## 1 Introduction  
With the development of industrialization, the accuracy of predicting the health status of equipment is becoming more and more demanding. Once an enterprise makes a wrong analysis of its health condition it is likely to cause a lot of property damage and even endanger the lives of employees. Therefore, timely and accurate assessment of equipment health and prediction of its remaining service life has become the object of more and more scholars' research. It is difficult to measure the cycle test data of the whole life of mechanical products, and the high cost and long period of obtaining life information through reliability tests lead to difficulties in the application of residual life prediction methods based on big data theory. Life test data generally have small sample sizes, unbalanced sample structure, and low information coverage of the data set. Therefore, in the process of residual life prediction, we can only fully exploit the potential value of these small-sample data to produce more accurate and credible residual life prediction results. Facing the engineering demand of residual life prediction in the context of small samples, the theory of residual life prediction for small samples has been developed significantly in recent years. With the progress of computing tools, the life prediction methods and accuracy have been continuously updated and improved. From the perspective of data types, the theory of small-sample residual life prediction can be divided into prediction method systems such as the residual life prediction method based on failure time data, the residual life prediction method based on performance degradation data, and the residual life prediction method based on multi-source data fusion. The method of residual life prediction based on the failure time data is usually on the basis of the failure time of the system. On the basis of assuming the form of the system life distribution, the parameters of the system life distribution are estimated by the method of statistical inference, and then residual life distribution of the system after a period of time is obtained. Whether the form of the system life distribution is suitable or not directly affects the accuracy of the residual life prediction results. [PERSON] (1988) and others summarized the commonly used lifetime distribution functions and discussed the parameter estimation methods for the corresponding distribution functions. In order to broaden the sources of available data and keep the failure mechanisms of the system constant in different environments, we can perform the residual life prediction by accelerated life test and the environmental factor folding method to obtain the failure time data in a short time and then convert it to the life distribution under a normal environment ([PERSON], 1991; [PERSON], 1991). It is too expensive for modern mechanical products through life testing to obtain failure time data, and with the rapid development of condition-monitoring technology, it is increasingly convenient and fast to obtain performance indicators characterizing the health status of the system, so the use of the residual life prediction method based on failure time data is gradually reduced, while residual life prediction methods based on performance degradation data are slowly gaining popularity among experts and scholars. The residual life prediction method based on performance degradation data can establish the performance degradation trajectory of the system based on the historical operation data of the system and determine the residual life of the system by setting the failure threshold of the system and determining the moment when the amount of performance degradation of the system reaches that value. This kind of method does not need complete monitoring data after complete system failure, but rather need to monitor the system based on actual predicted needs, considering constraints such as time and cost, so as to obtain the corresponding performance degradation data.