# Solution 6 - IE4230 Homework 6 Introduction to Reliability...

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IE4230 Homework 6 Introduction to Reliability Engineering 17/03/2015

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Conditional Probability Very often, we have additional information which may affect the probability of certain event. Suppose that P(A) > 0. Then the conditional probability of event B given A is defined as 𝑃 ? ? = 𝑃(?∩?) 𝑃(?) So that if A and B is independent we have 𝑃 ? ? = 𝑃(?) .
Bayes Formula A powerful formula in computing conditional probability is the Bayes formula. Suppose we have a series of mutually exclusive and collectively exhaustive events ? ? ? ? ∩ ? ? = ∅ for ? ≠ ? 𝑃 ? ? ? = 𝑃 ? ? ? 𝑃(? ? ) 𝑃 ? ? ? 𝑃 ? ? 𝑛 ?=1

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1. Suppose that the process yield is 90% and Appraiser Score, measuring the reliability of the appraiser, is 80%. What is the risk in discarding parts that deem to be defective? The probability that we are looking for is 𝑃 ? = ???? ? = 𝑇??? 𝐷?? . 𝑃 ? ? = P(??) P(?) = 𝑃 ? ? 𝑃(?) 𝑃 ? ? 𝑃(?)+𝑃 ? ? 𝑃(? ) = (0.2)(0.9) 0.2 0.9 + 0.8 (0.1) = 0.18 0.18+0.08 =0.692 It should be low otherwise we are throwing away good part.
2.1. What is the probability that a light bulb functioning at 3000 hrs will fail in the next 1000 hrs?

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• Winter '14
• Probability theory, Reliability theory, Cumulative distribution function, Failure rate

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