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Explain data collection and analysis for input modelling.

SELECTING INPUT MODELS WITHOUT DATA

• Unfortunately, it is often necessary in practice to develop a simulation model-perhaps for demonstration purposes or a preliminary study--before any process data are available.

• In this case, the modeler must be resourceful in choosing input models and must carefully check the sensitivity of results to the chosen models.

• There are a number of ways to obtain information about a process even if data are not available:

1. Engineering data: Often a product or process has performance ratings provided by the manufacturer (for example, the mean time to failure of a disk drive is 10000 hours; a laser printer can produce 8.pages/minute; the cutting speed of a tool is 1 cm/second; etc.). Company rules might specify time or production standards. These values provide a starting point for input modeling by fixing a central value.

2. Expert opinion: Talk to people who are experienced with the process or similar processes. Often, they can prov1de optimistic, pessimistic, and most-likely times. They might also be able to say whether the process is nearly constant or highly variable, and they might be able to define the source of variability.

3. Physical or conventional limitations: Most real processes have physical limits on performance-for example, computer data entry cannot be faster than a person can type. Because of company policies, there could be upper limits on how long a process may take. Do not ignore obvious limits or bounds that narrow the range of the input process.

4. The Nature of the process: When data are not available, the uniform, triangular, and beta distributions are often used as input models. The uniform can be a poor choice, because the upper and lower bounds are rarely just as likely as the central values in real processes. If, in addition to upper and lower bounds, a most-likely value can be given, then the triangular distribution can be used. The triangular distribution places much of its probability near the most likely value, and much less near the extremes. If a beta distribution is used, then be sure to plot the density function of the selected distribution; the beta can take unusual shapes.

DATA COLLECTION

The following suggestions might enhance and facilitate data collection, although they are not all inclusive.

1. A useful expenditure of time is in planning. This could begin by a practice or pre observing session. Try to collect data while pre observing. Devise forms for this purpose. It is very likely that these forms will have to be modified several times before the actual data collection begins. Watch for unusual circumstances, and consider how they will be handled. When possible, videotape the system and extract the data later by viewing the tape. Planning is important, even if data will be collected automatically (e.g., via computer data collection), to ensure that the appropriate data are available. When data have already been collected by someone else, be sure to allow plenty of time for converting the data into a usable format.

2. Try to analyze the data as they are being collected. Figure out whether the data being collected are adequate to provide the distributions needed as input to the simulation. Find out whether any data being collected are useless to the simulation. There is no need to collect superfluous data.

3. Try to combine homogeneous data sets. Check data for homogeneity in successive time periods and during the same time period on successive days. For example, check for homogeneity of data from 2:00 P.M. to 3:00 P.M. and 3:00 P.M. to 4:00 P. M., and check to see whether the data are homogeneous for 2:00 P. M. to 3:00P.M on Thursday and Friday. When checking for homogeneity, an initial test is to see whether the means of the distributions (the average inter arrival times, for example) are the same. The two-sample t test can be used for this purpose. A more thorough analysis would require a test of the equivalence of the distributions, perhaps via a quantile-quantile plot.

4. Be aware of the possibility of data censoring, in which a quantity of interest is not observed in its entirety. This problem most often occurs when the analyst is interested in the time required to complete some process (for example, produce a part, treat a patient, or have a component fail), but the process begins prior to, or finishes after the completion of, the observation period. Censoring can result in especially long process times being left out of the data Sample.

5. To discover whether there is a •relationship between two variables; build a scatter diagram. Sometimes an eyeball scan of the scatter diagram will indicate whether there is a relationship between two variables of interest.

6. Consider the possibility that a sequence of observations that appear to 1>e independent actually has autocorrelation. Autocorrelation can exist in successive time periods or for successive customers.

7. Keep in mind the difference between input data and output or performance data, and be sure to collect input data. Input data typically represent the uncertain quantities that are largely beyond the control of the system and will not be altered by changes made to improve the system. Output data, on the other hand, represent the performance of the system when subjected to the inputs, performance that we might be trying to improve. In a queueing simulation, the customer arrival times are usually inputs, whereas the customer delay is an output.