Effectiveness of a random compound noise strategy for robust parameter design

Robust parameter design has been widely used to improve the quality of products and processes. Although a product array, in which an orthogonal array for control factors is crossed with an orthogonal array for noise factors, is commonly used for parameter design experiments, this may lead to an unacceptably large number of experimental runs. The compound noise strategy proposed by Taguchi [30] can be used to reduce the number of experimental runs. In this strategy, a compound noise factor is formed based on the directionality of the effects of noise factors. However, the directionality is usually unknown in practice. Recently, Singh et al. [28] proposed a random compound noise strategy, in which a compound noise factor is formed by randomly selecting a setting of the levels of noise factors. The present paper evaluates the random compound noise strategy in terms of the precision of the estimators of the response mean and the response variance. In addition, the variances of the estimators in the random compound noise strategy are compared with those in the n-replication design. The random compound noise strategy is shown to have smaller variances of the estimators than the 2-replication design, especially when the control-by-noise-interactions are strong.