a satisfactory outcome for the customer when the center is in control

= Sum of all number of calls in each sample not resulting in a satisfactory resolution / Sum of calls in the sample

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

= 0.041

= 0.041

b.

Standard deviation of proportion of calls not resulting in a satisfactory outcome, s =

= 0.01983

Upper control limit = = 0.041 + 3 * 0.01983 = 0.10049

Lower control limit = =  0.041 - 3 * 0.01983 = -0.01849 = 0 (Limits of proportions cannot be negative)

c.

If a sample of 100 calls has 12 calls not resulting in a satisfactory outcome for the customer, the proportion of calls not resulting in a satisfactory outcome is 12/100 = 0.12

Since, the proportion p = 0.12 is greater than the upper control limit, the process is not in control.