ノイズ共変量に対するロバスト設計法:機能性の測度を用いた方策

摘要

望目特性ロバストパラメータ設計において，効果を減衰したい要因を実験要因として割り付けずに共変量として観測する場合の設計手順を提案する.いくつかの研究がこの設定を扱っているが，既存の研究は機能性の測度を定義せずに，正規線型モデルの誤差項の正規性にもとづいた検定のみを考えている.それに対して我？？は，有界な非線型函数を用いることによって自然な形で調合誤差因子実験に対応したsignal-to-noise ratioを定義し，それにもとづいた設計法をづえる.また，モデルの誤差項に正規分布を仮定せず，バラメータの最小白乗推定量の漸近正規性に基づいた検定を考える.%We consider a methodology of robust parameter designs in order to reduce effects of noisevariables which are random covariates, not designed values of noise factors. This problem setting is discussed in a few previous works whose design procedures are not based on a certain performance measure but on results of statistical tests of control-by-noise interaction effects which depends on the assumption of the normality in the Gaussian linear regression model. On the other hand, we introduce a model including a bounded nonlinear function, define a signal-to-noise ratio, which is a popular performance measure in the case of compound noise experiments, and propose a design procedure using this performance measure. Additionally, based on the asymptotic normality of least squares estimators for the model parameters, we provide a consistent test which corresponds to the tests in the previous works.