Warning This document is the property of United Technologies Corporation(UTC). You may not possess, use, copy or disclose this document or any information in it, for any purposewithout UTC's express written permission. Neither receipt nor possession of this document alone, from any source, constitutes such permission. Possession, use, copying or disclosure by anyone without UTC's express written permission is not authorized and may result in criminal and/or civil liability. IIInnntttrrroooddduuuccctttiiiooonnn tttooo MMMOOONNNTTTEEE CCCAAARRRLLLOOO SSSiiimmmuuulllaaatttiiiooonnn Jim Breneman P&W Fellow, Reliability & Statistics March 14, 2007 Export controlled Material Unpublished Work -© United Technologies Corporation 2006 Introduction to Monte Carlo Simulation … outline • Background • Definition & history of Monte Carlo Simulation •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• Monte Carlo simulation of fleet reliability Jim Breneman Introduction to Monte Carlo Simulation 860-565-3959 2of 116 Unpublished Work -© United Technologies Corporation 2007 Simulation Simulation is a modeling technique in which the cause- and-effect relationships of a system are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 Jim Breneman Introduction to Monte Carlo Simulation 860-565-3959 3of 116 Unpublished Work -© United Technologies Corporation 2007 Simulation History (Continued) • Increased awareness & understanding of technology.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 Jim Breneman Introduction to Monte Carlo Simulation 860-565-3959 4of 116 Unpublished Work -© United Technologies Corporation 2007 The Cliff-hanger..what’s his chance of surviving Jim Breneman Introduction to Monte Carlo Simulation 860-565-3959 5of 116 Unpublished Work -© United Technologies Corporation 2007 Monte Carlo Simulation Uses • Manufacturing systems: The possible permutations and combinations of workpieces,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 6of 116 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 7of 116 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™ Jim Breneman Introduction to Monte Carlo Simulation 860-565-3959 8of 116 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 9of 116 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