Nonparametric Predictive Inference for System Reliability

This thesis provides a new method for statistical inference on system reliability on the basis of limited information resulting from component testing. This method is called Nonparametric Predictive Inference (NPI). We present NPI for system reliability, in particular NPI for k-out-of-m systems, and for systems that consist of multiple ki-out-of-mi subsystems in series configuration. The algorithm for optimal redundancy allocation, with additional components added to subsystems one at a time is presented. We also illustrate redundancy allocation for the same system in case the costs of additional components differ per subsystem. Then NPI is presented for system reliability in a similar setting, but with all subsystems consisting of the same single type of component. As a further step in the development of NPI for system reliability, where more general system structures can be considered, nonparametric predictive inference for reliability of voting systems with multiple component types is presented. We start with a single voting system with multiple component types, then we extend to a series configuration of voting subsystems with multiple component types. Throughout this thesis we assume information from tests of nt components of type t

Nonparametric predictive inference with right-censored data

This thesis considers nonparametric predictive inference for lifetime data that include right-censored observations. The assumption A((_m)) proposed by Hill in 1968 provides a partially specified predictive distribution for a future observation given past observations. But it does not allow right-censored data among the observations. Although Berliner and Hill in 1988 presented a related nonparametric method for dealing with right-censored data based on A((_n)), they replaced 'exact censoring information' (ECI) by 'partial censoring information' (PCI), enabling inference on the basis of A((_n)). We address if ECI can be used via a generalization of A((_n)).We solve this problem by presenting a new assumption 'right-censoring A((_n))' (rc- A((_n)), which generalizes A((_n)). The assumption rc- A((_n)) presents a partially specified predictive distribution for a future observation, given the past observations including right-censored data, and allows the use of ECI. Based on rc-A((_n)), we derive nonparametric predictive inferences (NPI) for a future observation, which can also be applied to a variety of predictive problems formulated in terms of the future observation. As applications of NPI, we discuss grouped data and comparison of two groups of lifetime data, which are problems occurring frequently in reliability and survival analysis

Predictive inference for system reliability after common-cause component failures

This paper presents nonparametric predictive inference for system reliability following common-cause failures of components. It is assumed that a single failure event may lead to simultaneous failure of multiple components. Data consist of frequencies of such events involving particular numbers of components. These data are used to predict the number of components that will fail at the next failure event. The effect of failure of one or more components on the system reliability is taken into account through the system׳s survival signature. The predictive performance of the approach, in which uncertainty is quantified using lower and upper probabilities, is analysed with the use of ROC curves. While this approach is presented for a basic scenario of a system consisting of only a single type of components and without consideration of failure behaviour over time, it provides many opportunities for more general modelling and inference, these are briefly discussed together with the related research challenges

Modelling health state preference data using a non-parametric Bayesian method

This paper reports on the findings from the application of a recently reported approach to modelling health state valuation data. The approach applies a nonparametric model to estimate the revised version of the Health Utilities Index Mark 2 (HUI 2) health state valuation algorithm using Bayesian methods. The data set is the UK HUI 2 valuation study where a sample of 51 states defined by the HUI 2 was valued by a sample of the UK general population using standard gamble. The paper presents the results from applying the nonparametric model and compares these to the original model estimated using a conventional parametric random effects model. The two models are compared in terms of their predictive performance. The paper discusses the implications of these results for future applications of the HUI 2 and further work in this field

Nonparametric Bayes Modeling of Populations of Networks

Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections among brain regions are collected for each patient under study, motivating statistical models which can flexibly characterize the probabilistic generative mechanism underlying these network-valued data. Available models for a single network are not designed specifically for inference on the entire probability mass function of a network-valued random variable and therefore lack flexibility in characterizing the distribution of relevant topological structures. We propose a flexible Bayesian nonparametric approach for modeling the population distribution of network-valued data. The joint distribution of the edges is defined via a mixture model which reduces dimensionality and efficiently incorporates network information within each mixture component by leveraging latent space representations. The formulation leads to an efficient Gibbs sampler and provides simple and coherent strategies for inference and goodness-of-fit assessments. We provide theoretical results on the flexibility of our model and illustrate improved performance --- compared to state-of-the-art models --- in simulations and application to human brain networks