MAT 4830Mathematical Modeling05 Mean Time Between Failureshttp://myhome.spu.edu/lauw

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PreviewUse Monte Carlo Method to estimate the life of products

Emachine

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.

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)?

Analytic Solution

Analytic Solution

Monte Carlo Solution3 components

Monte Carlo Solution3 components

Let us watch this product fail over and over by simulation

Idea

Idea

Idea

Idea

Programming Outline

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

ClassworkIndividual (Each of you need to think through the process)

Problem 1The example above

Problem 1Maple Commands:

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

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

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