Simultaneous nonparametric confidence bands for load-sharing systems

AStA Advances in Statistical Analysis

Abstract

Abstract Load-sharing systems arise in many different reliability applications, for instance, when modeling tensile strength of fibrous composites in textile industry or lifetimes of redundant technical systems in engineering. Sequential order statistics serve as a flexible model for the ordered component failure times of such systems and allow the residual lifetime distribution of the components to change after each component failure. In a proportional hazard rate setting, the model consists of some baseline distribution function and several model parameters describing successive adjustments of the hazard rates of the operating components. This work provides nonparametric confidence bands for the baseline distribution function, where the model parameters may be known or unknown. In case of known model parameters, we show how to construct exact confidence bands based on Kolmogorov-Smirnov type statistics, which are distribution-free with respect to the baseline distribution. If the model parameters are unknown, finite sample inference turns out to be infeasible, and asymptotic confidence bands for the baseline distribution function are derived. As a technical tool, we extend the existing asymptotic theory of semiparametric estimators based on the profile-likelihood approach.

Authors 3

1. Stefan Bedbur corresponding Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Aachen, Germany

2. Johann Köhne corresponding

   University of Göttingen

   Affiliation as printed

   Institute of Mathematical Stochastics, University of Göttingen, Göttingen, Germany

3. Fabian Mies corresponding

   Delft University of Technology

   Affiliation as printed

   Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands