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Appendix

Randomizing order of runs for example in Table 2

To randomize the order of the eight runs

• select any column in the table of random numbers such as column 20.

• read the numbers in column 20 starting from the top (i.e. 1, 3, 5, 0, 6, 1, 4, 2, 1, 8, etc). Ignore the numbers that are less than 1 or greater than 8 such as 0 and 9. Also ignore any number when it appears a second time or more, as I does here.

• continue reading until 8 different numbers that are greater than 0 but less than 9 are selected (i.e. 1, 3, 5, 6, 4, 2, 8, 7).

• runs 1, 3, 5, 6, 4, 2, 8, and 7 are performed in that order as shown in Table 9.

Table 9

Run

Factor A

Factor B

Response

Actual example of a two-level factorial design

A locally-owned electronics company in Malaysia used this design to determine the critical factors at its screen printing operation. Four factors were investigated using 16 runs. The factors were varied over two different levels. Further details of this experiment as well as the conclusions that were obtained are given in the case study section of the guidesheet 'Design of Experiments; Improving Your Products and Processes' (Level: Advanced).

Actual example of a two-level fractional factorial design

An actual application of this design in related below. Universiti Sains Malaysia used this design to plan an experiment which involved 7 factors (Oh, 1995). The factors were thought to influence the performance of a machine vision system for measuring the finger length of rubber gloves produced by a manufacturing facility in Malaysia . Each factor was set at two levels. The factors and their levels are as shown in Table 10.

Table 10

Level

Factor

Low (-)

High (+)

1. Factor A-aperture size

2. Factor B-glove fixture

3. Factor C-binarization threshold

4. Factor D-cornerpoint threshold angle

5. Factor E-camera focus

6. Factor F-sobel edge detector threshold

7. Factor G-lightning mode

1.2

Circle

-0.95

1.5

Ambient lightning

2.5

Long

-0.55

5.0

510

External lightning

Only one quarter of the 27 = 128 possible combinations (i.e. 32 combinations) were carried out. The 32 combinations are as shown in Table 11.

Table 11

Number of run

Actual sequence

F = ABCD

G = ABDE

Note : '-' and '+' represents the low and high level of the factors.

The 32 combinations were carried out in a random manner. A single rubber glove was used. The length of the middle finger (in pixel) was measured for each of the combination. the actual length was 50 pixel.

Analysis of the experimental data showed that the factors that significantly affected the average measurement of finger length were A (aperture size), C (binarization threshold), and D (corner angle threshold). The interactions between A and C, between A and D, and between C and D were found to also significantly affect the average length of the middle finger. All of the factors affected the variability in the measurement of finger length. The practical interpretation of these findings are given below.

The high level of A produced average measurements that were close to the actual length (i.e. 50 pixel) for both the low and high levels of C and D. The high level of C produced average measurements that were close to the actual length for both the low and high levels of D. The high levels of A, B, C, D, and G produced less variability in the measurements. Therefore, it was recommended that all of the factors be set at the high level except for E and F. Confirmation runs confirmed that the measurements are close to the actual value when the factors are set at these levels.

The above findings and interpretations are valid over the factor levels that were investigated.

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