This study develops models for predicting the economic lifetime of drilling machines used in mining. It uses three cases, each represented by a MATLAB code, to develop an optimisation model. The resulting ORT is fed as input to an artificial neural network (ANN) and the results translated into a relatively simple equation. The study finds that increasing the purchase price and decreasing the operating and maintenance costs will increase a machine's ORT linearly. Decreased maintenance cost has the largest impact on ORT, followed by increased purchase price and decreased operating cost. The ANN method gives a series of basic weight and response functions which can be made available to any engineer without the use of complicated software. It also helps decision-makers determine the best time economically to replace an old machine with a new one; thus, it can be extended to more general applications in the mining industry.