Serwis Informacyjny "Mechatronika"


tytuł: On certain problems of adopting an a priori distribution in the process of bayesian updating
kategoria: materiały konferencyjne
dział: inne

Assuming the definition of probability as the degree of uncertainty related to the familiarity with a given phenomenon and the associated possibility of assuming a priori the information about the distribution of probability, the article will present the theoretical basis of Bayesian Updating. The method assumes that the parameters of the probability distribution of a function are not determined values but random variables that can be described with the use of probability distribution functions. As the name itself indicates, the method accounts for conditional probability, thus enabling the use of a priori information to reduce the uncertainty of the a posteriori distribution. The uncertainty of parameters’ estimation depends on the size of the sample, which is a serious problem in reliability research, especially in the case of newly manufactured objects or the ones that have been modernized as well as the situations when an object operates in new, different conditions. While applying Bayesian updating, we can use the a priori information about the distribution of parameters (the information on the distribution of parameters prior to the modernization of an object or change of its operating conditions, e.g. occurrence of degradation detected with the use of vibroacoustic diagnosis) in order to reduce the uncertainty of reliability characteristics. The paper will present the method of determining the characteristics of distribution of the time distribution parameters until the moment of defect occurrence while relying on Fisher’s information matrix. We will also discuss the issue of determining the form of distribution of the above parameters and the method of solving this problem by means of the exemplary software used for reliability analyses while accounting for Bayesian updating.

rok wydania: 2007
wydawnictwo: VI SDST
autorzy: Robert Gumiński, Stanisław Radkowski


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