A particular type of integrated circuit (IC) is known to have an electromigration-related failure...

A particular type of integrated circuit (IC) is known to have an electromigration-related failure mode. A life test was conducted at a temperatureof 120°C in order to learn more about the life distribution and when failures might be expected to occur. A total of 20 ICs were tested and 5 failed before 500 hours, when the test was stopped. Failure times were at 252, 3 15, 369, 403, and 474 hours. ML estimates of the lognormal parameters are = 6.56 and l? = S34. The variance-covariance matrix estimate for @ and i?is h .0581 .0374 T-ji,(; = [.0374 .04051 * Recall that exp(j2) = exp(6.56) = 706 hours is the ML estimate of the lognormal median. (a) Make a lognormal probability plot of the failure data. (b) Compute ML estimates of the lognormal F(200) and F( 1000) and use these to draw a line representing the lognormal estimate of F(r). (c) Use jl and i? to compute an estimate of the mean of the lognormal distribution (equation given in Section 4.6). Compare this with the estimate of the lognormal median. Comment on the difference. (d) Compute 71, the ML estimate of the . I quantile of the life distribution. (e) Compute the standard error for 71. Explain the interpretation of thih quantity. (f) Compute an approximate 95% confidence interval for t Include this interval in the plot in part (a). Explain the interpretation of this interval and the justification for the approximate method that you use.