Stochastic and Fuzzy Decision Problems in Three-Workpiece Lapping Process

Abstract

The basic, remarkable properties lying in the three-workpiece lapping process were previously described by the authors. It was assured there that highly flat surfaces can be obtained predicting and controlling the change in shape of the three workpieces. A methodology of an optimal handling of the process was also developed in another paper, regarding the process as a deterministic one. A modified but more practical discussion is taken up here taking into consideration the stochastic behavior of the process. In so doing, a stochastic treatment in the dynamic programming approach is introduced with the reformulation of the process dynamics as a stochastic differential equation. The concept of fuzzy sets is also employed in order to overcome the difficulty in setting the criterion for optimal policies, which seems to be useful in manufacturing fields.