试验设计是试验成败的重要因素。在实施之前,应该检查其试验点分布的均衡性和变量之间的相关性。如果设计中包含 完全相关的因子,这些相关的因子一定会使回归分析的增广矩阵蜕化,计算溢出导致计算失败。某些防止计算崩溃的措施可能导致因素选择不正确,这种错误使不显著的因子被选取,而显著因子被舍弃,推断的优化工艺没有意义。即使设计中包含高相关因子,也存在矩阵蜕化的风险。
向后逐步回归分析允许设计有一定的相关性,可以得到比较准确的效应估计,但完全或甚高相关仍然是不允许的。向前逐步回归过程可能会选取不显著因子,漏掉显著因子。因此,向前逐步回归在某些方面有用,但不赞成用向前逐步回归作为因子筛选工具。如果您没有向后逐步回归程序,就应该严格地审查试验设计的质量。
试验点分布很不均衡的设计应该避免,特别是试验点集中分布在一两条直线上包括 “X”形分布的情况。它同样包含导致错误的实验结论的风险。
本程序通过各种参数审查试验设计的相关性和试验点分布的均衡性, 供试验设计工程师参考。
Figure 1: The main interface of EDExaminer, a matrix of 9 × 13 is loaded in where
The experimental design is an important factor for the success or failure of the experiment. Before implementation, It should be checked whether the distribution of experiment points is balanced and whether the correlation between variables is weak enough should be checked. If the design included completely correlated factors, then these correlated factors will definitely make the augmented matrix of the regression analysis degenerated, and the calculation will overflow and cause the calculation to fail. Some measures that prevent the program from crashing caused the factors selection to be incorrect, This error may cause insignificant factors to be selected but significant factors to be discarded, the forecast equation is incorrect, the inferred optimized process may be meaningless. Even if the design contains high correlation factors, there is a risk of matrix degradation.
Using the backward stepwise regression analysis, a certain degree of correlation between factors is allowed, and a more accurate effect estimate can be obtained, but complete or very high correlation is still not allowed. Using the forward stepwise regression, insignificant factors may be selected but significant factors may be omitted. The forward stepwise regression is useful in some aspects, but it is discouraged as a factor screening tool. If you did not the backward regression procedure, you should strictly review the quality of the trial design.
Designs including very uneven distribution of experiment points should be avoided, especially when the experiment points are concentrated on one or two straight lines included and the "X"-shaped distribution, who contains the risk of causing false experimental conclusions.
This program examining the correlation of the experimental design and the balance of distribution of the experiment points for reference of experiment designers.