Question

50 components are placed on a life test. The recorded times to failure, in hours, are 16.2 18.9 68.4 84.7 112 143 154 201 212 229 231 292 366 371 412 439 441 490 548 561 609 610 662 662 673 703 836 957 1020 1045 1047 1130 1131 1137 1179 1215 1240 1275 1410 1512 1635 1651 1694 1698 1973 2301 2496 2827 3142 4966 he sample data are suspected of coming from a population of lifetimes that can be ade- uately modeled by an exponential distribution. Analyze the sample data as follows: a. Construct a histogram using cell intervals of size 500 (from 0 to 5000). b. Estimate à and the MTTF using the actual data points. c. Estimate the median time to fail using the population formula given in the text and the estimate just calculated for 2. d. Test the adequateness of the exponential model using the chi-square goodness-of- fit test and a confidence (or significance level of 90%. Use the same intervals as in part a, combining everything greater than 2000 hours into one group. e. Suppose the test had been planned to stop upon the fifth failure and hence ended at 112 hours. What would the estimated MITF be for this experiment? Suppose instead the test had been planned to stop at 150 hours. What MTTF estimate would have resulted?

Answer 1