Journals Proceedings

Abstract

The problem of constructing one-sided exact statistical tolerance limits on the kth order statistic in a future sample of m observations from a distribution of log-location-scale family on the basis of an observed sample from the same distribution is considered. The new technique proposed here emphasizes pivotal quantities relevant for obtaining tolerance factors and is applicable whenever the statistical problem is invariant under a group of transformations that acts transitively on the parameter space. The exact tolerance limits on order statistics associated with sampling from underlying distributions can be found easily and quickly making tables, simulation, Monte Carlo estimated percentiles, special computer programs, and approximation unnecessary. Finally, numerical examples are given, where the tolerance limits obtained by using the known methods are compared with the results obtained through the proposed novel technique, which is illustrated in terms of the extreme-value and two-parameter Weibull distributions. The aim of this technique is to develop and publish original scientific contributions and industrial applications dealing with the topics covered by Prognostics and Health Management (PHM) of complex systems. PHM is a set of means, approaches, methods and tools that allows monitoring and tracking the health state of a system in order to detect, diagnose and predict its failures. This information is then exploited to take appropriate decisions to increase the system's availability, reliability and security while reducing its maintenance costs. The proposed technique allows one to construct developments and results in the areas of condition monitoring, fault detection, fault diagnostics, fault prognostics and decision support.