Imprecise probability theories are considered useful in reliability and risk assessments, but some of them were found to be unsatisfactory. This paper summarizes the authors' experience in dealing with the Dempster--Shafer theory of evidence and demonstrates the authors' advances in the application of the theory of coherent imprecise probabilities for reliability assessments. The obtained lower and upper reliabilities of series, parallel and general systems have very specific useful properties that cannot be obtained in the framework of standard probability theory.
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