# Graphical Analysis Conclusions

As can be seen by the example above, Design of experiments can optimize a process or a product easily and quickly by using very simple mathematical techniques. It is also not necessary to have an in-depth understanding of the physics or the chemistry of the process or product to be optimized.

This particular example illustrates how the process average can be shifted to the desired level, in this case to the maximum possible. A similar method can be applied to reduce the variability，with several replications for each experiment line. Four replications are preferable for more than 30 points of analysis, approximating the population distribution of bonding. A mathematical transformation can convert the four numbers into a single number indicating variability. The graphical analysis for variability can be performed on the transformed number. The two analyses for average and variability can be contrasted and factor level selected for the most efficient process improvement through trade-offs of average and variability, if any.

There are two important terms used in DoEs. One is the design space, which is the limit of the investigation of the factors, as bounded by the selection of the levels for each factor. The other is the “direction of steepest ascent.” This is direction of increasing or decreasing the amount of factor level values when expanding the current DoE analysis results in future DoEs.

In the design, space for the bonding DoE, the selection of the levels for factor By the time for ultrasonic cleaning, was optimal, as shown by Figure 7.6. The best-level position was in the middle of the three levels. The maximum point can be calculated by drawing a best fit curve through the three points and thus can be determined accurately, rather than declaring that 3 minutes (level 2) are better than 1 or 5 minutes (levels 1 and 3) of cleaning. A second-order equation can be fitted through the three points and the maximum point can be determined by setting the derivative to zero.

For factor 1, the oven temperature, the design space is not optimal. It can be seen from Figure 7.6 that the level 3 temperature (70°C) results in the highest peel force. But what happens if the oven temperature is higher than 70°C? The current design space does not allow for any conclusions regarding higher temperatures than 70°C. If more information is desired regarding the bonding process, then a second DoE could be performed. Some factors could be expanded in the direction of steepest ascent such as having higher temperature levels, while other factors could be dropped from the experiment (such as chemical used) in favor of partial or full factorial analysis.