The primary objective of manufacturing processes is to manufacture products that will perform consistently and acceptably in end-use applications as determined not just by the product attributes (measured infrequently at some point during manufacture), but ultimately by the end-use customer. Manufacturers, hardly ever able to measure these product attributes directly and regularly, are virtually incapable of determining actual product performance. Actual customer feedback on product performance is therefore the most directly relevant indicator of whether or not the product met its end-use performance requirements. Such customer information can (and ought to) be used to adjust the process operations appropriately to ascertain consistent attainment of desired product end-use performance characteristics. However, this feedback is completely missing from the control schemes typically employed on manufacturing processes. One key reason for this omission is the non-availability of a comprehensive technique for utilizing customer feedback information to ensure acceptable product end-use performance.
In traditional manufacturing processes, the most common control schemes adjust process manipulated variables u, (e.g., for a reactive extrusion process, material feed rate and extruder screw speed) to control process variables y, (die pressure, melt temperature, motor power) for the purpose of reducing process variability; some processes may even include higher level schemes for controlling product quality variables q, (e.g. melt index, viscosity) by manipulating set-points for the process variables y. At the next level up in the hierarchy, end-use properties, w, (e.g. tensile strength, toughness, UV resistance) are hardly ever controlled because, if available at all, these measurements are obtained far too infrequently to be useful in any traditional scheme. In refs [1,2] Garge et. al presented a scheme for achieving end-use property control and demonstrated its application on an industrial pilot scale process. From the perspective of the customer, however, that scheme, even if implemented perfectly, constitutes no more than a “predictive feedforward” control of end-use properties; not until the product is used by the customer can we be certain of its actual performance. Just as with standard feedback control, where actual measurements of the desired process outputs are used to adjust process inputs, it is necessary not just to obtain customer feedback, but to employ it directly within a control scheme to take rational corrective action if the product does not perform in end-use precisely as designed. Such a control scheme does not currently exist.
We have developed a technique that addresses this unmet need directly. The customer feedback regulator utilizes customer feedback information (z) to determine appropriate set-point targets for the product end-use properties (w). The key design issues are associated with the following important characteristics of the customer data: it is intrinsically binary in nature (the product either performs as designed, in which case z=1, or not (z=0)); it is available infrequently (once a week, or worse); and it may be delayed significantly. The challenge involved is twofold:
(i) how does one model the customer data z as a function of the end-use characteristics w, particularly because while w is continuous, the dependent variable z is binary?
(ii) How does one use such a model to implement a feedback controller?
First, we discuss the modeling approach which employs binary logistic regression (BLR) [3] whereby w, the continuous end-use characteristics variable, is used to compute π(w), the probability that z=1, i.e. the product with the indicated set of end-use characteristics meets the customer performance requirements. Next, we present a sequential estimation procedure for identifying the BLR model parameters from customer data, and derive a control strategy that uses this model to compute targets for w required to maximize π(w) subject to economic and process constraints. Finally, we illustrate the application with a simulation case study of a prototypical industrial plastic manufacturing process. The results show how, in response to an unmeasured disturbance that shifted process operation into a region where the product acceptability was dramatically reduced, the customer feedback regulator successfully restored customer acceptability to desired levels.
References
1. S.C. Garge, M. D. Wetzel, and B. A. Ogunnaike, On Control of Reactive Extrusion Processes, AIChE Conference, 2006;
2. S.C. Garge, M. D. Wetzel, and B. A. Ogunnaike, An Inference-based Scheme for Controlling Product End-use Properties of Reactive Extrusion Processes, in preparation 2007.
3. D.W. Hosmer and S. Lemeshow, Applied Logistic Regression, 2nd Ed. Wiley Interscience, NY., 2000.