In order to reduce the equipment failure frequency and maintenance cost, equipment failure must be effectively predicted. Consider that the actual failure interval of equipments is to contribute to maintenance planning and scheduling, it is used to statistical analysis the failure trend. According to the historical data of maintenance, the failure time distribution function can be built by gray prediction theory. This paper discussed the influence on model relative error made by the

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... of GM(1, 1) model background value. The result is that the model relative error can be reduced through adjust the value of the background. The application of PSO optimized the background value of GM(1,1) model. Finally, an engineering example verified the conclusion.