Refer to Problem 1 concerning waiting time for customers at a bank (data stored in BankTime). Suppose management has set a USL of five minutes on waiting time and specified that at least 99% of the waiting times must be less than five minutes in order for the process to be considered capable.
a. Estimate the percentage of the waiting times that are inside the specification limits. Is the process capable of meeting the company policy?
b. If management implemented a new policy, stating that 99.7% of all waiting times are required to be within specifications, is this process capable of reaching that goal? Explain.
Problem 1:
The manager of a branch of a local bank has the business objective of reducing the waiting times of customers for teller service during the 12:00 noon-to-1:00 p.m. lunch hour. A subgroup of four customers is selected (one at each 15-minute interval during the hour), and the time, in minutes, is measured from when each customer enters the line to when he or she reaches the teller window. The results over a four-week period, stored in BankTime, are as follows:
Day |
| Time (Minutes) |
| |
1 | 7.2 | 8.4 | 7.9 | 4.9 |
2 | 5.6 | 8.7 | 3.3 | 4.2 |
3 | 5.5 | 7.3 | 3.2 | 6.0 |
4 | 4.4 | 8.0 | 5.4 | 7.4 |
5 | 9.7 | 4.6 | 4.8 | 5.8 |
6 | 8.3 | 8.9 | 9.1 | 6.2 |
7 | 4.7 | 6.6 | 5.3 | 5.8 |
8 | 8.8 | 5.5 | 8.4 | 6.9 |
9 | 5.7 | 4.7 | 4.1 | 4.6 |
10 | 3.7 | 4.0 | 3.0 | 5.2 |
11 | 2.6 | 3.9 | 5.2 | 4.8 |
12 | 4.6 | 2.7 | 6.3 | 3.4 |
13 | 4.9 | 6.2 | 7.8 | 8.7 |
15 | 7.1 | 5.8 | 6.9 | 7.0 |
16 | 6.7 | 6.9 | 7.0 | 9.4 |
17 | 5.5 | 6.3 | 3.2 | 4.9 |
18 | 4.9 | 5.1 | 3.2 | 7.6 |
19 | 7.2 | 8.0 | 4.1 | 5.9 |
20 | 6.1 | 3.4 | 7.2 | 5.9 |
a. Construct control charts for the range and the mean.
b. Is the process in control?
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