MAT 4830 Mathematical Modeling

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MAT 4830Mathematical Modeling

• 05
• Mean Time Between Failures

http//myhome.spu.edu/lauw
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Reading for Next Wednesday

• MCM Contest Rules, Registration and Instructions
• http//www.comap.com/undergraduate/contests/mcm/in
  structions.php

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Preview

• Use 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 Solution

• 3 components

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Monte Carlo Solution

• 3 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

• gt MTBF(1000)
• The mean is approximately 10.138361
• The standard deviation is approximately 1.355540

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Classwork

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

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Problem 1

• The example above

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Problem 1

• Maple Commands

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HW Problem 1

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

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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.

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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.