An Integrated Performance Modeling System
An integrated performance modeling system is presented for use in general decision making problems including engineering design, manufacturing process and quality control, and other applications. The system relies on a function matrix that relates decision variables to performance variables. The system utilizes both global and local linearization of non-linear functions, after which the Extensive Simplex Method is used to derive the set of all feasible decisions based upon the specification limits for the performance variables and the control limits on the decision variables. Beyond current Six Sigma best practices, the described system explicitly considers both modeling uncertainty and uncontrolled variation. The specification limits may be automatically tightened by the confidence intervals and variation limits to ensure feasibility to a desired level of confidence and robustness. Three sets of feasible decisions are established including 1) the global feasible set that establishes the extreme limits of feasibility by allowing all the decision variables to vary simultaneously within their range of the control limits, 2) the local feasibility, which shows the immediate feasibility for each decision variable holding other decision variables at their current value, and 3) the controllable feasibility for each performance variable holding other performance variables at their current value. The system provides a perspective view of 1) the function matrix, 2) a historical view of the decision variables which may be used in a manner similar to statistical process control X-Bar charts, 3) a historical view of the performance variables which may be used in a manner similar to statistical quality control charts, 4) a set of decision windows showing the joint feasibility of all pairs of decision variables, which may be used in a manner similar to process windows, and 5) a set of performance windows showing the joint feasibility of all pairs of performance variables, which may be used in a manner similar to Pareto Optimal graphs. An example is provided for a beam design model with four decision variables and three performance variables.