Discussion, with reply, on "Estimating the cumulative probability of failure data points to be plotted on Weibull and other probability paper

Authors:
  • MCM. Cacciari
    M. Cacciari
  • GMG.C. Montanari
    G.C. Montanari
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Abstract
It is pointed out that the Bernard estimator is very accurate, with respect to other median or mean approximated ranks, confirming results presented by J.C. Fothergill in the above-titled paper (see ibid., vol.25, p.489-92, 1990). However, it is argued that the weighted Blom seems the most accurate estimator, among graphical ones, for normally sized samples and a reliable one for small sample sizes, although the Bernard and Filliben estimators are better than Weibull and Blom for small sample sizes. Statistical and graphical estimators are compared by plotting the percent deviations of the values of the Weibull parameters alpha and beta (scale and shape parameters, respectively) estimated by weighted Blom, Bernard, Weibull, maximum likelihood estimation (MLE), and Bain-Engelhardt (BE), with respect to the true values, as well as the estimates obtained by MLE and BE, as functions of the sample size. In replying, Fothergill states that for small sample sizes, the advantages of more sophisticated techniques do not seem warranted.