Critical values of the test statistic proposed by Al‐Shiha and Yang (1999) for analyzing unreplicated factorials are estimated by fitting an appropriate linear model. Some important properties of the test are also provided.

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A multistage procedure, which is based on the likelihood principle, is proposed to identify active effects in unreplicated factorial designs and their fractions. The proposed procedure controls the experimental error rate (EER) at any prespecified level in industrial and biomedical experiments. Extensive comparison with Lenth's (1989) test is discussed.

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The design criterion considered is minimization of the variance of the estimated slope of a response surface mazimized over dl points in the factor space. Optimal designs under the minimaz criterion, within some classes of commonly used designs, are derived for third-order polynomial models over hypercubic regions.