Numerical approximation approach to the producibility of composite position tolerance specifications for pattern of holes

This paper presents an iteration scheme to approximate the producibility of a pattern of holes controlled by a composite position tolerance and produced by an imperfect process. First, the producibility of a two-hole pattern subject to any of three composite position tolerance variants was evaluated by way of numerical integration. The method was then extended to the evaluation of any pattern of n holes (n > 2) by decomposing the pattern and embedding the two-hole numerical approximation algorithm in an iteration scheme. A performance evaluation of the results returned by the numerical approximation against those obtained by simulation was performed and showed very satisfactory performance with a substantial saving in computation time.