Statistical guidance for setting product specification limits

Abstract

This document outlines a data-driven probabilistic approach to setting product acceptance testing limits. Product Specification (PS) limits are testing requirements for assuring that the product meets the product requirements. After identifying key manufacturing and performance parameters for acceptance testing, PS limits should be specified for these parameters, with the limits selected to assure that the unit will have a very high likelihood of meeting product requirements (barring any quality defects that would not be detected in acceptance testing). Because the settings for which the product requirements must be met is typically broader than the production acceptance testing space, PS limits should account for the difference between the acceptance testing setting relative to the worst-case setting. We propose an approach to setting PS limits that is based on demonstrating margin to the product requirement in the worst-case setting in which the requirement must be met. PS limits are then determined by considering the overall margin and uncertainty associated with a component requirement and then balancing this margin and uncertainty between the designer and producer. Specifically, after identifying parameters critical to component performance, we propose setting PS limits using a three step procedure: 1. Specify the acceptance testing and worst-case use-settings, the performance characteristic distributions in these two settings, and the mapping between these distributions. 2. Determine the PS limit in the worst-case use-setting by considering margin to the requirement and additional (epistemic) uncertainties. This step controls designer risk, namely the risk of producing product that violates requirements. 3. Define the PS limit for product acceptance testing by transforming the PS limit from the worst-case setting to the acceptance testing setting using the mapping between these distributions. Following this step, the producer risk is quantified by estimating the product scrap rate based on the projected acceptance testing distribution. The approach proposed here provides a framework for documenting the procedure and assumptions used to determine PS limits. This transparency in procedure will help inform what actions should occur when a unit violates a PS limit and how limits should change over time.