Planning inspections in service of fatigue-sensitive aircraft structure components for initial crack detection

Based on a random sample from the Weibull distribution with unknown shape and scale parameters, lower and upper prediction limits on a set of m future observations from the same distribution are constructed. The procedures, which arise from considering the distribution of future observations given the observed value of an ancillary statistic, do not require the construction of any tables, and are applicable whether the data are complete or Type II censored. The results have direct application in reliability theory, where the time until the first failure in a group of m items in service provides a measure regarding the operation of the items, as well as in service of fatigue-sensitive aircraft structures to construct strategies of inspections of these structures; examples of applications are given.