Constructing a Competing Risks Model for the Combined Structure with Dependent Relations

The rapid growth of engineering technology and the emergence of systemized and large-scale engineering systems have resulted in complexity and uncertainty throughout the lifecycle activities of engineering systems. This complex and large-scale engineering system consists of numerous components, but system failure can be caused by failure of any one of a number of components. There is a real difficulty in managing such a complex and large-scale system as a part. In order to efficiently manage the system and have high reliability, it is necessary to structure a system with a complex structure as a sub-system. Also, in the case of a system in which cause of failures exist at the same time, it is required to identify the correlation of the components lifetime and utilize it for the design policy or maintenance activities of the system. Competitive risk theory has been used as a theory based on this concept. In this study, we apply the competitive risk theory to the models with combined structure of series and parallel which is the basic structure of most complex engineering systems. We construct a competing risks model and propose a mathematical model of net lifetime and crude lifetime for each cause of failure, assuming that the components consisting a parallel system are mutually dependent. In addition, based on the constructed model, the correlation of cause of failure is mathematically analyzed and the hazard function is derived by dividing into net lifetime and crude lifetime