Abstract: In a polyester staple fibre plant the spin pack is one of the key facilities in the process of polyester staple spinning and its performance directly affects the productivity and fibre quality. The spin packs have to be replaced periodically. The problem is to determine the time that the spin packs should be replaced so as to minimize the total cost in a given planned period, including the operating cost and replacement cost. As an equipment updating problem, it is modeled with a dynamic programming (DP) method given to solve it. The model and algorithm are applied to the actual data collected from a large-scale petrochemistry plant, and the computational results are compared to the data generated manually in the plant to verify the effectiveness of the proposed method. It is found that 6%-10% of the total cost is saved on average.