Nonparametric Predictive Inference for
System Failure Time

Abstract

This thesis presents the use of signatures within nonparametric predictive inference
(NPI) for the failure time of a coherent system with a single type of components,
given failure times of tested components that are exchangeable with those in the
system. NPI is based on few modelling assumptions and here leads to lower and
upper survival functions. We also illustrate comparison of reliability of two systems,
by directly considering the random failure times of the systems. This includes
explicit consideration of the difference between failure times of two systems. In
this method we assume that the signature is precisely known. In addition, we show
how bounds for these lower and upper survival functions can be derived based on
limited information about the system structure, which can reduce computational
effort substantially for specific inferential questions. It is illustrated how one can
base reliability inferences on a partially known signature, assuming that bounds for
the probabilities in the signature are available. As a further step in the development
of NPI, we present the use of survival signatures within NPI for the failure time of
a coherent system which consists of different types of components. It is assumed
that, for each type of component, additional components which are exchangeable
with those in the system have been tested and their failure times are available.
Throughout this thesis we assume that the system is coherent, we start with a
system consisting of a single type of components, then we extend for a system
consisting of different types of components.