Development of a highly efficient and resistant robust design

Abstract

Robust design uses the ordinary least squares method to obtain adequate response functions for the process mean and variance by assuming that experimental data are normally distributed and that there is no major contamination in the data set. Under these assumptions, the sample mean and variance are often used to estimate the process mean and variance. In practice, the above assumptions are not always satisfied. When these assumptions are violated, one can alternatively use the sample median and median absolute deviation to estimate the process mean and variance. However, the median and median absolute deviation both suffer from a lack of efficiency under the normal distribution, although they are fairly outlier-resistant. To remedy this problem, we propose new robust design methods based on a highly efficient and outlier-resistant estimator. Numerical studies substantiate the new methods developed and compare the performance of the proposed methods with the ordinary dual-response robust design.