Non-parametric prediction intervals for the lifetime of coherent systems

In this paper, nonparametric methods are proposed to construct prediction intervals for the lifetime of a coherent system with known signatures. An explicit expression for the coverage probability of the prediction intervals is presented based on Samaniego’s signature. The existence and optimality of these intervals are discussed. In our derivation, we also obtain an exact expression for the marginal distribution of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$i$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>i</mi> </math> </EquationSource> </InlineEquation>th order statistic from a pooled sample. Copyright Springer-Verlag Berlin Heidelberg 2014