STAT 496, Spring 2009 Homework Assignment #8, Due by Friday, May 1 1. A study is done on the time to failure for turbine engine windings. The engine windings are put on test at high temperature (100oC) and their times to failure (hours) are recorded. Several of the engines have censored times because they were removed from the study prior to failing. Below are the data for the forty engines that were tested. With the exception of plotting the survivor function, this problem should be done by hand. Time Censor? Time Censor? Time Censor? Time Censor? 6 No 25 No 38 No 62 Yes 10 No 27 No 39 No 64 Yes 11 No 29 No 40 No 68 No 14 No 30 No 45 No 69 No 16 No 32 No 45 No 72 No 18 No 35 No 46 No 76 No 18 No 36 No 46 No 77 Yes 18 No 36 No 47 No 84 Yes 22 No 37 No 48 No 97 Yes 24 No 38 No 54 No 101 Yes a) Construct an estimate of the survivor function and plot this. Do the calculations for the probability of survival by hand. It will be helpful if you construct a table similar to the one for the censored data bearing example given in Tape 26. You may use JMP or another program to actually plot the survivor function. b) Estimate the chance that an engine winding will survive for 30 hours. Include an approximate 95% confidence interval for this estimate. c) Estimate the 50th percentile (median) time to failure using the estimated survivor function. On the next page are two plots. Use these to answer the following questions. d) Which distribution, exponential or Weibull, appears to fit the data the best? Why? e) From the exponential plot estimate the value of the parameterλ. f) Use the estimated value of λ from e) to compute the probability that an engine winding will survive 30 hours. g) According to the exponential model with the value ofλfrom e), what is the median time to failure? h) From the Weibull plot estimate the values of the parameters λ andβ. i) Use the values of the estimates ofλ and βfrom h) to compute the probability that an engine winding will survive 30 hours. j) According to the Weibull model, what is the median time to failure? k) How much different are the estimates of the survival probability at 30 hours and the median time to failure based on the survivor function and the two models, exponential and Weibull? 2. Use JMP, or another program, to analyze these data. Turn in annotated computer output indicating what part of the output corresponds to each of the questions above.
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