Reliability Parameter Interval Estimation of NC Machine Tools considering Working Conditions

Abstract

Aiming at the problem that the parameter interval estimation of NC machine tool's reliability model considering working conditions established by Hongzhou is difficult to implement, given that it has several independent variables, an improved interval estimation method based on Bootstrap is proposed. Firstly, the two-step estimation method was used to calculate the point estimation of NC machine tool's reliability parameter in test field, based on which resamplings are generated based on the point estimation. The reliability parameter's point estimation of the resamplings was obtained by maximum likelihood estimation. Permutation of point estimations was made in ascending order and the interval estimations were obtained by the quantile of the permutation. Case study indicated that the location and length of the interval estimation of NC machine tools' reliability parameter, under different levels of working condition covariates, vary obviously.

Reliability Estimation of Retraction Mechanism Kinematic Accuracy under Small Sample

“…Furthermore, the classical interval estimation method estimates a range of possible values of performance characteristic parameters based on test data. Li et al [12] proposed an improved interval estimation method based on Bootstrap and applied it to the interval estimation of reliability parameters of the NC machine tools under different working conditions. Similarly, Li et al [16] utilized the parameter Bootstrap method for the interval estimation of reliability parameters in the context of rolling bearings within an intelligent tool changing robot system.…”

“…and 𝛽 0 = 𝑣 0 𝜎 0 2 + 𝑘 0 (𝜇 Δ − 𝜇 0 ) 2 (9) with hyper parameters: and the inverse gamma distribution as the prior distribution of 𝜎 𝛥 2 , as shown in Eq. (12).…”