Building models of freight cars refusals involving bayesian approach

TLDR: The paper, based on Bayesian method was done combining two models: the failures of freight cars and the changing physical and mechanical properties of composite materials, and the posterior probability determined a priori probability of failures given using the model change of physical and Mechanical properties and the likelihood function that takes into account the additional value failures.

Abstract: Based on the theoretical analysis and Bayesian statistics ordinary shown that Bayesian analysis begins with the known data from the following consideration changes in knowledge process of obtaining new information and mathematical statistics methods of sample observation comes only with the knowledge of some group of objects. Using Bayesian formula, we can determine the probability of any event, provided that there was another statistically correlated with it an event that counted with greater accuracy the likelihood. This used previously known information and data obtained as a result of new observations. The study of failures of freight cars, the Bayesian approach allows you to evaluate the occurrence of each failure of parts or assemblies separately, as well as through changes in the formula for the total probability. The paper, based on Bayesian method was done combining two models: the failures of freight cars and the changing physical and mechanical properties of composite materials. This posterior probability determined a priori probability of failures given using the model change of physical and mechanical properties and the likelihood function that takes into account the additional value failures. Using the expression for the posterior probability held specification mentioned developments (run) freight wagon to failure.

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b
Fig. 1. Dependence of the probability of failure of freight cars from the path:
a – the mechanical wear; b – fatigue wear