Reliability models of m-out-of-n systems under incomplete information

Most methods of reliability analysis of m-out-of-n systems assume that the precise probability distributions of the component time to failure are available and the system components are independent. However, this assumption may be unreasonable in a wide scope of cases (software, human–machine systems). Therefore, imprecise reliability models of m-out-of-n systems are proposed in the paper under condition that there is only some partial information about component lifetime distributions including points of unknown distributions, probabilities on nested intervals, and interval mean times to failure. It is shown how the reliability assessments may vary with the type of the available information. The impact of the component independence condition on the reliability of systems is studied.