Product Screening to Multicustomer Preferences: Multiresponse Unreplicated Nested Super-ranking

Abstract

Modern production methods demand the synchronous multicharacteristic optimization of goods. There is a need to diversify a basic product to the importance placed on its individual quality components by a wide spectrum of concerned customers. This work shows how the super-ranking concept may be utilized taking into account relative weights among the implicated responses. The theoretical development is focused on the difficult situation where the optimization is attempted through unreplicated and saturated fractional factorial designs. A nested super-ranking scheme is devised to accommodate a dual weight assignment, first by setting up a single consolidated response per implicated customer and then, in a subsequent step, by incorporating a customer importance rating thus rendering an overall single master response. A demonstration of the proposed method on a pragmatic problem arising in aluminum milling involves optimization due to seven controlling factors concurrently influencing nine product responses modulated by six preference ratings set by a given customer base, respectively. Key benefits of this method are the offered ease of intermixing numerical and categorical data in mainstream multiresponse optimization problems, and keeping customer preferences in perspective through economical, short-cycle screening while relaxing stringent data normality and possible multidistributional effects among the implicated quality characteristics.