Degradation Models and Implied Lifetime Distributions

In experiments where failure times are sparse, degradation analysis is useful for the analysis of failure time distributions in reliability studies. This research investigates the link between a practitioner\u27s selected degradation model and the resulting lifetime model. Simple additive and multiplicative models with single random effects are featured. Results show that seemingly innocuous assumptions of the degradation path create surprising restrictions on the lifetime distribution. These constraints are described in terms of failure rate and distribution classes

On the social induction of Alzheimer's disease: An index theorem aging model for amyloid formation

The central 'risk factor' for Alzheimer's disease (AD) is age. From first principles, we construct a mathematical model of protein folding and its in vivo regulation that gives this result in a natural manner. We extend the basic approach using topological information theory methods, and examine a case history of socially-induced premature aging in the United States

Manifestations of the onset of chaos in condensed matter and complex systems

We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated with the attractors at period-doubling accumulation points and at tangent bifurcations to describe features of glassy dynamics, critical fluctuations and localization transitions. We recall that trajectories pertaining to the routes to chaos form families of time series that are readily transformed into networks via the Horizontal Visibility algorithm, and this in turn facilitates establish connections between entropy and Renormalization Group properties. We discretize the replicator equation of game theory to observe the onset of chaos in familiar social dilemmas, and also to mimic the evolution of high-dimensional ecological models. We describe an analytical framework of nonlinear mappings that reproduce rank distributions of large classes of data (including Zipf's law). We extend the discussion to point out a common circumstance of drastic contraction of configuration space driven by the attractors of these mappings. We mention the relation of generalized entropy expressions with the dynamics along and at the period doubling, intermittency and quasi-periodic routes to chaos. Finally, we refer to additional natural phenomena in complex systems where these conditions may manifest.Comment: 20 pages, 7 figures. To be published in European Physical Journal Special Topics. Special Issue: "Nonlinear Phenomena in Physics: New Techniques and Applications

Influence of heat treatment on the microstructure and tensile properties of Ni-base superalloy Haynes 282

The effect of heat treatment on the microstructure and mechanical properties of Ni-base superalloy Haynes 282 was investigated. Applying a standard two-step ageing (1010 °C/2 h +788 °C/8 h) to the as-received, mill annealed, material resulted in a the presence of discrete grain boundary carbides and finely dispersed intragranular γ′, with an average size of 43 nm. This condition showed excellent room temperature strength and ductility. The introduction of an additional solution treatment at 1120 °C resulted in grain growth, interconnected grain boundary carbides and coarse (100 nm) intragranular γ′. The coarser γ′ led to a significant reduction in the strength level, and the interconnected carbides resulted in quasi-brittle fracture with a 50% reduction in ductility. Reducing the temperature of the stabilization step to 996 °C during ageing of the mill annealed material produced a bi-modal γ′ distribution, and grain boundaries decorated by discrete carbides accompanied by γ′. This condition showed very similar strength and ductility levels as the standard ageing of mill-annealed material. This is promising since both grain boundary γ′ and a bi-modal intragranular γ′ distribution can be used to tailor the mechanical properties to suit specific applications. The yield strength of all three conditions could be accurately predicted by a unified precipitation strengthening model

Generalising Exponential Distributions Using an Extended Marshall-Olkin Procedure

This paper presents a three-parameter family of distributions which includes the common exponential and the Marshall–Olkin exponential as special cases. This distribution exhibits a monotone failure rate function, which makes it appealing for practitioners interested in reliability, and means it can be included in the catalogue of appropriate non-symmetric distributions to model these issues, such as the gamma and Weibull three-parameter families. Given the lack of symmetry of this kind of distribution, various statistical and reliability properties of this model are examined. Numerical examples based on real data reflect the suitable behaviour of this distribution for modelling purposes