Abstract: To apply Bayesian theory to numerical control(NC) system reliability assessment, a method to get two-parameter joint prior distribution is proposed by maximum entropy principle. The general analytical two- parameter prior distribution of Weibull is obtained using maximum entropy principle under several different constraints. Then considering to solve the specific form of the joint prior distribution, a method to get the two parameters’ moments is introduced by using bootstrap to generate two parameters’ samples, and also how to devolve the unknown parameters of joint prior distribution is shown using nonlinear least square jointed Newton iteration method. At last the robustness of prior distribution is introduced. Combining a set of NC system life data, the robustness of the prior distribution is discussed from two aspects: one is to consider higher moments and the other is to introduce inequality restrictions. Studies show that the robustness of prior distribution is greatly improved considering inequality restrictions. It’s fit for NC system reliability assessment to solve the joint prior distribution using maximum entropy principle with inequality restrictions.

Key words: Bayes method, Maximum entropy, Numerical control system, Reliability assessment