# Two alternative designs have been proposed for processing

Two alternative designs have been proposed for processing customers in a service center. To compare the performance of the two alternative system designs, we generated 10 days of customer traffic, where a day's traffic consists of a new simulated sequence of customer arrival times and the associated service times (in other words, 10 independent replications). For day 1 of simulated operation, we ran the traffic through the system operating under design A to compute the average time in system for all the customers processed on that day/replication. Day I's traffic is also run through the system operating under design B to compute the average time in system for all the customers processed on that day/replication. The process was repeated for all 10 days of simulated traffic, yielding average time in system (in minutes) for all the customers processed on each day as follows:

Replication
3
8
4
6
10
Design A
Average Time in
System
55.2
60.2
45.6
65.2
43.6
38.3
37.5
67.8
88.2
65.7
Design B
Average Time in
System
50.9
55.2
50.8
57.8
45.6
27.8
34.5
66.9
77.4
46,7
(a) Compute the sample mean, sample variance, sample standard deviation, t-value, and half-
lengths of the 95% confidence intervals for the expected time in system for each of the two
alternative designs separately