Integrated robust design using probability of conformance metrics

This paper presents an integrated approach to robust product design using a probability of conformance metric. By integrated we imply that parameter design and tolerance design are performed simultaneously. The probability metric measures conformance of quality characteristics (responses) with respect to their specified limits, or tolerances. Probability is calculated from joint probability distributions of the design variables using first order reliability methods (FORM). When multiple quality characteristics arise, it is convenient to determine the probability of the union of the non-conformance regions. This probability combined with unit scrap costs is used to directly evaluate the so-called loss of quality costs. Any appropriate model of the production costs may be invoked. The methods used in this paper are model-based and the models can be mechanistic or derived using response surface methodology or any other method. An algorithm is presented that minimises the sum of production costs and loss of quality costs. The method herein is quite different from the expected loss approach. In this paper, the method is discussed and compared with expected loss approaches using two supporting examples.