This paper outlines the development of a mathematical model for predicting the system reliability of the cutting tools for an automated machining system with various carbide inserts and spares subject to Weibull failures. A numerical method using Simpson's Rule was selected as a method to address the problem of multiple integration resulting from the Weibull distribution in the spares model. A recursive algorithm was developed for predicting the system reliability of the cutting tools. This paper demonstrates the application of the developed reliability prediction model with a realistic example in the interrupted cutting process.