Abstract: A method of applying fractional GM(r,1) to forecast the demand of the spare parts is proposed for a new concept weapon because of the lack of comparable existing equipment, less historical data on spare parts demand, and the lack of understanding the supportability of equipment. The perturbation bound of GM(r,1) is proven to be smaller than the perturbation bound of GM(1,1) by using the matrix perturbation theory. p-order cumulative matrix is obtained by the first-order cumulative matrix and its matrix multiplication. Based on fractional order differential equation theory, the p-order accumulative matrix is extended to the r fractional order accumulative matrix, and a fractional accumulative gray model GM(r,1) is established. r fractional order difference matrix is obtained by matrix inversion, and the calculation method of r fractional difference is simplified. The optimal value of r in GM(r,1) is determined through genetic algorithm (GA). The GM(r,1) model is applied to forecast the demand of spare parts. The experimental results show that GM(r, 1) model has better prediction performance than GM (1,1) model. Key

Key words: ordnancescienceandtechnology, equipmentsupport, greymodel, sparseparts, demandforecasting, fractionalorder, geneticalgorithm