1. MAT 4830 Mathematical 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/c ontests/mcm/instructions.php http://www.comap.com/undergraduate/c ontests/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

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

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.