Statistical-based tolerance setting by eliciting the loss function reasoining

An issue still open in the statistical-engineering literature concerns the tolerance allocation, i.e. the setting of admitted limits for critical characteristics or performances of interest of the system under study. A common approach to tolerance allocation is based on the idea of Loss function initially developed by Taguchi. Unfortunately, some obstacles prevent from a full exploitation of the Taguchi approach, since despite its clarity and elegance, it is poorly operational. Based on Taguchi’s proposal, researchers have been more concerned on developing different analytical models of loss function than clarifying the reasoning behind the loss function idea. So there is a missing link for a complete interpretation and debate on the loss function. In this paper the authors provide a method to operatively build loss functions from field data and to finally set tolerance limits, starting from an elicitation of the rationale hidden behind the loss function concept. An illustrative example completes the paper.