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This paper concerns the role of experimentation in engineering design, especially the process of making improvements through parameter design. A simple mathematical model is proposed for studying experimentation including a model of adaptive one-factor-at-a-time experimentation. Theorems are proven concerning the expected value of the improvement provided by adaptive experimentation. Theorems are also proven regarding the probability that factor effects will be exploited by the process. The results suggest that adaptive one-factor-at-a-time plans tend to exploit two-factor interactions when they are large or otherwise exploit main effects if interactions are small. As a result, the adaptive process provides around 80% of the improvements achievable via parameter design while exploring a small fraction of the design alternatives (less than 20% if the system has more than five variables).

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Abstract. This paper considers the application of game theoretic concepts to the dynamics of interactions among the designers in an engineering systems design problem under a distributed decision making environment. Among all the possible distributed frameworks, we focus on two types of frameworks in the system design field, the simultaneous and the sequential response frameworks. In the investigation of the simultaneous response framework, we apply the concepts of learning theory to construct insights into the dynamics among the designers and to address convergence and other challenges of the decentralized design problems. We use a special class of games, the potential game, to demonstrate the effectiveness of the sequential response framework which points out a prospective application of game theoretic concepts to future distributed engineering systems problems.

This paper considers the problem of achieving improvements through adaptive experimentation. To limit the focus we consider only design spaces with discrete two-level factors. We prove that, in a Bayesian framework, one factor at a time experimentation is an optimally efficient response to step by step accrual of sample information. We derive Bayesian predictive distributions for experimentation outcomes given natural conjugate priors. Using an example based on fatigue life of weld repaired castings, we show how to use our results.