Reliability and MTTF prediction of k-out-of-n complex systems with components subjected to multiple stages of degradation

In some environments the components may not fail fully but can degrade, and there may be multiple stages of degradation. In such cases, the efficiency of the system may decrease. In this study we present a model for predicting the reliability of k-out-of-n:G systems assuming that components are subjected to several stages of degradation as well as catastrophic failures. In the analysis we consider the state-dependent transition rates far the catastrophic failures and degradation processes. We also present the expressions to determine the reliability and mean time to failure (MTTF) of the k-out-of-n systems. Reliability and MTTF expressions for a special case of the model without catastrophic failures are also presented. Several numerical examples are given to illustrate the results.