Resampling Approach for the Calculation Processes and Information Systems Models Estimation

TL;DR

This paper analyzes the Resampling method's application to system reliability estimation, compares it with classical methods, and explores optimization and confidence interval construction through numerical examples.

Contribution

It extends the Resampling method to reliability estimation, introduces optimization for sample size, and develops algorithms for confidence interval construction.

Findings

Resampling method improves reliability estimation accuracy.

Optimization reduces variance of estimators.

Algorithms for confidence intervals are effective in practical examples.

Abstract

The work is devoted to the analysis of the Resampling method proposed by A. Andronov and to the analysis of the Resampling method application possibility to the estimation and simulation of the calculation and logical systems reliability. The work Simple and Hierarchical method properties are considered, algorithms for variance are shown. The methods are applied for processes in the multitask operation system and queries to database analysis, a comparison with the classical method, that uses the empirical distribution functions, is made. Numerical examples illustrate the influence of different factors on the Resampling method efficiency. The task of the sample size optimization has been considered. The dynamic programming method is applied to minimize the variance of the Resampling estimator. Optimization is applied for the analysis of queries to database, the numerical example illustrates the value of optimization. The case of partially known distributions is considered. It is shown how to use the Resampling approach in the case when the distributions of some input variables are known. The method is applied to database query analysis and a comparison with Hierarchical Resampling is made. The construction of the Resampling confidence intervals is considered. The algorithm for construction of the Resampling confidence intervals is shown and actual coverage probabilities are calculated. Examples for the multitask operation system analysis illustrate the calculation of the actual coverage probability algorithm.