## 1 Introduction  
Measurement accuracy is one of the most important indexes of a measurement system. However, it has been discovered in practice that measurement accuracy is not always constant and that it gradually declines as time goes on [1]. This phenomenon is called \"accuracy loss\". In general, a measurement system often has some components. The accuracy loss of the whole system is a comprehensive result of that of each component. Due to difference principles, structures and parameters, the accuracy loss laws of components are generally different. Once the accuracy loss value exceeds the allowable value, the component is considered as \"failure in accuracy\". There are two situations that can occur in a measurement system: one is that the whole system does not fail in accuracy but some components do, and the other is that the system fails in accuracy but some components do not. Whether the system or its components fail in accuracy, the whole system would be unable to perform normal measurement functions. The emergence of either of these two situations leads to the waste of effective equipment resources and costs. If designers pay attention to the accuracy loss laws of the designed system and its components, and make the accuracy loss values reach their allowable values at the same time, the system can be optimally designed to save resources and costs as much as possible. Much work has been carried out on the accuracy loss laws of some typical systems with mechanical structures, such as screw balls, linear guides, mechanical wear and sensors [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. [PERSON] et al. considered the combined effect of intermittent contact between balls and screw grooves, as well as the multiscale contact effect of surface microtopography, and a modified Archard wear model was proposed to investigate the precision loss [2]. In the stable wear stage, the error between the measured data and the predicted precision loss value was less than 11.94%. [PERSON] et al. conducted a study on the contact wear of a double-nut ball screw, and a precision loss model was established based on raceway fractal characteristics and a full ball load distribution theory [3]. [PERSON] and [PERSON] et al. studied the precision loss law of ball screws under the sliding/rolling mixed motion mode [4; 5]. The precision loss rate was the maximum when the screw rotation speed was 40 r/min and the axial load was 4000 N. [PERSON] et al. proposed a mathematical model to calculate the geometric errors of sliding due to contact deformation and then predicted the positioning errors after long-term operation [6]. To describe the precision loss law of linear ball guides under load conditions, [PERSON] et al. proposed a wear loss model based on the Hertz contact theory and Archard wear theory [8]. [PERSON] et al. studied the accuracy loss laws of main units in a pressure sensing system, and a precision loss model was built based on a neural network (NN) [9]. Moreover, [PERSON] et al. also employed a support vector machine (SVM), an artificial neural network (ANN) and wavelet analysis (WA) to model and forecast the measurement accuracy loss laws [11; 12]. Based on the awareness that the performance of measurement systems will continuously degrade with time, some scholars are committed to developing lifetime prediction methods of mechanical structures [13; 14; 15; 16; 17]. [PERSON] et al. proposed a screw lifetime prediction method based on a wavelet neural network (WNN) and empirical mode decomposition (EMD) [13]. To predict the performance degradation trend of rolling bears, [PERSON] et al. proposed a lifetime prediction method based on an improved regression support vector machine (SVR) [14]. The prediction results of the proposed method are better than those of common methods. [PERSON] et al.