Oil breakdown voltage. The following summary statistics were calculated from the base e logs of data like that of Problem 5.3, but all eight sample sizes are 25 here
(a) Choose a test condition and estimate the Weibull parameters.
(b) Calculate two-sided approximate 90% confidence limits for each parameter at your test condition.
(c) Estimate all shape parameters.
(d) Calculate two-sided approximate 90% confidence limits for all shape parameters.
(e) Plot all shape parameter estimates and confidence limits on semilog paper. Are the estimates consistent with theory, which says that all eight distributions have the same shape parameter value?
Problem 5.3, Cylinder life. For certain engines, each piston failure causes its cylinder to fail. Also, there are cylinder failures due to other causes. The table below shows an actuarial estimate of the reliability function of current pistons and a separate actuarial estimate of the reliability function of cylinders. A proposed new piston design would eliminate cylinder damage from piston failure. The following shows how much cylinder life (mileage) would be improved with the new piston.
(a) Make a Weibull probability plot of the estimate of the reliability function of current pistons. Relabel the probability scale with reliability percentages.
(b) On the same paper, plot the cylinder reliability function estimate.
(c) Use the reliability function estimates to calculate an estimate of the reliability function for cylinders with the new piston design. This estimate of reliability increases at some mileages.
(d) Plot the estimate from part (c) on the same Weibull paper
(e) Compare the failure rates of the three distributions-increasing or decreasing with mileage?
(f) Discuss whether you think customers could be induced to pay a premium price for the new piston design. What important economic considerations determine whether cylinder life has been improved significantly?