This document intends to provide a quick guide to determine the factors/ interaction of factors that would have statistically significant effect on the output of interest. A simple way to do so is by constructing a normal probability plot of effects. Figure 1 is an example of such plot. Data points that fall along the straight line (black dots) correspond to factorial effects with negligible influence on the output; while outliers that deviate greatly from the line (red dots) are factors/ interaction of factors that have a significant effect on the output. Figure 1 illustrates that factors A,C,D, and the interaction between factors A and D, are primary factorial effects that influence the output.
Figure 1: An example of normal probability plot
The experiment of interest aims to evaluate the joint effects of four factors on injection molding products’ critical dimension. The four factors are listed in Table 1, with an alphabet assigned to each factor for easy referral in this report. AMold Temperature
Table1: Four factors under investigation
Single replicate Factorial design is chosen for the investigation as it provides the smallest number of runs for which k factors can be studied in a complete factorial design. With four factors of interest, each at two levels, an experimental measurement from each of treatment combinations are required for the analysis. Table 2 shows the setting of the four factors for all treatment combinations.
3.0Construction of Normal Probability Pots
This section provides instruction on how to construct a normal probability plot with measurements obtained from the treatment combination runs in Section 2.0. Step 1: Tabulate effect estimates for each factorial effect Formulas for the calculation of effect estimate of each factorial effect can be determined from the factorial chart shown as Table 3. Sample calculation of effect estimates for factorial effect A and AB are in Appendix A. Plus or minus signs in the Table 3 indicates the sign of each treatment combination term in the formula; is the number of replicates performed per treatment (n=1) and is the number of factors under investigation (n=4).
**Note: Random numbers are assigned as measurement values from each treatment combination run for demonstration purpose. One must replace the values in the table with actual experiment observations once all the treatment combination runs are performed. Step 2: Rank the effect estimates of all factorial effects in ascending order. Let be the effect estimates resulted from step 1. Arrange the values in an order of , such that is the smallest observation, with being the largest. Let be the total number of terms . Step 3: Constructing the plot
Plot (y-axis) against the ordered values (x-axis) on a piece of normal probability paper. Draw a line of best fit through the plotted points. When the best fit line is drawn, one should focus more on points near the middle of the plot rather than the extreme points. A good of thumb is to draw the line approximately between the 25th and 75th percentile points. Step 4: Observe the plot
Data points that deviate from the best fit line are factorial effects with significant effect on the output.