Prob_Stat Oct 30 - Dealing with uncertainty in design and...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
ME 250 Fall 2007 Dealing with uncertainty in design and manufacturing Applications of probability and statistics October 30, 2007 ME 250 Fall 2007 Coursepack Chapter: Uncertainty in design & manufacturing Sections: 1, 2, 3, 4 and 9
Background image of page 1

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

View Full DocumentRight Arrow Icon
ME 250 Fall 2007 Auto warranty wars 10 YEAR / 100,000 MILES Covers repair or replacement of powertrain components (i.e. selected Engine and Transmission/Transaxle components), originally manufactured or installed by Hyundai that are defective in material or factory workmanship, under normal use and maintenance. Sept 2006: Extension of GM's warranty. Coverage of the powertrain expands from 5 years/60,000 miles to 5 years/100,000 miles…. ME 250 Fall 2007 “US Auto Warranty Costs Soar,” Ed Garsten, Detroit News , 9/14/04 Auto companies incur ~$12 Billion annually to fix vehicles under warranty A typical recall can cost the OEM on average $1M a day Warranty costs shave 1-3% off revenues according to AMR Research Critical issue for OEM: Controlling costs
Background image of page 2
ME 250 Fall 2007 Reliability Reliability is a measure of the ability of a product / system / service to perform its intended function under a prescribed set of conditions Reliability is a “probability” ME 250 Fall 2007 Reliability and probability Reliability: the probability that a product, service, component or system will perform its intended function under a prescribed set of conditions If a powertrain has 95% reliability then the probability that it will fail within 100,000 miles (warranty) is 5%. In other words, five out of every 100 warranty will cost the OEM $$$ to repair
Background image of page 3

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

View Full DocumentRight Arrow Icon
ME 250 Fall 2007 Probability Example: ¾ Toss two dice and get a 7 Probability that a certain outcome may occur can be determined by a) Identifying all possible outcomes 2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11, 7,8,9,10,11,12 b) Counting all possible outcomes Æ 36 ME 250 Fall 2007 Probability d) Probability of occurrence (of the event) is m 1,2,. .., j outcomes all of number occurrence of times of number = = = N n P j j n j = number of times of occurrence of a particular event N = total number of all outcomes m = number of events e) For the case of rolling the total number of 7 the probability is 6 1 36 6 outcomes all of number occurrence of times of number = = = j P
Background image of page 4
ME 250 Fall 2007 Probability Distribution A probability distribution is a collection of probabilities for all outcomes and can be represented in a table or graph. Also called a frequency function or probability density . ¾ Note all probabilities should sum to 1 Notice the lower case “f” 0 1/36 1/18 1/12 1/9 5/36 1/6 1234567891 01 11 2 Probability = f(x) R a n d o m V a r i a b l e , x 0 1 1 1 2 T o t a l Probability = f(x) 0 1/36 1/18 1/12 1/9 5/36 1/6 5/36 1/9 1/12 1/18 1/36 1 1 1 = = m j j P ME 250 Fall 2007 Cumulative Probability Function or Distribution Cumulative Probability function or distribution F(x i ) is defined as: Notice the capital F R a n d o m V a r i a b l e , x1234567891 0 1 1 1 2 Cumulative Probability Function, F (x i ) 0 1/36 1/12 1/6 5/18 5/12 7/12 13/18 5/6 11/12 35/36 1 0 1/12 1/6 1/4 1/3 5/12 1/2 7/12 2/3 3/4 5/6 11/12 1 0 1 1 1 2 Cumulative Probability Function, F (x i) < = i j x x j i x f x F ) ( ) (
Background image of page 5

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

View Full DocumentRight Arrow Icon
ME 250 Fall 2007 Recap reliability If a transmission has a 99% reliability
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/04/2008 for the course ME 250 taught by Professor Dutta during the Fall '07 term at University of Michigan.

Page1 / 34

Prob_Stat Oct 30 - Dealing with uncertainty in design and...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online