Reliability analysis of systems considering clusters of dependent degrading components

A new system reliability model is developed for complex multi-component systems when each component experiences multiple failure processes, and component degradation paths are stochastically dependent. The components degrade in clusters that behave similarly. Gamma process models are used to model the stochastic processes of individual component deterioration. Degradation paths of different components are clustered into different classes corresponding to different operational conditions or stresses. In this new model, hard and soft failure processes for each component are dependent due to simultaneous shared exposure to a shock process, and furthermore, degradation paths among components are also considered to be probabilistically dependent. Degradation paths of components, not considering shock exposure, are often assumed to be independent, which is a common assumption, and it is often a realistic assumption. However, this new model is for the cases when pure degradation paths of different components are dependent in such a way that they can be classified into groups. One reason degradation paths could be dependent is because the components can be physically in contact or close to each other, and the degradation of one component impacts the other ones. Alternatively, random factors like temperature, wind speed, exposure to a polluted environment, etc., can affect degradation paths of all the components at the same time when components exist in a shared environment, causing another form of dependence. The new reliability model, considering stochastically dependent degradation paths among components, can be more realistic and practical for some applications. This is a new model when stochastically dependent component degradation paths are used in reliability models for systems subject to dependent competing failure processes.