Use the life data on insulation system 3 in Problem 3.1. Assume life has a lognormal distribution and use base 10 logarithms

(a) For each temperature, estimate µ  and σ.

(b) For each temperature, calculate two-sided 95% confidence limits for µ and σ

(c) Estimate the 1% point for each temperature.

(d) How large a sample is needed to estimate σ at 225°C within a. factor of 2 with 90% confidence? Is the approximation satisfactory?

(e) Calculate a prediction and 90% prediction limits for a single unit at 225°C.

Problem 3.1 insulations. Specimen lives (in hours) of three electrical insulations

(a) On separate lognormal probability paper for each insulation, plot the data from the three test temperatures.

(b) Are there any pronounced peculiarities in the data?

(c) How do the three insulations compare at 200"C, the usual operat-ing temperature, with respect to the median and spread in life?

 (d) How do the three compare at 225 and 250°C occasional operating temperatures?

(e) How do the three compare overall, and are any differences convincing to you?

(f) On a lognormal probability paper make three plots of the data for insulation 2 at 225"C, using the (1) "midpoint", (2) "mean", and (3) median plotting positions. (I) How do the graphical estimates of the distribution median, 1% point, and u compare for the three plotting positions? (2) Which yields the most conservative (pessimistic) and optimistic estimates for reliability purposes? (3) Do the differences in the estimates look large compared to the uncertainties in the estimates?