Imprecise reliability of cold standby systems

Most methods of reliability analysis of cold standby systems assume that the precise probability distributions of the component times to failure are available. However, this assumption may be unreasonable in a wide scope of cases (software, human‐machine systems). Therefore, the imprecise reliability models of cold standby systems are proposed in the paper. These models suppose that arbitrary probability distributions of the component time to failure are possible and they are restricted only by available information in the form of lower and upper probabilities of some events. It is shown how the reliability assessments may vary with a type of available information. The impact of the independence condition on reliability of systems is studied. Numerical examples illustrate the proposed models.