A Regression Approach for Discovering Small Variation Around a Target

SUMMARY In the rubber industry, experiments are performed to examine how certain output characteristics are related to the design factors in the development of a rubber compound for tyre tread. Traditional approaches focus on adjusting the mean of an output characteristic to a target value. Our aim is to search for levels of the design factors which minimize the between‐units variation of the output characteristic, subject to the constraint that the mean be still on target. In this regard a regression approach is now proposed and its relationship with some traditional methods, such as the ‘performance measure independent of adjustment’ (PERMIA), is examined. The regression approach enjoys the following properties: it permits a two‐step optimization, and a subsequent change in the targeted value can be easily accommodated by adjusting the variables identified in the second stage; it does not require the form of PERMIA to be known in advance; it is computationally simple, requiring only standard regression routines. Another example, dealing with effects of factors in the ability of a printing machine to apply colouring ink, is also given for illustration. The method, as a by‐product, suggests a suitable transformation of the response for the approach advocated by Box.