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15. SIMULATION
•Some complex systems can’t be modeled because of,
-random events
-changing operating conditions
-too many interactions
-exact solutions don’t exist
•Simulation is used to determine how these systems will behave
•Simulation typically involves developing a model that includes discrete stations and events that occur with some probable distribution.
•We can then examine the simulation results to evaluate the modeled system. Examples include,
-machine utilization
-lead time
-down time
-etc.
•This is a very effective tool when considering the effect of a change, comparing decision options, or refining a design.
•Some simulation terms include,
System - the real collection of components
Model - a reasonable mathematically (simpler) representation of the system
State - the model undergoes discrete changes. A state is a ‘snapshot’ of the system Entity - a part of the system (eg machine tool)
Attributes - the behavior of an entity
Event - something that changes the state of a machine
Activity - when an entity is going through some activity. (eg, press cycling) Delay - a period of time with no activity
•Good approach to simulation,
1.Determine what the problem is
2.Set objectives for the simulation
3.Build a model and collect data
4.Enter the model into a simulation package
5.Verify the model then check for validity
6.Design experiments to achieve goals
7.Run simulations and collect results
8.Analyze and make decisions
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15.1 MODEL BUILDING
•If we are building a model for a plant floor layout, we will tend to have certain elements,
-material handling paths (transfer)
-buffers/waiting areas (delays)
-stock rooms (source)
-shipping rooms (destination)
-machine tools (activities)
•Some of these actions can be stated as exact. For example, a transfer time can be approximated and random (manual labor), or exact (synchronous line), or proportional to a distance.
•Some events will occur based on availability. For example, if there are parts in a buffer, a machine tool can be loaded and activity occurs.
•Some activities and events will be subject to probabilities. Consider that the operation time in a press may vary, and there is probability of scrapping a part.
•The random variations can be modeled as,
-discrete - for individual units
-continuous for variations
•Well known distributions include,
Normal/Gaussian
mean |
Probability Density |
1 |
0.5 |
0 |
mean |
Cumulative Probability |
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Poisson/Exponential
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Probability Density |
Cumulative Probability |
Uniform
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Normal/Gaussian
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• This data may be found using data provided by the manufacturer, sampled in-house, etc.
15.2 ANALYSIS
• To meet goals, simple tests may be devised. These tests should be formulated as hypotheses. We can then relate these to the simulation results using correlation.
cov = ∑ ( xi – µ x) ( yi – µ y) – µ xµ y |
corr = |
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xσ y |
where,
cov = covariance of data sets x and y corr = correllation of sets x and y
corr = 1 completely related corr = 0 no relationship corr = -1 inversely related
• Simulation software will provide information such as,