Allocation of the equipment path in a multi-stage manufacturing process

The allocation of equipment in a multi-stage process is discussed in this article. In most of the multi-stage manufacturing processes, multiple equipment are operated to minimize the waiting times between stages. Thus, the allocation of the equipment path becomes an issue in choosing the equipment for the next stage. In solving the allocation problem of the multi-stage process, it is assumed that main effects and two-way interaction effects for the two adjacent stages are significant. The efficient allocation problem for the multi-stage process for a given historical data is solved by the general linear model approach, and then the predicted responses are ordered to choose the subsequently optimal equipment paths. The effectiveness of the proposed allocation strategy is evaluated in terms of the probabilities for detecting all true effects and detecting optimal equipment path for three cases of precisions: baseline, precise errors and noisy errors. It turns out that the noisy error case is less efficient than the others. When it is possible to use pilot experiments, the efficiency of the product design of orthogonal arrays for two-level and three-level fractional factorial designs is compared to that of the random selection of factorial design points. It is shown that the former is more efficient than the latter in a case study.