| The experimental design has received much attention and extensive development,and been used in industry and agriculture to improve the quality,reduce the costs and prolong the life of the products since Fisher used it in agricultural production in 1920s.Replication is one of the fundamental principles in the experimental design.However,when we carry out an experiment,with the constraint of the costs and other external conditions,we have to run the experiment without replication in most cases.Due to the fact that the two level experiment is commonly used,we mainly study two level unreplicated factorials.It is one of the important issues to identify significant effects in unreplicated experi-ments.Daniel(1959,1976)used the half-normal plot or normal plot to identify significant effects.But this method is somewhat subjective.Box and Meyer(1986)calculated the poste-rior probability of the effects to identify significant effects.This method requires specialized software and the computation is complex.Lenth(1989)provided a simple and effective method(PSE method).However,this method is too conservative and cannot identify the potential significant effects whose levels of significance are not very high.Dong(1993a,1993b)used the average of the sum of square of the nonsignificant effects as an estimate of the variance of the experiment error,and gave a new method(modified PSE method)for identifying significant effects.This method does not perform very well when the levels of significant effects are not very high.This thesis proposes two methods to identify significant effects.The first method uses the relationship between range and median of the absolute effects to identify significant effects.The second method uses the geometric average of the absolute effects as the estimate of the standard deviation of the error to construct test statistic for identifying significant effects.In the first method,when the range is greater than a times the median,the effect with the largest absolute value is significant,where the value of a is obtained through simulation.Repeat this process to identify all significant effects.The second method firstly uses 60%of the effects with the smallest absolute value to estimate the standard deviation of the error.If some effects of the remaining 40%are nonsignificant,then we estimate the standard deviation by combining the nonsignificant effects with the first 60%effects.Repeat the process until all the remaining effects are significant.We compare the two methods with the PSE method and the modified PSE method through simulation.The results show that the proposed methods have an increase in the frequency of the recognized significant effects that contain the true significant effects.At last,we apply the two new methods to five examples and compare them with the half-normal plot method,posterior probability method and PSE method.Results show that the two new methods can identify more potentially significant effects than the half-normal plot method,posterior probability method and PSE method. |
