Grey theory is an effective method for studying the performance degradation law of inertia device and for predicting its lifetime.To enhannce the value of new information, the non-equal interval GM (1, 1) model is improved with a weighted model.Considering that it is impossible to obtain an exact predictive value to chaotic data sequence, a new method of grey interval prediction is proposed, making use of the whole data trend together with extreme point information, which can overcome the shortage of extracting boundary function by only using the extreme point.Smooth ratio of the parameter sequence is examined firstly before modeling.The parameter sequence meeting the quasi-smooth condition is to be modeled directly with weighted grey model, and otherwise, grey interval prediction is performed.The example shows that:in direct modeling, the weighted model improves the prediction accuracy to level 1 from level 2;in grey interval prediction, the real value lies within the prediction interval, with the average relative error of its upper and lower boundary prediction being 4.88%, and the prediction effect is significantly improved.