# Review of Machining Equipment Reliability Analysis Methods based on Condition Monitoring Technology
## 4 Reliability Assessment of Machining Equipment based on Condition Information
### Operational Reliability Assessment Method of Machining Equipment
#### 4.1.1 Probability and Statistics Method  
The state information characteristics can reflect the condition of the equipment. So, there must be some mapping relationship between them. In the absence of empirical information to make it difficult to determine the failure threshold, a small amount of historical failure data from similar equipment can be used to establish a mathematical model which describes the potential failure mechanism [65]. There are several representative models, such as the proportional failure rate model, the proportional covariate model and the logistic regression model.  
[PERSON] et al. [66] have proposed a method for analyzing the failure data of aircraft and marine engines using the Weibull proportional failure rate model. The metal element content of the engine was used as a covariate. The research team developed the EXAKT software based on PHM technology. [PERSON] et al. [67] have used the PHM model and the logistic regression model to evaluate the performance degradation and failure probability of the bearing and predict the remaining life of the bearing. [PERSON] et al. [68] have combined the supervised learning method of the correlation vector machine with the logistic regression model to analyze the degradation data of the bearing to predict its failure probability. [PERSON] et al. [69] have evaluated the reliability of the tool and predicted the remaining life of the tool by monitoring the vibration signal during the cutting process and combining the logistic regression model. Combined with Gaussian Mixture Models, [PERSON] [70] has used the negative log-likelihood probability as the degradation evaluation index of rolling bearings and realized the degradation state evaluation of rolling bearings successfully. [PERSON] et al. [71] have proposed a hybrid Weibull Proportional Hazard Model and realized the degradation state assessment and life prediction of high-pressure water pumps. They also demonstrated that the model is suitable for evaluating the performance degradation trend of mechanical equipment systems with multiple failure modes.  
The common idea of the above model is to use the condition monitoring feature index of the historical failure equipment and its corresponding time information to estimate the parameters of the degenerate trajectory model, and then obtain a mapping relationship between the state feature and the health degree. After the new state feature sequence is obtained, the reliability analysis can be performed. Figure 5 shows a flow chart of the reliability evaluation method based on the proportional covariate model. The model established by this method is simple and intuitive. It can quickly determine the degraded trajectory by directly fitting the degraded data. If there is a good understanding of the failure mechanism of the product, the degradation trajectory model can be determined according to the corresponding physico-chemical process by deeply analyzing the failure mechanism of the product. For the mixed effect model of a single random coefficient, the parameter estimation is relatively simple. For the mixed effect model with multiple random coefficients, the calculation process is slightly complicated. The stochastic process model starts with the data. And the degradation model can be given directly according to the characteristics of the data. Then the degradation analyses are performed through data fitting. This method can well describe the uncertainty of the experimental data.  
The above methods have been widely used in the field of mechanical product reliability. But these methods are more based on historical data. In a complex operating environment, due to some external factors, it may cause abnormalities in product performance degradation. These methods cannot optimize the model based on the current state, making the model less accurate.