Abstract
The concept of balanced systems has been evolved with many meanings recently, and the research on this topic is a hot and significant issue in the reliability field. In this paper, the system consisting of two components does not fail immediately when it is unbalanced. An imminent unbalanced state is defined that the system experienced before reaching its final failure. According to the sojourn time of the system in the imminent unbalanced state and the number of transitions from the balanced to imminent unbalanced states, two new failure criteria are proposed. Combined with the situation where the system components may be permanently damaged, three types of competing risk models are developed for multi-state balanced systems with multiple failure criteria, which are time threshold models, count threshold models and the mixed threshold model. The closed-form formulas of reliability indexes of the multi-state balanced system under five proposed models are obtained by using the theory of aggregated stochastic processes, such as the probability density function of the system lifetime. The extensions to systems with multiple components are discussed. Finally, numerical examples are provided to illustrate the proposed model and the obtained results.
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