1 / 22

MAT 4830 Mathematical Modeling

MAT 4830 Mathematical Modeling. 05 Mean Time Between Failures. http://myhome.spu.edu/lauw. Reading for Next Wednesday. MCM Contest Rules, Registration and Instructions http://www.comap.com/undergraduate/contests/mcm/instructions.php. Preview.

duc
Download Presentation

MAT 4830 Mathematical Modeling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related