The Weighted Loss Function as a Means of Optimizing Performance

Article

Wong, Henry H.   (1990, ASQC)   Nova Petrochemicals Inc., Sarnia, Ontario, Canada

Annual Quality Congress, San Francisco, CA    Vol. 44    No. 0
QICID: 9490    May 1990    pp. 442-448
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Article Abstract

In designing a product or developing an application, we often have to balance incongruent demands. One way to arrive at a solution is to use a weighted loss function. The components of this weighted loss function are normalized Taguchi loss functions representing each of the demanding specifications. Attached to each of these individual normalized loss functions is a weighting factor that quantifies the relative importance of the specific specification. It is important to agree on these weighting factors before the actual experiment. To do otherwise, may lead to biased interpretations or worse still, a contest of opinions. While the weighted loss function provides us with an objective function that consolidates the output variables, such as the physical properties of a rubber compound, we still need to know how these output variables are influenced by the input variables, such as the ingredients of a rubber compound. Such relationships can be determined with a designed experiment, based on a factorial design or a response surface design. In our applications, we prefer to use fixed designs rather than sequential designs.

There are two major reasons for this choice. The first is that we would like to understand the entire region of interest, so that the knowledge can be applied generally. The second is that the relative weights for the objective function can be different for different customers. In fact, even for a given customer, they can be different for different applications or for the same application at a different time. Once we have determined the system of equations, relating the input variables to the output variables, we can optimize the overall performance by searching the factor space. The algorithm we use involves the following steps: calculate the loss function for each of the apexes, pick the apex associated with the minimum loss, reduce the range of each of the dimensions by one third and then recalculate for the new apexes of the reduced space. We have found that a good estimate of the optimal condition can be obtained with approximately ten iterations. This estimate, however, should always be confirmed by an actual experiment.

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