Traditional reliability assessment of spindle systems of machine tools suffers from long testing time and high cost. Accelerated life testing is an alternative that overcomes the shortcomings of traditional reliability testing. In a life testing, identification of critical factors of service life and an accurate model are important. Based on the characteristic analysis and engineering experience, four reliability factors, which are the average power of spindle systems, the number of tool changing, the number of spindles restarting and environment temperature, are selected as accelerating environment variables. An accelerated failure time model is used to describe the inverse relationship between the variables and reliability for the catastrophic failure mode and the degradation failure mode separately. Then a competing risk model is built by considering competing risks of two modes. Parametric reliability models are proposed to capture the statistical independency and dependency separately, in which the Gumbel–Hougaard copula function is used to establish the joint cumulative distribution for dependency. Thereby the hypothesis testing is developed to determine the failure modes dependency. The reliability sensitivity of each environment variable is analyzed. Finally, the proposed model is illustrated with a real field case study.

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A spindle system is one of the key subsystems of machine tools, whose reliability affects machining precision and production cycle directly. In the field, spindle systems expose to operating environmental conditions and complex working conditions that are referred to as stresses in this article collectively, which can accelerate or decelerate the process of failure. In order to analyze field reliability of spindle systems, the main structure, failure modes of spindle systems are analyzed, and main stresses involved with reliability are determined preliminarily. Then, based on the failure mode and the characteristics of stresses, a linear relationship of stresses and field reliability is built based on generalized Arrhenius models assuming that stresses are independent of each other. The non-linear, coupling relationship of stresses is described by a support vector machine model, whose parameters are selected by cross-validation. Then, two models are integrated to a composite model for minimum assessment error using optimal combined forecasting method. Finally, the proposed model is validated by a real case study, and the assessment errors conform to the production requirement.

Accurate optimal design for the test plan with limited prior information is impossible since the optimal design method of a three-stress accelerated degradation test plan for a motorized spindle is based on the determination of model parameters. In order to optimize the test plan with poor prior information, a “dynamic” optimal design method is proposed in this article. Firstly, a three-stress accelerated degradation model with a stress coupling term is established based on the correlation of the degradation rate of the motorized spindle, and the parameters in the model are regarded as variables to represent the deviation between the prior information and the true value of the motorized spindle when the prior information is poor. Then, based on the information theory and the sequential design method, an optimal design method of the three-stress accelerated degradation test plan of the motorized spindle with the information entropy as the objective function is proposed to realize the “dynamic” optimization of the test plan. Finally, the usability of the proposed method is verified by taking a Chinese model spindle as an example, and the validity of the method is verified by checking the model accuracy of the accelerated degradation model of the motorized spindle after the test.

This paper presents a new optimization criterion considering stress weight based on Ds-optimality to solve the low estimation accuracy problem of some stress model parameters when using the existing optimization design criteria to optimize the multistress accelerated degradation test scheme. First, the accelerated degradation model and constraints are determined by analyzing the test characteristics of step-stress accelerated degradation test (SSADT) with multistress. Then, the weight of each stress is identified by fault tree analysis and potential improvement value methods. Combined with the tabu search–particle swarm optimization (TS-PSO) algorithm, the SSADT with multiple stresses of the optimization design process is given. Finally, taking the SSADT with multistress optimization design of motorized spindle as an example, the practicability of the method is verified, and the optimization results are compared with those under D-optimality and Ds-optimality to validate the effectiveness of the method.