Recent Advances in Statistical Methods for System Reliability Using Bernoulli Sampling of Components

摘要

The paper provides a survey of results in statistical inference in systems reliability using Bernoulli sampling of individual components. Particular attention is given to the notion of Buehler optimally and its implementation in such problems. Recent results of the authors on Buehler optimal confidence bounds on the reliability of series and parallel systems are discussed. For series systems, these results employ a generalization of an inequality of Sudakov. For parallel systems. Buehler optimal bounds are obtained for small numbers of failures using the notion of Schur concavity. Estimates of the optimal bounds are obtained in those cases for which the property of Schur concavity does not hold. (Author)