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

Info icon This preview shows pages 1–6. Sign up to view the full content.

IE4230 Homework 6 Introduction to Reliability Engineering 17/03/2015
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

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(?) .
Image of page 2
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
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

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.
Image of page 4
2.1. What is the probability that a light bulb functioning at 3000 hrs will fail in the next 1000 hrs?
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 6
This is the end of the preview. Sign up to access the rest of the document.
  • Winter '14
  • Probability theory, Reliability theory, Cumulative distribution function, Failure rate

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern