Simulation of Engineering Systems
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Transcript of Simulation of Engineering Systems
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Simulation of Engineering
SystemsDr. Ashraf S. Youssef
Industrial Engineering Dept., Fayoum University
Lecture - 1
What is simulation?
What is being modeled?
Advanta es of simulation
Different kinds of simulation and Programming
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What is Simulation? Simulation is defined as a numerical
ec n que or con uc ng exper men s on a
digital computer.
Simulation is becoming more and moreaccepted tool for design of new facilities, for
investing the operational aspects of existing
p an s an or es ng con ro s ra eg es or automated factories.
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What is being modeled?DecisionVariables
simulation dealswith models of
systems.
SYSTEM
facility or process,
either actual or
planned.Outcomes
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System examples Manufacturing plant with M/Cs, People, transport
, , .
A bank or other personal service operations.
.
A computer network with servers, client, disk drivers,
rinters, and networkin ca abilities.
A supermarket with inventory control and customer
services.
A fast-food restaurant with workers of differenttypes.
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Advantages of simulation Allows us to study systems without disturbing
, ,
huge expenses.
,
problem refine designs without incurring
actual system.
design to parameter uncertainties.
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.
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Advantages of simulation (cont.) Simulation can be used to study a proposed
somewhat sketchy.
,
to solve a problem.
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What is a model? A model is an abstraction of the system.
Model Types
Physical Model Textual Model Graphical ModelMathematical
Model
Simulation of a system is a computer-base model
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Different Kinds of simulations
. .
.
Deterministic Vs. Stochastic.
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Simulation Programming
Usin eneral ur ose lan ua es Fortran,
C++, Visual Basic,etc)
Using Simulation languages (GPSS,
SIMSCRIPT, SLAM, and SIMAN)
High-Level simulators (SIMFACTORY,
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Steps in a simulation study Formulate problem and plan the study.
Collect data and define a model. Valid.
ons ruc a compu er program an ver y.
Make pilot runs.
.
Design Experiments.
Make roduction runs.
Analyze output data.
Document and implement results.
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S stems
Lecture - 2 Manual Simulation
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Example For M/M/1 Queue process, MTBA=29, and
= , es ma e e o ow ng:
AWT
erver za on
Average Queue Length.
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Solution
= - * -
ST = -2*ln(1-R)
Generate Random No. and calculate TBA,
and ST for the first 16 arrivals.
USE MS Excel
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Homework 1 Use manual simulation to calculate the
, ,
20 arrivals, and AQL if you know that the TBA
Standard deviation = 5, Service time is a
=
and max value = 30.
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S stems
Lecture - 3 Goodness-of-Fit test
Chi-Square Test
Kolmo orov-Smirnov Test
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Chi-Square Test
It is suitable for discreet
an con nuous
distributions= 1
2i
=k iExpected
xpecteserve
Calculatedf
freedom is equal to k-1-p, where p is the number of
population parameters
22
1
0
:
:
CalculatedCritical
CalculatedCritical
H
H
=
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Kolmogorov-Smirnov Test
It is suitable for continuous distributions Onl
H : K-S From table >= K-S statistics
H1:K-S From table < K-S statistics
K-S statistics is equal the maximum difference
between the cumulative frequency and the
theoretical cumulative frequency. The degrees offreedom is equal to N
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Important Rule
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large sample size; at least 100observations.
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have small sample size.
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Example:
Use Chi-Square test and K-S test to evaluate
the following data at
= .05: 12.36, 14.15, 6.76, 14.46, 7.47, 5.71, 16.83, 5.17,
0.03, 19.65, 16.79, 19.33, 17.46, 15.45, 16.08,
18.01, 11.99, 10.72, 11.51, 11.99, 5.12, 20.18,
. , . , . , . , . , . , . , . ,
19.41, 6.31, 6.21, 9.83, 14.66, 8.58, 15.83, 12.52,
16.39, 6.57, 8.42, 12.87, 8.03, 9.6, 5.42, 15.56,
18.04, 8.97, 17.11, 7.79, 10, 12, 16, 18, 14, 18,17, 15, 19, 13
Dr. Ashraf S. Youssef