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Estimating Mean Time Between Failures Using Monte Carlo Simulation

This document outlines a procedure for estimating the Mean Time Between Failures (MTBF) of a product comprising multiple components. By employing the Monte Carlo method, we can analyze the time until failure for a product where each component has a time before failure that follows a normal distribution with specific means and standard deviations. The goal is to determine a guarantee for customers and calculate the MTBF. The outline includes programming guidance for simulating failures and offers insights into analytic and Monte Carlo solutions along with sample output.

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Estimating Mean Time Between Failures Using Monte Carlo Simulation

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  1. MAT 4830Mathematical Modeling 05 Mean Time Between Failures http://myhome.spu.edu/lauw

  2. Reading for Next Wednesday • MCM Contest Rules, Registration and Instructions • http://www.comap.com/undergraduate/contests/mcm/instructions.php

  3. Preview • Use Monte Carlo Method to estimate the life of products

  4. Emachine…

  5. Mean Time Between Failures Suppose that we make a product composed of n components where the ith component is guaranteed by its manufacturer to possess a time before failure that is normally distributed about the mean i with standard deviation i.

  6. Mean Time Between Failures Assume that our product will fail when any one of its components fail. Questions: What guarantee can we offer our customers for our product? What is our product's mean time between failures (MTBF)?

  7. Analytic Solution

  8. Analytic Solution

  9. Monte Carlo Solution • 3 components

  10. Monte Carlo Solution • 3 components • Let us watch this product fail over and over by simulation

  11. Idea

  12. Idea

  13. Idea

  14. Idea

  15. Programming Outline

  16. Sample Output > MTBF(1000); The mean is approximately 10.138361 The standard deviation is approximately 1.355540

  17. Classwork • Individual (Each of you need to think through the process)

  18. Problem 1 The example above

  19. Problem 1 Maple Commands:

  20. HW Problem 1 A manufactured product consists of three components. Suppose the time before failure for the parts are given by

  21. HW Problem 1 The first component is a backup for the second; i.e., either both must fail or the third component must fail before the construct fails.

  22. HW Problem 1 • Write a program to estimate the mean and standard deviation of the life of the product. • Briefly explain the key underlying methodology of your program.

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