Data analysis guide for Single Replicate Factorial Designs

1.0Introduction

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

2.0Experiment Design

The experiment of interest aims to evaluate the joint effects of four factors on injection molding productsâ€™ 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

BHolding Pressure

CInjection Rate

DCooling Time

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. Runs

Treatment Combination Factorial Effect

ABCD

1(1)----

2a+---

3b-+--

4ab++--

5c--+-

6ac+-+-

7bc-++-

8abc+++-

9d---+

10ad+--+

11bd-+-+

12abd++-+

13cd--++

14acd+-++

15bcd-+++

16abcd++++

Table 2:Test matrix showing possible treatment combinations for a four...

1.0Introduction

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

2.0Experiment Design

The experiment of interest aims to evaluate the joint effects of four factors on injection molding productsâ€™ 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

BHolding Pressure

CInjection Rate

DCooling Time

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. Runs

Treatment Combination Factorial Effect

ABCD

1(1)----

2a+---

3b-+--

4ab++--

5c--+-

6ac+-+-

7bc-++-

8abc+++-

9d---+

10ad+--+

11bd-+-+

12abd++-+

13cd--++

14acd+-++

15bcd-+++

16abcd++++

Table 2:Test matrix showing possible treatment combinations for a four...

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