A regression approach for discovering small variation around a target

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 ouptut characteristic to a target value. The present aim is to search for levels of the design factors which minimize the between-units variation of the output characteristics, 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.