Path modeling and process control

Many production processes are carried out in stages. At the end of each stage, the production engineer can analyze the intermediate results and correct process parameters (variables) of the next stage. Both analysis of the process and correction to process parameters at next stage should be performed regarding the foreseeable output property y, and with respect to an admissible range of correcting actions for the parameters of the next stage. In this paper the basic principles of path modeling is presented. The mathematics is presented for processes having only one stage, having two stages and having three or more stages. The methods are applied to a process control of a multi-stage production process having 25 variables and one output variable. When moving along the process, variables change their roles. It is shown how the methods of path modeling can be applied to estimate variables of the next stage with the purpose of obtaining optimal or almost optimal quality of the output variable. An important aspect of the methods presented is the possibility of extensive graphic analysis of data that can provide the engineer with a detailed view of the multi-variate variation in data.