# The DoE Analysis Tool Set

The DoE analysis tool set consists of using graphical as well as statistical analysis to determine which individual factors are significant， and how to set the quality characteristic to its design goal or reduce its variability.

The graphical analysis takes advantage of the Cramer's rule of the solution of simultaneous equations to solve for each value of factor levels. In the L9 orthogonal array in Table 7.5, it takes nine experiments to perform a solution of four factors at three-level saturated design. The average of the results of the first three experiments, Y1, Y2 and Y3, is the average performance of the product or process due to selecting level 1 of factor A, whereas the other factors negate themselves by averaging out their levels. The average of Y2, Y5, and Y8 is the effect of selecting level two of factor B. In this manner, the average of all 12 possible combinations (factors A, C, and D and their levels 1, 2, and 3) is examined in terms of attaining the best result for the product or process specifications. For an L9 with n repetitions, the level values for factor A can be calculated as follows:

The data can be plotted graphically so the intended results of either maximum, minimum, or targeted quality characteristic values can be used to manipulate the design to the intended or “expected” values.

The expected value (EV) of the DoE output is the result of applying all of the recommended levels. This is constructed from the overall experiment average, then the contribution of each recommended level is added to the EV. The contribution is the recommended level value minus the experiment average. The contribution of interactions can be calculated from the selected levels of primary factors.

The EV value is usually calculated for significant factors only. The significant factors are determined by performing the F test using the ANOVA analysis in the next section. The contribution of nonsignificant factors could be lost within the error of the experiment (the confidence interval of EV). If the selected factor levels are within the experiment design as one of the experiment lines, the expected value should equal the value attained by the experiment line, and no calculations are necessary. All expected values are bounded by the confidence interval of the error, as mentioned in Chapter 5.