Introduction to MONTE CARLO Simulation

116 Pages·2007·1.46 MB·English

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Jim Breneman
P&W Fellow, Reliability & Statistics
March 14, 2007
Export controlled Material
Unpublished Work -© United Technologies Corporation 2006
Introduction to Monte Carlo Simulation … outline
• Background
• Definition & history of Monte Carlo
Simulation
• Fundamentals of using EXCEL™ for
Monte Carlo simulation
• In-class examples
• Buffon needle problem
• Tolerancing using Monte Carlo Simulation
• Calculating Load
• Monte Carlo simulation of fleet reliability
Jim Breneman
Introduction to Monte Carlo Simulation 860-565-3959
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Unpublished Work -© United Technologies Corporation 2007
Simulation
Simulation is a modeling technique in which the cause-
and-effect relationships of a system are captured in a
computer model, which then becomes capable of
generating the same behavior that would occur in the
actual system.
Simulation is a powerful analysis tool that helps make
intelligent and timely decisions in the design and
operation of a system.
Jim Breneman
Introduction to Monte Carlo Simulation 860-565-3959
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Unpublished Work -© United Technologies Corporation 2007
Simulation History (Continued)
• Increased awareness & understanding of technology.
• Increased availability, capability & ease-of-use of
simulation software.
• Increased computer memory
and processing speeds.
• Declining computer
hardware costs.
Jim Breneman
Introduction to Monte Carlo Simulation 860-565-3959
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Unpublished Work -© United Technologies Corporation 2007
The Cliff-hanger..what’s his chance of surviving
Jim Breneman
Introduction to Monte Carlo Simulation 860-565-3959
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Unpublished Work -© United Technologies Corporation 2007
Monte Carlo Simulation Uses
• Manufacturing systems:
The possible permutations and combinations of
workpieces, tools, pallets, transport vehicles, routes,
operations.
• Service systems:
The complexities of customer scheduling, staffing,
resource management, customer flow, and info
processing.
• Design systems:
Variation in stresses, temperatures, mission,
tolerances, flow, pressure drop, material properties.
Jim Breneman
Introduction to Monte Carlo Simulation 860-565-3959
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Unpublished Work -© United Technologies Corporation 2007
Objective
• Apply the basics of Monte Carlo simulation in EXCEL to solve simple
simulation problems.
Jim Breneman
Introduction to Monte Carlo Simulation 860-565-3959
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Unpublished Work -© United Technologies Corporation 2007
Detailed Learning Objectives
The objective of this class is to introduce the Monte Carlo simulation concept, to learn how
to use Monte Carlo simulation in EXCEL, and to learn how to use the results to answer
various engineering questions.
This “Introduction to Monte Carlo” simulation class is ~3 hours in length and has the
following major learning objectives:
1. Understanding Monte Carlo simulation and its uses.
2. How to generate random numbers in EXCEL.
3. How to generate a flow chart for a typical Monte Carlo simulation.
4. Using EXCEL software; how to build a simple Monte Carlo simulation.
5. Introduction to Monte Carlo Simulation with Crystal Ball™
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Introduction to Monte Carlo Simulation 860-565-3959
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Unpublished Work -© United Technologies Corporation 2007
Example of Monte Carlo simulation link to Standard Work
SDCI/RMS:DP-IN: 97-211
Jim Breneman
Introduction to Monte Carlo Simulation 860-565-3959
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Unpublished Work -© United Technologies Corporation 2007
History of Monte Carlo simulation
• Monte Carlo Simulation is a method that has many
applications and flavors.
• “simulation” refers to the fact that we build an artificial model
of a real system in order to study and understand the
system.
• The “Monte Carlo” part of the name alludes to the
randomness inherent in the analysis.
• The name “Monte Carlo” was coined by [physicist
Nicholas] Metropolis (inspired by [Stanislaw] Ulam's
interest in poker) during the Manhattan Project of
World War II, because of the similarity of statistical
simulation to games of chance, and because the
capital of Monaco was a center for gambling and
similar pursuits
Jim Breneman
Introduction to Monte Carlo Simulation 860-565-3959
10of 116
Unpublished Work -© United Technologies Corporation 2007