Question: A critical dimension of the service quality of a call center is the wait time of a caller to get to a sales representative. Periodically, random samples of three customer calls are measured for time. The results of the last four samples are in the following table:
| Sample | Time (Sec) |
|
|
| 1 |
495 |
501 |
498 |
| 2 |
512 |
508 |
504 |
| 3 |
505 |
497 |
501 |
| 4 |
496 |
503 |
492 |
a. Assuming the management is willing to use three-sigma control limits, and using only the historical information contained in the four samples, show that the call center access time is in statistical control.
b. Suppose that the standard deviation of the process distribution is 5.77. If the specifications for the access time are 500 +/_ 18 sec., is the process capable? Why or why not? Assume the three-sigma performance is desired.