Abstract
Cautious reliability estimates of multi-state and continuum-state systems are studied in the paper under condition that initial data about reliability of components are given in the form of interval-valued observations, measurements or expert judgments. The interval-valued information is processed by means of a set of the imprecise Dirichlet model which can be regarded as a set of Dirichlet distributions. The developed model of reliability provides cautious reliability measures when the number of observations or measurements is rather small. It can be viewed as an extension of models based on random set theory and robust statistical models. A numerical example illustrates the proposed model and an algorithm for computing the system reliability.
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