Perspective on Weibull proportional-hazards models

This note uses a paper of Elsayed & Chan (1990) to illustrate some of the advantages and some of the limitations of the proportional hazards approach. The role of proportional hazards as one of several tools for exploratory data analysis is described. The emphasis is on exploratory techniques as a way of: (1) measuring the importance of factors influencing system behavior; and (2) determining the form of the model. The semi-parametric version of proportional hazards shows the relative importance of explanatory factors in determining the failure behavior regardless of whether the model is strictly correct. Thus the relative chance of failure can be assessed, but not the absolute chance. The advantage of proportional hazards is that it always yields a quantitative measure of importance for each influence factor. Although Elsayed & Chan clearly establish the importance of temperature as the most critical factor in thin-oxide breakdown, the other analysis technique indicates that more needs to be done to validate a particular model of system behavior. In this case, the failure mechanism remains open, and the use of accelerated test data to predict performance under usual conditions needs further investigatio

Estimation of Paris-Erdogan law parameters and the influence of environmental factors on crack growth

Following earlier stochastic models of crack growth a simple function of the crack length follows a normal distribution. From this observation the parameters of the Paris-Erdogan model are readily evaluated without the need to estimate the crack growth rate. Moreover, the approach lends itself to the analysis of properly designed experiments to determine the effect of environmental factors on the parameters of the Paris-Erdogan equation through the medium of accelerated failure time models borrowed from reliability theory

A critical look at some point process models for repairable systems

The use of a modeldriven approach to the analysis of repairable systems is considered and shown to be useful as a way of understanding the characteristics of such a system. However, considerable statistical problems arise from the use of a set of standard model-building elements. In particular, identification problems arise in many of the models. The argument is illustrated by examples from software reliability and mechanical reliability. The conclusion is that, in many cases, the exploratory data-analysis approach is as effective as the use of more sophisticated models

Why no additive hazards models?

The intuitively attractive additive hazards model is compared with the proportional hazards and accelerated failure time models. The lack of identifiability limits the use of the model and prevents the application of regression versions using covariates. Fortunately, data analysis based on nonhomogeneous Poisson processes or on proportional hazards is likely to yield most of the information available in the data, even though they: 1) do not necessarily represent the underlying process, and 2) even seem unlikely in certain situations. In particular, proportional hazards modeling appears very robust and requires few assumptions

Bayesian reliability analysis with imprecise prior probabilities

The Bayesian framework for statistical inference offers the possibility of taking expert opinions into account, and is therefore attractive in practical problems concerning reliability of technical systems. Probability is the only language in which uncertainty can be consistently expressed, and this requires the use of prior distributions for reporting expert opinions. In this paper an extension of the standard Bayesian approach based on the theory of imprecise probabilities and intervals of measures is developed. It is shown that this is necessary to take the nature of experts knowledge into account. The application of this approach in reliability theory is outlined. The concept of imprecise probabilities allows us to accept a range of possible probabilities from an expert for events of interest and thus makes the elicitation of prior information simpler and clearer. The method also provides a consistent way for combining the opinions of several experts

A Bayes-competing risk model for the use of expert judgement in reliability estimation

In an analysis of the reliability of heat exchangers, a number of causes of failure and a number of potential failure patterns were identified. To allow a simplification of the analysis, five independent groups of failure causes were defined and formed the basis of a competing risks model. Further, lack of data and poor quality data required the experience of ‘experts’ to be used in a quantitative way through Bayesian methods. Lastly, to simplify the elicitation of the prior densities, a shape, scale and location parameter model for the failure time distributions was adopted

A relevância da família como unidade de análise nos estudos sobre pluriatividade.

O fenômeno da pluriatividade passou a ser mais estudado no Brasil na década de 1990, quando foram publicados trabalhos em todas as regiões do país. Um dos elementos centrais desta discussão diz respeito à unidade de análise relevante para se analisar a complexidade desse fenômeno. Em consonância com a literatura internacional, este artigo defende a idéia de que a família, e não a unidade de produção, deve ser o elemento balizador de estudos sobre a pluriatividade na agricultura familiar brasileira

Proximity effect at superconducting Sn-Bi2Se3 interface

We have investigated the conductance spectra of Sn-Bi2Se3 interface junctions down to 250 mK and in different magnetic fields. A number of conductance anomalies were observed below the superconducting transition temperature of Sn, including a small gap different from that of Sn, and a zero-bias conductance peak growing up at lower temperatures. We discussed the possible origins of the smaller gap and the zero-bias conductance peak. These phenomena support that a proximity-effect-induced chiral superconducting phase is formed at the interface between the superconducting Sn and the strong spin-orbit coupling material Bi2Se3.Comment: 7 pages, 8 figure