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ISU STAT 496 - Homework assignment #8

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STAT 496, Spring 2005Homework Assignment #81. A study is done on the time to failure for turbine engine windings. The engine windings areput on test at 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 priorto failing. Below are the data for the forty engines tested. With the exception of plotting thesurvivor function, this problem should be done by hand.Time Censor?Time Censor? Time Censor? Time Censor?6 No 25 No 38 No 62 Yes10 No27 No 39 No 64 Yes11 No29 No 40 No 68 No14 No 30 No 45 No 69 No16 No 32 No 45 No 72 No18 No 35 No 46 No 76 No18 No 36 No 46 No 77 Yes18 No36 No 47 No 84 Yes22 No 37 No 48 No 97 Yes24 No 38 No 54 No 101 Yes(a) Construct an estimate of the survivor function and plot this. Do the calculation byhand. It will be helpful if you construct a table similar to the one for the censored databearing example given in Tape 26. You may use JMP or another program to actuallyplot the survivor function.(b) Estimate the chance that an engine winding will survive for 30 hours. Include an ap-proximate 95% confidence interval for this estimate.(c) Estimate the 50thpercentile (median) time to failure using the estimated survivor func-tion.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 parameter λ.(f) Use the value of λ from (f) to compute the probability that an engine winding willsurvive 30 hours.(g) According to the exponential model with the λ from (f), what is the median time tofailure?(h) From the Weibull plot estimate the parameter λ and β.(i) Use the values of λ and β from (i) to compute the probability that an engine windingwill 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 themedian time to failure for the two models?2. Use JMP, or another program, to analyze these data. Turn in annotate computer outputindicating what part of the output corresponds to each of the questions


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ISU STAT 496 - Homework assignment #8

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