Partitioning the Production Processes When Assembling a Bore and Shaft

The problem of assembling of two mating parts is considered. Making use of the probability distributions of the bore and shaft, and the specifications on the fit between them, it is desired to define the dimensions of separate groups for the bore and for the shaft that these parts can be placed in, such that the specifications on the fit when parts in these groups are assembled will be met with certainty. This is accomplished by formulating an optimization problem such that the number of such groups is made a minimum subject to a specified lower bound on the sum of the probabilities of a sample lying in each group, and introducing a method of generating approximate solutions. The method makes use of the ‘solver’ and ‘chart wizard’ functions that are contained in Microsoft Excel. Using the dimensions of the groups, an expression for the expected number of assemblies generated by each group is presented.