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In the 1980s, Genichi Taguchi, a Japanese quality advisor, claimed that most of the variability affiliated with the response could be attributed to the company of unmanageable (noise) factors. In some practical cases, his modeling proposition evidence leads the quality improvement to many runs in a crossed array. Hence, several researchers have em-braced noteworthy attitudes of response surface methodology along with the robust parameter design action as alternatives to Taguchi's plan. These alternatives model the response's mean and variance corresponding to the combination of control and noise factors in a combined array to accomplish a robust process or production. Indeed, using response surface methods to the robust parameter design minimises the impression of noise factors on assembling processes or productions. This paper intends to develop further modeling of the predicted response and variance in the presence of noise factors based on unbiased and robust estimators. Another goal is to design the experiments according to the optimal designs to improve these estimators' accuracy and precision simultaneously.

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Production of high-quality products necessitates identifying the most influential factors, among many factors, for controlling and reducing quality variation. In such a setting, the factorial designs are utilized to determine the active factors with maximal information and model an appropriate relation between the factors and the variable of interest. In this regard, robust parameter designs dividing the factors to control- and noise factors are efficient methods for offline quality control for stabilizing the quality variation in the presence of the noise factors. Interestingly, this could be achieved through exploiting active control by noise interactions. One needs to experiment with numerous treatments to detect the active interaction effects. Search designs are suggested to save treatments, and a superior one is recommended among the appropriate ones. To determine the superior design, one needs a design criterion; however, the existing criteria could be more beneficial for robust parameter designs. In this paper, we proposed a criterion to rank the search designs and determine the superior one.