Systems and Means of Informatics
2018, Volume 28, Issue 3, pp 54-61
BETA-POLYNOMIAL A PRIORI DENSITIES IN BAYESIAN RELIABILITY MODELS
- A. A. Kudryavtsev
- S. I. Palionnaia
- S. Ya. Shorgin
Abstract
The Bayesian approach to constructing models of the reliability theory is considered. Within this approach, the model is considered to be incomplete in a certain sense - it is assumed that the key parameters of the system are random variables with known a priori distributions. At some time points, the modifications are introduced to the system to improve reliability; however, each modification may either increase or reduce the reliability of the system. Thus, system's reliability characteristics depend on the ratio of the modification means' parameters of "efficiency" to the parameters of "defectiveness." Such relation can be called the "system's balance index." In this paper, the case of beta-polynomial a priori distributions is considered, where one of the parameters of the system has an a priori beta distribution and the density of the other parameter has the form of a polynomial. For various combinations of given a priori distributions, the formulas for calculating the probabilistic characteristics of the balance index are provided.
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[+] About this article
Title
BETA-POLYNOMIAL A PRIORI DENSITIES IN BAYESIAN RELIABILITY MODELS
Journal
Systems and Means of Informatics
Volume 28, Issue 3, pp 54-61
Cover Date
2018-09-30
DOI
10.14357/08696527180304
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Bayesian approach; modifiable information systems; reliability theory; polynomial densities; beta distribution; balance index
Authors
A. A. Kudryavtsev  , S. I. Palionnaia , and S. Ya. Shorgin 
Author Affiliations
Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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