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Tutorial for Discrete Rate Systems
A basic discrete rate model
When finished, the model should look similar to the one above.
When you run the model, the mixing process should output 80 gallons per minute and the entire process will yield about 37,600 gallons of yogurt. This is an interesting model to run with animation on. (Be sure to have animation set to the slowest speed.) When you do this, the rate displayed at the top of the Yogurt Process icon is sometimes displayed as the fraction 72/ 100. This is the ratio of the effective rate to the Valve’s maximum rate. In this model, there is sometimes not enough fruit and the entire process becomes constrained, so the effective rate can be less than the specified maximum rate.
In validating the model, notice that the effective rate for the yogurt part of the process can never be higher than 72. Since the maximum output of the fruit process is 8 gallons per minute, and the mixing process requires a ratio of 9 portions of plain yogurt to 1 portion of fruit, the maximum amount of plain yogurt that can be required is 72 (8*9) gallons per minute.
☞ A complete description of the animation information shown on the icons for Rate library blocks is given on “Animation” on page 442.
A common situation is for a process to have a slow production rate when some of the equip- ment is down for maintenance and a faster rate the rest of the time.
The fruit process has a slow rate of 2 gallons per minute during equipment maintenance and a normal rate of 8 gallons per minute. Maintenance occurs approximately every 60 minutes with a random duration of a minimum of 5 minutes, a maximum of 20 minutes, and a mostly likely time of 15 minutes. To reflect this:
Add a Shutdown block (Item library) to the model. There are two ways to do this:
Click the Add Shutdown button in the Valve’s dialog. This automatically connects a Shutdown block to the Valve’s R (maximum rate) input connector and opens the Shutdown’s dia- log.
Place the Shutdown block on the worksheet from the Rate library. If you do this, connect the output of the Shutdown block to the Fruit Process Valve’s R (maximum rate) value input connector.
In the Shutdown block’s dialog:
For the shutdown configuration, enter Down value: 2 and Up Value: 8
For the time between failures (TBF) choose an Exponential distribution with a Mean: 60
For the time to repair (TTR) select a Triangular distribution with a Minimum: 5, Maxi- mum: 20, and Most likely: 15
Label the block Maintenance Shutdown.
☞ Like the Lookup Table block, the Shutdown block outputs its information without being prompted. Thus the Valve does not need to ask it for data and it should not be set to poll con- straints. Polling constraints is discussed more on page 378.
Discrete Rate

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