Robustness in design of experiments in manufacturing course

Design of experiment (DOE) is a statistical method for testing effects of input factors into a process based on its responses or outputs. Since the influence of these factors and their interactions are studied from the process outputs, then quality of these outputs or the measurements play a significant role in a correct statistical conclusion about the significance of factors and their interactions. Linear regression is a method, which can be applied for the DOE purpose, the parameters of such a regression model are estimated by the ordinary least-squares (OLS) method. This method is sensitive to the presence of any blunder in measurements, meaning that blunders significantly affect the result of a regression using OLS method. This research aims to perform a robustness analysis for some full factorial DOEs by different robust estimators as well as the Taguchi methodology. A full factorial DOE with three factors at three levels, two replicants, and three replicants are performed is studied. Taguchi's approach is conducted by computing the signal-to-noise ratio (S/N) from three replicants, where the lower noise factor means the stronger signal. Robust estimators of Andrews, Cauchy, Fair, Huber, Logistic, Talwar, and Welsch are applied to the DOE in different setups and adding different types and percentages of blunders or gross errors to the data to assess the success rate of each. Number and size of the blunders in the measurements are two important factors influencing the success rate of a robust estimator. For evaluation, our measurements are infected by blunders up to different percentages of data. Our study showed the Talwar robust estimator is the best amongst the rest of estimators and resists well against up to 80% of presence of blunders. Consequently, the use of this estimator instated of the OLS is recommended for DOE purposes. The comparison between Taguchi’s method and robust estimators showed that blunders affect the signal-to-noise ratio as the signal is significantly changed by them, whilst robust estimators suppress the blunders well and the same conclusion as that with the OLS with no blunder can be drawn from them