On Constructing Prediction Intervals for Samples from a Weibull or Extreme Value Distribution

Assume that a (possibly censored) sample is available from a population having a Weibull or extreme value distribution, and that a single future observation is to be obtained from the same population. This paper provides Monte Carlo estimates of percentiles of the distribution of a statistic S, that may be used to construct prediction intervals to contain the future observation. Such intervals are of practical importance to reliability engineers and to those investigating treatment of undesirable habitual behavior. An approximation is given for the distribution of S that is in very close agreement with the Monte Carlo results that are presented. The approximation applies also when the single future observation of interest is the smallest in a lot (or sample) of size m > 1.