Robustness Of Some Methods Of Analyzing Saturated Unreplicated Factorial Designs

In many industrial applications, unreplicated factorial designs become more and more popular. Because they need less experiments and focus on more contrasts, they can bring great benefit. No degrees of freedom left to estimate the error variance when the data of this design are analyzed, so the standard ANOVA can't be used. Some methods of analyzing unreplicated factorial designs have been used in practice so far. Usually they assume that the experiment indexes are normally distributed. But in fact the experiment indexes are not always like that. For example, the lives of products are often from some Weibull distribution in the reliable experiments. This paper studies five representative methods of analyzing saturated unreplicated factorial designs on identifying active contrasts and their tests performance when the experiment indexes are separately from normal distribution, exponential distribution and Weibull distribution, and also discusses the relation between power and the inverse of coefficient of variation by Monte Carlo method when the experiment design is two-level factorial design.