- In the previous bank example and other places, we used some artificial
data as input to a simulation model.
- An alternative is to use past data as input (historical input data).
Sometimes this is called
*trace-driven*simulation. - To conduct a validation test using historical input data, it is
important that all the input data and all the system response data
be collected during the same time period.
- Example 11.3 (The Candy Factory)
- The Candy Factory has three machines, the Candy maker, the Candy packer, and the Box maker.
- The three machines are connected by two conveyors.
- The machines have random break-down time.
- When a machine breaks down, it causes its incoming conveyors to be full and out-going conveyors to be empty.
- The time-to-failure (operating time) and down-time of each
machine is recorded. For machine
*i*

- The system responses: the production level , the number and the time of occurence of operator interventions were recorded.
- The model responses ( ) for the same parameters were collected for comparison to the corresponding system responses.
- The differences between and can be used to build
test statistics (in this case the Student Test
*t*) to see if the model is statistically the same as the real system. - If there is only one set of input data, only one set of output can be obtained. The result doesn't carry much statistical significance.
- If
*K*sets of input data are available,*K*runs of tests can be conducted. See Table 11.6 for an example. - Let be the system responses and be the model responses, the differences are approximately normally distributed with mean and variance
- If the mean is zero, then statistically are
the same as . A
*t*test is conducted

and

- The
*t*statistic is computed as

- The critical value
where
*K*is the degree of freedom. In our example,*K*is the number of input data sets (thus, the number of experiments run). - If do not reject , otherwise reject .

- Example 11.4 (The Candy Factory continued) Use actual numbers (e.g. K = 5, etc.) to show how the above example works.