Reliability assessment of the spindle systems with a competing risk model

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.