Current public health guidelines on physical activity and sleep duration are limited by a reliance on subjective self-reported evidence. Using data from simple wrist-worn activity monitors, we developed a tailored machine learning model, using balanced random forests with Hidden Markov Models, to reliably detect a number of activity modes. We show that physical activity and sleep behaviours can be classified with 87% accuracy in 159,504 minutes of recorded free-living behaviours from 132 adults. These trained models can be used to infer fine resolution activity patterns at the population scale in 96,220 participants. For example, we find that men spend more time in both low- and high- intensity behaviours, while women spend more time in mixed behaviours. Walking time is highest in spring and sleep time lowest during the summer. This work opens the possibility of future public health guidelines informed by the health consequences associated with specific, objectively measured, physical activity and sleep behaviours.

The concept of survival signature has recently been introduced as an alternative to the signature for reliability quantification of systems. While these two concepts are closely related for systems consisting of a single type of component, the survival signature is also suitable for systems with multiple types of component, which is not the case for the signature. This also enables the use of the survival signature for reliability of networks. In this article, we present the use of the survival signature for reliability quantification of systems and networks from a Bayesian perspective. We assume that data are available on tested components that are exchangeable with those in the actual system or network of interest. These data consist of failure times and possibly right‐censoring times. We present both a nonparametric and parametric approach.

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the number of cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) -a simulation approach which is typically used for stochastic differential equation models -can be applied in reliability problems by carefully controlling the bias-variance tradeoff in approximating large system behaviour. In this first exposition of MLMC methods in reliability problems we address the canonical problem of estimating the expectation of a functional of system lifetime for non-repairable and repairable components, demonstrating the computational advantages compared to classical Monte Carlo methods. The difference in computational complexity can be orders of magnitude for very large or complicated system structures, or where the desired precision is lower.

It is often difficult for a phased mission system (PMS) to be highly reliable, because this entails achieving high reliability in every phase of operation. Consequently, reliability analysis of such systems is of critical importance. However, efficient and interpretable analysis of PMSs enabling general component lifetime distributions, arbitrary structures, and the possibility that components skip phases has been an open problem.In this paper, we show that the survival signature can be used for reliability analysis of PMSs with similar types of component in each phase, providing an alternative to the existing limited approaches in the literature. We then develop new methodology addressing the full range of challenges above. The new method retains the attractive survival signature property of separating the system structure from the component lifetime distributions, simplifying computation, insight into, and inference for system reliability.

An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through bounds on the functioning probability. Given component level test data these bounds are propagated to bounds on the posterior predictive distribution for the functioning probability of a new system containing components exchangeable with those used in testing. The method further enables identification of prior-data conflict at the system level based on component level test data. New results on first-order stochastic dominance for the Beta-Binomial distribution make the technique computationally tractable. Our methodological contributions can be immediately used in applications by reliability practitioners as we provide easy to use software tools.