Assessing Wear Evolutions in Railway Wheelsets Using a Survival Modeling Approach

The present paper provides a method to predict maintenance needs for the railway wheelsets by modeling the wear out affecting the wheelsets during its life cycle using survival analysis. Wear variations of wheel profiles are discretized and modelled through a censored survival approach, which is appropriate for modeling wheel profile degradation using real operation data from the condition monitoring systems that currently exist in railway companies. Several parametric distributions for the wear variations are modeled and the behavior of the selected ones is analyzed and compared with wear trajectories computed by a Monte Carlo simulation procedure. This procedure aims to test the independence of events by adding small fractions of wear to reach larger wear values. The results show that the independence of wear events is not true for all the established events, but it is confirmed for small wear values. Overall, the proposed framework is developed in such a way that the outputs can be used to support predictions in condition-based maintenance models and to optimize the maintenance of wheelsets.

Compreensões Probabilísticas de Crianças Brasileiras e Portuguesas Acerca de Justiça em Jogos

ResumoFrequentes dificuldades na compreensão probabilística exigem que se identifiquem crenças intuitivas das crianças para apoiar a promoção pedagógica dessas aprendizagens. O presente estudo versa analisar as compreensões de crianças brasileiras e portuguesas acerca de justiça em jogos, considerando demandas cognitivas da probabilidade referentes à aleatoriedade, ao espaço amostral e à comparação de probabilidades. A pesquisa envolveu a análise de seis jogos e foi realizada por meio de uma entrevista clínica com 15 crianças brasileiras e 15 portuguesas, com média de idade de 11 anos. Os resultados revelam que as crianças apresentaram facilidade em avaliar um jogo injusto quando envolvia aleatorizadores viciados e em perceber a justiça num jogo cujas regras mantinham equilíbrio, permitindo que houvesse chances iguais para os jogadores. No entanto, observou-se que apresentaram incompreensões acerca da independência de eventos, conduzindo a avaliações equivocadas sobre a justiça em jogos. Nenhuma criança conseguiu apresentar justificativa coerente quando necessário comparar probabilidades considerando eventos de espaços amostrais distintos. Também não conseguiram utilizar o raciocínio proporcional, e, portanto, não avaliaram corretamente a justiça nesses jogos. Finalmente, os resultados não apontam para diferenças substanciais nas compreensões dos dois grupos estudados. Só em termos de linguagem, as expressões mais utilizadas nas justificativas por ambos os grupos foi ‘chance’, mas as crianças brasileiras usaram mais a ‘sorte’ e as portuguesas os termos ‘possibilidade’ e ‘probabilidade’. Estes resultados implicam a necessidade de viabilizar ações pedagógicas interventivas realizadas com o apoio de jogos que se configuram num importante recurso para o redimensionamento das aprendizagens probabilísticas. Palavras-chave: Aleatoriedade. Espaço Amostral. Comparação de Probabilidades. Justiça em Jogos. Crianças. AbstractFrequent difficulties in probabilistic understanding require the identification of children's intuitive beliefs to support the pedagogical promotion of these learnings. The present study focuses on analyzing Brazilian and Portuguese children understandings about fairness in games, considering cognitive demands of probability regarding randomness, sample space and comparison of probabilities. The research involved the analysis of six games and was carried out through a clinical interview with 15 Brazilian and 15 Portuguese children, with an average age of 11 years. The results reveal that the children were able to evaluate an unfair game when it involved addicted randomizers and to perceive justice in a game whose rules maintained balance, allowing the players to have equal chances. However, it was observed that they presented misunderstandings about the independence of events, leading to mistaken assessments of fairness in games. No child was able to present a coherent justification when there was a need to compare probabilities considering events from different sample spaces. They were also unable to use proportional reasoning, and therefore did not correctly assess justice in these games. Finally, the results do not point to substantial differences in the understandings of the two groups studied. Only in the language, the most used expressions in the justifications by both groups was ‘chance’, although Brazilian children used more ‘luck’ and Portuguese used ‘possibility’ and ‘probability’. These results imply the need to make feasible interventional pedagogical actions carried out with the support of games which are an important resource for the resizing of probabilistic learning. Keywords: Randomness. Sample Space. Comparison of Probabilities. Fairness in Games. Children.

Application of probability and statistics methods in arrangement of railway transportation

Complex economic and mathematical methods are becoming more widespread in training of specialists in the field of railroad communication arrangement. The purpose of this study is to develop an effective methodology for mathematical training of railway transportation specialists on the basis of active training methods. The article deals with application of probabilistic and statistical methods to problems in design of railway transportation, for example, fluctuations in loading of railway stations and distribution of the time interval between arrival of trains. Using the example of the flow of arriving trains, the technology of testing the hypothesis that the time between arrival of trains is distributed according to the exponential law and the hypothesis of independence of events in the flow is displayed in detail. When confirming each of these hypotheses, it must be concluded that the flow of trains arriving at the station is according to the simplest (Poisson’s) model. This conclusion allows using the apparatus of Markov chains to describe a random process.

Crianças de Anos Iniciais Levantando Espaços Amostrais: Relações Entre Pensamentos Combinatório e Probabilístico

Estudos em Educação Matemática têm apontado conhecimentos que crianças de anos iniciais já possuem e suas dificuldades com alguns conceitos em particular. Nesse texto são discutidos quatro argumentos. 1) Crianças em início de escolarização já possuem conhecimentos básicos de alguns conceitos mais complexos, tais como os associados à Probabilidade e à Combinatória. 2) Em situações de jogo, com uso de recursos adequados e por meio de estratégias próprias, as crianças evidenciam noções sobre aleatoriedade, independência de eventos e equiprobabilidade, bem como demonstram compreensão de situações combinatórias variadas – produtos cartesianos, arranjos, combinações e permutações. 3) Trabalhar de modo articulado com a Probabilidade e a Combinatória – por meio do levantamento de espaços amostrais, por exemplo – constitui-se um modo eficiente de integrar conhecimentos matemáticos diversos. 4)Por demandarem formas mais complexas de pensamento, recomenda-se que se inicie cedo o estímulo ao desenvolvimento dos raciocínios combinatório e probabilístico. Esses argumentos são aqui discutidos a partir de resultados de pesquisas e são apontadas implicações para o ensino escolar.Palavras-chave: Crianças. Anos Iniciais. Espaços Amostrais. Raciocínios Combinatório e Probabilístico.AbstractStudies in Mathematics Education have pointed out knowledge that children in initial studying already have and their difficulties with some concepts in particular. In this text four arguments are discussed. 1) Children in initial schooling already have basic knowledge of some more complex concepts, such as those associated with Probability and Combinatorics. 2) In game situations, using appropriate resources and through their own strategies, children show notions about randomness, independence of events and equiprobability, as well as demonstrate understanding of varied combinatorial situations – Cartesian products, arrangements, combinations and permutations. 3) Working in an articulated way with Probability and Combinatorial – by means of raising sample spaces, for example – is an efficient way to integrate diverse mathematical knowledge. 4) Because they require more complex forms of thinking, it is recommended that the stimulus to the development of combinatorial and probabilistic reasoning be initiated early. These arguments are discussed from research results and implications for school teaching will be pointed out.Keywords: Children. Initial Schooling. Sample Spaces. Combinatorial and Probabilistic Reasoning.