Abstract: The reliability model established by the traditional statistical method for small sample failure data may be biased in the real case, so a modified reliability modeling method for small sample was proposed using Bootstrap-Bayes approach. Firstly, the reliability function about time between failures using empirical modeling method was established, and then the accurate the parameters prior distribution of Bayes method was provided. This method improves the precision of prior distribution built by traditional empirical method. In order to calculate the posterior distribution of parameters, Monte Carlo simulation was developed. Finally, a real-world example of the spindle of one kind of machining center was presented using the proposed approach to show its potential application. The results show that the proposed method can provide an accurate reliability model for small sample failure data.

Key words: machine tool, CNC machine tool, Bootstrap, Bayes, reliability, small sample