Optimal Mean and Tolerance Allocation Using Conformance‐based Design

In this paper, we invoke probability constrained optimization to establish a framework for allocating means and tolerances in design for quality that focuses on customer satisfaction at predictable cost levels. The optimal allocation minimizes the production costs while ensuring that responses conform probabilistically to their specification limits. An overall system probability of conformance is obtained from a quality policy (e.g. defect rate, process capability index). Probabilities are evaluated using limit‐state functions and fast integration methods. The three quality metrics (i.e. target/larger/smaller‐is‐best) and robustness are addressed naturally. The methodology is developed in detail and compared with the traditional minimum total cost approach. Optimal means and tolerances are found for an electro‐mechanical servo system and a power division circuit to illustrate the practicality and potential of the approach.