A probabilistic search method for sequential tolerance control

Tolerance control is the set of practices used to ensure that parts are made within their specifications. Sequential Tolerance Control (STC) is the practice of using the results of earlier operations in the execution of a process plan to locate appropriate set points for later operations. In a previously developed set-point adjustment method, the largest sphere that fits into the remaining feasible space is moved to its extreme positions in the coordinate direction of the next operation, x_k, and the next set point is positioned at the mean of the kth coordinates of the centres in these two positions. Scaling the feasible space in proportion to the variability of each operation has also been investigated. This paper presents a probabilistic search method for STC. This method finds the new set point by using the Nelder-Mead downhill simplex method to optimize an estimation of the expected process yield. Probabilistic search is found to be about as effective as sphere-fitting methods for normally distributed process deviations, but for skewed distributions, the search method is shown to yield better set points than previous methods.