Identifying Significant Effects In Two-level Experiments

In industrial experiments,a basic purpose is to identify significant effects which affect the response.Due to experimental conditions and costs,the experimenters usually cannot afford a large number of experimental runs.Then the unreplicated fractional factorial designs are often used.In the unreplicated factorial experiments,we cannot conduct the variance analysis unless we assume that some high-order effects are zero and use the corresponding degrees of freedom to estimate the error variance.There are lots of methods for identifying significant effects in unreplicated regular two-level factorial experiments.Some methods are straightforward but highly subjective,such as half-normal plot method(Daniel,1959,1976).Some methods are a little more efficient but complex and hard to operate,such as Box and Mayer's method(1986).Some methods are easy to operate but less efficient,such as Lenth's method(1989),Dong's method(1993),Ye and Hamada's method(2001).The similarity of these three methods is that both the methods give a robust estimate ? of the standard deviation ? of the response variable and define a statistic using effect estimators and ?.Lenth's method is robust to the outliers,in which ? is estimated with the median,but it is a little conservative in practice.Dong's method is an improvement of Lenth's method,but the estimate of ? becomes too large with the increase of the ratio of the significant effects.Then the test efficiency gradually decreases.Ye and Hamada modified the critical value of the statistic in Lenth's method,which increases the efficiency of identifying significant effects.But when the ratio of the significant effects is a little higher,the test efficiency becomes much lower.This thesis proposes a new method to estimate ?,i.e.,gives an estimate of ? with pre-judging ba:sed on prior information,then defines a statistic with it.The new estimate is more accurate,and the proposed method is objective,easy-to-operate,and high-efficient.This thesis compares the proposed method with Lenth's method and Dong's method about the power,the the probability of correctly selecting the significant effects and the MSE of the estimators of ? using two types of Monte Carlo simulation.When the ratio of significant effects is smaller(e.g.5%,10%),Dong's method performs best,and the proposed method is sightly worse than Dong's method and obviously better than Lenth's method.When the ratio of significant effects is larger than 20%,the proposed method performs much better than Lenth's method and Dong's method.The thesis analyzes five real examples to compare the proposed method with Lenth's method,Dong's method,and half-normal plot method.Results show that the proposed method can not,only identify stronger-significant effects which Lenth's method,Dong's method and half-normal plot method can identify,but also weaker-significant effects which the three other methods cannot identify.In practice,we usually cannot know the ratio of significant effects ahead of time.The proposed method performs well and stable in each case,so it can be widely used.Especially when we know in advance that the ratio of significant effects is higher or there are some relatively weaker-significant effects,the proposed method is a good choice.