Accelerated Life Reliability Evaluation of Grating Ruler for CNC Machine Tools Based on Competing Risk Model and Incomplete Data

Grating rulers are high-precision linear displacement sensors used in the servo control system of CNC machine tools. Due to the long lifetime of these rulers, evaluating their reliability level by using traditional methods takes huge amounts of time and resources. Meanwhile, some incomplete data are observed in the failure data, which will cause inaccurate evaluation results. In this study, an accelerated life reliability evaluation method of a grating ruler based on a competing risk model and incomplete data is proposed. Firstly, according to the characteristics of the grating ruler, the life distribution model based on competitive risk is established. The representation and conversion methods of failure data, considering incomplete data, are also proposed. Secondly, the accelerated life test (ALT) system is set up, and the 4500 h step stress ALT is conducted. Results indicate that the reliability level of the grating ruler is MTBFt = 8864.12 h, and that of each subsystem is MTBFt(MS) = 13,351.98 h, MTBFt(OS) = 14,283.48 h and MTBFt(ES) = 17,038.65 h. The advantages of the proposed method are that it is helpful in determining the subsystem with the highest failure rate in each stage and puts forward targeted suggestions for subsequent improvement designs.