IBM Journal of Research and Development · 1959 · 18 citations · 10 references
EngineeringSystems EngineeringMaintenance EngineeringProbability TheorySurvival AnalysisHazard FunctionsReliabilityReliability ModelingRenewal ProcessesRenewal TheorySurvival FunctionsComponent Reliability ModelingEquipment ReliabilityLife-cycle ReliabilityLifetime DistributionsLifetime EstimationProbabilistic Reliability ModelingRenewal Rate AnalysisSystem Reliability Modeling
Probability functions are defined for use in reliability studies of equipments which are maintained over a long period of time through replacement of components. These are: lifetime distribution function, lifetime density function, probability of survival, hazard, expected number of replacements, and renewal rate. Theoretical results of renewal theory are adapted to reliability studies of complex systems.
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A Mathematical Theory of Communication
Claude E. Shannon · Bell System Technical Journal · 1948 · 80.7K citations
ON THE SUPERPOSITION OF RENEWAL PROCESSES
David R. Cox, Walter L. Smith · Biometrika · 1954 · 228 citations