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MAT 4830Mathematical Modeling05 Mean Time Between Failureshttp://myhome.spu.edu/lauw
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Reading for Next WednesdayMCM Contest Rules, Registration and Instructionshttp://www.comap.com/undergraduate/contests/mcm/instructions.php
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PreviewUse Monte Carlo Method to estimate the life of products
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Emachine
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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.
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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)?
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Analytic Solution
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Analytic Solution
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Monte Carlo Solution3 components
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Monte Carlo Solution3 components
Let us watch this product fail over and over by simulation
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Idea
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Idea
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Idea
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Idea
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Programming Outline
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Sample Output> MTBF(1000);The mean is approximately 10.138361The standard deviation is approximately 1.355540
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ClassworkIndividual (Each of you need to think through the process)
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Problem 1The example above
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Problem 1Maple Commands:
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HW Problem 1A manufactured product consists of three components. Suppose the time before failure for the parts are given by
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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.
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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.