Locomotive control (Weibull). The following STATPAC output shows the ML fit of a Weibull distribution to the locomotive control data of Section 2. CENTER: a and SPREAD = ß
(a) Make a Weibull plot of the data, and assess how well the Weibull distribution fits the data (both on an absolute basis and in comparison with the lognormal fit)
(b) Does the shape parameter estimate suggest that the failure rate increases or decreases with age? Do the confidence limits for the shape parameter provide convincing evidence that the failure rate increases (or decreases)?
(c) What are the ML estimate and the two-sided approximate 95% confidence limits of the percentage failing on an 80-thousand mile warranty? How do they compare with those from the lognormal fit?
(d) Plot the fitted Weibull distribution and the confidence limits for the percentiles on the Weibull plot from (a). Also, plot the fitted lognormal distribution (a curve) and the lognormal confidence limits for the percentiles on the same plot. How do the estimates and confidence limits compare (for practical purposes) in (1) the range of the data (particularly the middle), in (2) the lower tail beyond the data, and in (3) the upper tail beyond the data.
(e) Would the key conclusions concerning the failure rate and the percentage failing or warranty depend on which distribution is used?