Question

At a call centre, callers have to wait till an operator is ready to take their call. To monitor this process, 5 calls were recorded every hour for the 8-hour working day. The data below shows the waiting time in seconds:

Time	Sample Number
	1	2	3	4	5
9 a.m	8	9	15	4	11
10	7	10	7	6	8
11	11	12	10	9	10
12	12	8	6	9	12
1 p.m.	11	10	6	14	11
2	7	7	10	4	11
3	10	7	4	10	10
4	8	11	11	11	7

(i) Use the data to construct control charts for mean and comments about the
process. If process is out of control, then calculate the revised control limits.

(ii) Construct the CUSUM chart when the process is under control and draw the conclusion about the process.

(iii) If the specification limits as the 8±2, then calculate the process capability index Cpk and impetrate the result.

(iv) Also find the percentage of calls lie outside the specification limits assuming that calls follow the normal distribution.