Reliability modeling of a series system with correlated or dependent component degradation processes

A system reliability model is developed and demonstrated when the individual components within the system are each subject to individual degradation processes, and for a series system, the system fails when any of the individual failure processes reaches a component-specific failure threshold. For this system model, the component degradation paths can be correlated or dependent. This is a practical and realistic consideration because for many operating systems, all components are exposed to shared environmental or operating stresses which may simultaneously influence the failure behavior of each component. In this new model, component degradation paths are mathematically represented as a linear combination of an independent component degradation contribution and a proportional common degradation contribution which influences each component. Instead of taking an integral of a joint normal probability density function to determine reliability, which is hard to obtain in this case, a mathematical model is developed conditioned on the common factor to derive the failure probability density function and the system reliability function. Maximum likelihood estimators are developed to estimate model parameters. Two realistic numerical examples to illustrate the efficiency of the proposed procedure are also presented. One example is for the critical components of a processing plant each monitored by sensor outputs, and the second example pertains to a mechanical structure subjected to cyclical loading with wear measures recorded at different critical component locations.