Factorial experiments for two factors
A factorial experiment is the most efficient way to estimate the separate effects of two factors on a response. Usually factorial experiments are designed with the same number of experimental units used for each combination of factor levels. Using the terminology of experimental design, this is expressed as the same number of replicates for each treatment.
The design of factorial experiments should also include random allocation of the treatments (factor combinations) to the pool of experimental units.
When designing experiments, never forget to randomise the allocation of treatments.
A few examples of data from factorial experiments are given below.
Catalyst surface area
Researchers conducted an experiment to investigate how the mole contents of cobalt and the calcination temperature affected the surface area of an ison-cobalt hydroxide catalyst. Four cobalt levels and five temperatures were used in the experiment and one sample of catalyst was created and tested at each of the 20 combinations of a cobalt level and temperature. The table below shows the results of the experiment.
Temperature (°F) | |||||
---|---|---|---|---|---|
Cobalt (mole) | 200 | 300 | 400 | 500 | 600 |
0.6 | 90.6 | 82.7 | 58.7 | 43.2 | 25.0 |
1.0 | 127.1 | 112.3 | 19.6 | 17.8 | 9.1 |
2.6 | 53.1 | 52.0 | 43.4 | 42.4 | 31.6 |
3.0 | 40.9 | 37.9 | 27.5 | 27.3 | 19.0 |
Note that layout of the data in the table does not correspond to the order of the experimental runs — the treatments were used in random order.
Torque of locknuts
A manufacturer was finding unwanted differences in the torque values of a locknut that it made. Torque is the work (i.e. force × distance) required to tighten the nut. An experiment was therefore conducted to determine what factors affected the torque values. The type of plating process was isolated as the most probably factor to impact torque. Researchers also wanted to assess the difference in torque between threading the locknut onto a bolt or a mandrel (like a bolt but harder). Twenty locknuts were manufactured with different types of plating: cadmium and wax (C&W), no plating (HT) and phosphate and oil (P&O); ten were tested on bolts and ten on mandrels. A manual torque wrench was used to determine the torque of each.
Plating type | |||
---|---|---|---|
C&W | HT | P&O | |
Bolt | 20 16 16 19 17 14 18 15 15 24 |
26 30 40 26 28 38 38 45 38 38 |
25 45 40 49 30 33 17 30 16 20 |
Mandrel | 24 23 18 14 17 18 17 12 15 11 |
32 28 22 27 30 28 35 30 32 30 |
10 14 13 11 17 14 16 15 15 16 |
Television screen brightness
An experiment was conducted to study the effect of glass type and phosphor type on the brightness of a television screen. The variable measured is the current in microampleres necessary to produce a certain brightness; the larger this current, the poorer the screen characteristics.
Phosphor type | |||
---|---|---|---|
Glass type | A | B | C |
Type 1 | 280 290 285 |
300 310 295 |
270 285 290 |
Type 2 | 230 235 240 |
260 240 235 |
220 225 230 |
The 18 screen samples were tested in random order.