We consider a methodology of robust parameter designs in order to reduce effects of noise variables 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.

The Mahalanobis-Taguchi (MT) method is one of the Taguchi methods and a standard method of multivariate analysis for detecting anomalies or recognizing patterns. Particularly in recent years, some case studies have been reported that have used this method for monitoring the operating conditions of production equipment, whose data are acquired from sensors. However, it is difficult to estimate the essential correlation structure from the learning data, because the sensors might record noisy data.

To estimate the essential correlation structure from the data, we propose applying a regularization process based on Gaussian graphical modeling to the MT method. In our proposed procedure, we focus on the fact that the correlation structure estimated by the original procedure is based on the precision matrix. Then, by reducing the number of parameters by replacing the majority of the non-diagonal elements of the matrix to zeroes, we can estimate the essential correlation structure accurately. By analyzing the data from the UCI machine learning repository, and the Monte Carlo simulations, we show that even when the noisy data have been observed, the essential correlation structure can be estimated accurately in our proposed procedure.