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 provided is of high quality. Ten 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.

5

7

4

3

4

4

5

6

5

9

(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 manufacturing process, assuming each sample has 100 calls.

(c)

With the results of part (b), what conclusion should be made if a sample of 100 has 15 calls not resulting in a satisfactory resolution for the customer?

(d)

Compute the upper and lower limits for the npchart.

(e)

With the results of part (d), what conclusion should be made if a sample of 100 calls has 15 not resulting in a satisfactory conclusion for the customer?

Answer 1

Answer:

Given Data

From the given Data

n =100

Given number of calls in each sample not resulting in a satisfactory resolution for the customer is as follows :    5+7+4+3+4+4+5+6+5+9

n = 100 * 10

= 1000

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.

The estimate of the proportion =

b) Construct the upper and lower limits for a p chart for the manufacturing process, assuming each sample has 100 calls.

  

  

q = 1 - p

= 1 - 0.052

= 0.948

Lower limit = 0.052 - 0.4470

= - 0.395

LCL = -0.395

Upper limit = 0.052 + 0.4470

= 0.499

UCL = 0.499

c) With the results of part (b), what conclusion should be made if a sample of 100 has 15 calls not resulting in a satisfactory resolution for the customer.

Sample  Proportion (p) =

(p) = 0.15

Since the Sample  Proportion = 0.15 is outside . the control limits , the process is not in the control.

d) Compute the upper and lower limits for the np chart.

Upper control limit = 5.2 + 6.8412

= 12.0412

UCL = 12.0412

Lower control limit = 5.2 - 6.8412

= -1.6412

LCL = -1.6412

e) With the results of part (d), what conclusion should be made if a sample of 100 calls has 15 not resulting in a satisfactory conclusion for the customer.

Since the number of calls not resulting in a satisfactory conclusion

It is outside the control limits , the process is not under control for the sample.