Nonparametric Predictive Inference for System Failure Time

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

Nonparametric predictive inference for system failure time based on bounds for the signature

System signatures provide a powerful framework for reliability assessment for systems consisting of exchangeable components. The use of signatures in nonparametric predictive inference has been presented and leads to lower and upper survival functions for the system failure time, given failure times of tested components. However, deriving the system signature is computationally complex. This article presents how limited information about the signature can be used to derive bounds on such lower and upper survival functions and related inferences. If such bounds are sufficiently decisive they also indicate that more detailed computation of the system signature is not required

Nonparametric predictive inference for failure times of systems with exchangeable components

The theory of system signatures (Samaniego, 2007) provides a powerful framework for reliability assessment for systems consisting of exchangeable components. For a system with m components, the signature is a vector containing the probabilities for the events that the system fails at the moment of the jth ordered component failure time, for all j = 1,…, m. As such, the signature represents the structure of the system. This paper presents how signatures can be used within nonparametric predictive inference, a statistical framework which uses few modelling assumptions enabled by the use of lower and upper probabilities to quantify uncertainty. The main result is the use of signatures to derive lower and upper survival functions for the failure time of systems with exchangeable components, given failure times of tested components that are exchangeable with those in the system. In addition, it is shown how the failure times of two such systems can be compared. This paper is the first in which signatures are combined with theory of lower and upper probabilities; related research challenges are briefly discussed

Nonparametric predictive inference for system reliability using the survival signature

The survival signature has recently been presented as an attractive concept to aid quantification of system reliability. It has similar characteristics as the system signature, which is well established, but contrary to the latter it is easily applicable to systems with multiple types of components. We present an introductory overview of the survival signature together with new results to aid computation. We develop nonparametric predictive inference for system reliability using the survival signature. The focus is on the failure time of a system, given failure times of tested components of the same types as used in the system