1. Copyright © SystatS Consulting Sdn. Bhd. No part may be reproduced without written permission from SystatS Consulting Sdn. Bhd. Weibull Analysis for Reliability in the Field Page: 1 UNIMAP P RESENTATION Exercises 1.The time to fail for a fluorescent light in an office building is Weibull(  =1,  =320 days) given by R(t) = exp[-t/320] with t in days. a)Find the design life for 95% reliability. b)Suppose a warranty of 30 days is planned to be offered. What fraction of lights will fail this warranty period? c)If the cost of a warranty failure is RM20.00, find the expected cost per unit for a failure. d)What does the parameter  need to be in order for the design life to equal 30 days?

2. Copyright © SystatS Consulting Sdn. Bhd. No part may be reproduced without written permission from SystatS Consulting Sdn. Bhd. Weibull Analysis for Reliability in the Field Page: 2 UNIMAP P RESENTATION Exercises 2.Suppose the reliability function for a certain turbine blade is Weibull(  =0.5,  =10000 days) given by R(t) = exp[-(t/10000) 0.5 ] with t in days. a) Find the reliability after 365 days. b) Find the design life for 95% reliability. c) Suppose a burn-in of 150 days is planned. Calculate P(T>365+150). Calculate P(T>150). d) The company who supplies the blades would like to offer a 365 day warranty. It needs the reliability 365 days after any burn-in to be at least 90%. Compute the conditional probability that the blade will survive 365+150 days given that it has survived 150 days. Hint: P(T>365+150 | T>150) = P({T>365+150}  {T>150}) / P(T>150) = P(T>365+150)/ P(T>150). Can this burn-in achieve a 90% reliability at a warranty period of 365 days?

3. Copyright © SystatS Consulting Sdn. Bhd. No part may be reproduced without written permission from SystatS Consulting Sdn. Bhd. Weibull Analysis for Reliability in the Field Page: 3 UNIMAP P RESENTATION Exercises 3.Fit a Weibull distribution to the rubber seal failure time data in months. There are 52 other seals currently in use which have not failed. Copy the seal data in “Weibull Fit.xls: sheet: Rubber Seal TTF” to Cells B7:B33 in the file “Weibull Fit.xls: sheet: Weibull Fit”. Input the number of good units into cell A7 of “Weibull Fit.xls: sheet: Weibull Fit”. Copy the data in Col B to Col D and sort in ascending order. a)What is the Weibull shape parameter? b)What is the Weibull scale parameter? c)Is there a wear-out mechanism or infant mortality mechanism for these seals? d)What is the design life for this rubber seal?

4. Copyright © SystatS Consulting Sdn. Bhd. No part may be reproduced without written permission from SystatS Consulting Sdn. Bhd. Weibull Analysis for Reliability in the Field Page: 4 UNIMAP P RESENTATION Exercises 4. Show that the median of the Weibull distribution is median=  [-ln(1-1/2)] 1/ . 5. A set of 16 fuel pumps are put on test with 16 failures: 0.01, 0.3, 0.4, 2.0, 2.1, 4.6, 18.6, 20.1, 28.4, 32.9, 59.4, 310.4, 345.3, 786.2, 885.7, 890.0. a) Fit a Weibull distribution and find the fitted shape and scale parameters. b) What is the reliability at the end of a 50 day warranty period? c) Calculate the warranty cost for an average repair cost of $30.00 and warranty period of 50 days. e) If a 10 day burn-in is made on the fuel pumps, then the reliability would be calculated using conditional probability as R( 50|10) = P( t>50 | t>10 ) = P( t>50 and t>10 )/P( t>10 ) = P( t>50 )/P( t>10 ) = R(50)/R(10). What is the conditional reliability by using a burn-in period of 10 hours and find the decrease in warranty costs.

5. Copyright © SystatS Consulting Sdn. Bhd. No part may be reproduced without written permission from SystatS Consulting Sdn. Bhd. Weibull Analysis for Reliability in the Field Page: 5 UNIMAP P RESENTATION Lab Exercise Take two different diameter wires. Bend each diameter wire and count the number of bends until breakage. Take at least 20 observations of breakage counts for each wire diameter. Fit a Weibull distribution for each diameter type. Are the two shape parameters different? Which diameter wire has the larger MTTF? Why?