1. Factorials
This type of experiment is suitable for studying efficiently and Economic the effect of factors on the variable of interest.
Example 1:
Study the effect over time of a certain chemical reaction with the variation in the temperature and concentration of a reactant, as shown in scheme below.
| Variable Answer | Y: Reaction time |
|---|---|
| Factors | A: Concentration of Reagent (Levels $V_{-1}$=10% e $V_{+1}$=20%) |
| B: Temperature (levels $T_{-1}$=80ºC e $T_{+1}$=90ºC) | |
| Treatment | $V_{-1}$ $T_{-1}$ - concentration in 10% e temperature in 80ºC ((0)),$\quad$ & |
| $V_{+1}$ $T_{-1}$ - concentration in 20% e temperature in 80ºC (a), | |
| $V_{-1}$ $T_{+1}$ - concentration in 10% e temperature in 90ºC (b) | |
| $V_{+1}$ $T_{+1}$ - concentration in 20% e temperature in 90ºC (ab) | |
| (The number of treatments is 2k, in this case $2^2$=4) | |
| Experimental Unit | Time period for each reaction |
| Replicas | Repetition of the experiment done under the same conditions |
| experimental, in the case of the example under the same temperature | |
| level and reagent. How much more replicas, more reliable the | |
| results of the experiment. |
To make statistical analysis, simply configure as shown in the figure below.
By clicking on Calculate we obtain the results. You can also generate the analyses And download the results in Word format.
The results are:
Full factorial
| Order | A | B | A:B | |
|---|---|---|---|---|
| 1 | 1 | -1 | -1 | 1 |
| 2 | 2 | 1 | -1 | -1 |
| 7 | 3 | -1 | 1 | -1 |
| 8 | 4 | 1 | 1 | 1 |
| 6 | 5 | 1 | -1 | -1 |
| 3 | 6 | -1 | 1 | -1 |
| 4 | 7 | 1 | 1 | 1 |
| 5 | 8 | -1 | -1 | 1 |
Example 2:
An experimenter wants to evaluate the wear behavior of the engine pinion. engine of a sugar cane harvesting machine, in relation to four factors: chassis side opening, cup window, disc shape and roll format. The goal is to determine what settings a less pinion wear. Using 8 machines of the same model, same year of manufacture and using the same work front, we carry out a Fractional factorial experiment 24-1 with three repetitions.
To carry out the Experiment Planning, we will carry out the next steps:
By clicking Calculate we get the results. You can also generate the analyses And download the results in Word format.
The results are:
Fractional Factor
| V1 | |
|---|---|
| factors | 4 |
| 2^(k-p) | 2^(4-1) |
| Fraction | '1/2 |
| Resolution | IV |
| Runs | 8 |
| Generators | D=ABC |
| Definition ratio | i=ABCD |
Fractional Desing
| Order | A | B | C | D | |
|---|---|---|---|---|---|
| 7 | 1 | -1 | -1 | 1 | 1 |
| 16 | 2 | 1 | 1 | 1 | 1 |
| 2 | 3 | 1 | 1 | -1 | -1 |
| 19 | 4 | 1 | -1 | 1 | -1 |
| 11 | 5 | 1 | -1 | 1 | -1 |
| 9 | 6 | -1 | -1 | -1 | -1 |
| 20 | 7 | -1 | 1 | 1 | -1 |
| 21 | 8 | 1 | -1 | -1 | 1 |
| 17 | 9 | -1 | -1 | -1 | -1 |
| 5 | 10 | 1 | -1 | -1 | 1 |
| 24 | 11 | 1 | 1 | 1 | 1 |
| 4 | 12 | -1 | 1 | 1 | -1 |
| 14 | 13 | -1 | 1 | -1 | 1 |
| 10 | 14 | 1 | 1 | -1 | -1 |
| 1 | 15 | -1 | -1 | -1 | -1 |
| 22 | 16 | -1 | 1 | -1 | 1 |
| 15 | 17 | -1 | -1 | 1 | 1 |
| 8 | 18 | 1 | 1 | 1 | 1 |
| 12 | 19 | -1 | 1 | 1 | -1 |
| 13 | 20 | 1 | -1 | -1 | 1 |
| 6 | 21 | -1 | 1 | -1 | 1 |
| 23 | 22 | -1 | -1 | 1 | 1 |
| 18 | 23 | 1 | 1 | -1 | -1 |
| 3 | 24 | 1 | -1 | 1 | -1 |
–
Examples 3:
Fluorescent lamps are devices that use discharges. electricity to produce light energy. For its operation require auxiliary equipment, called reactors, which their objective is to control and stabilize the electrical current. The useful life of the lamps and the amount of light they produce depend on the power. of the reactors. The reactor is a product basically composed of sheets of steel, enameled wire, resin (for encapsulation) and capacitors (when necessary). A reactor manufacturing industry wants to improve the the performance of your product by 10%. For this he decided to carry out a 24 factorial experiment with the following factors:
-
A - Weight of the Steel Core;
-
B - Weight of Copper Wire;
-
C - Resin curing temperature;
-
D - Capacitor type.
To carry out the Experiment Planning, we will carry out the next steps:
By clicking on Calculate we obtain the results. You can also generate the analyses And download the results in Word format.
The results are:
Factorial Block
| V1 | |
|---|---|
| Chosen effect | A:B:C:D |
| Confounded interactions | A:B:C:D |
Factorial Block
| Order | Block | A | B | C | D | A:B | A:C | B:C | R:D | B:D | C:D | A:B:C | A:B:D | A:C:D | B:C:D | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 1 | Block2 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 |
| 15 | 10 | Block1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 |
| 8 | 11 | Block1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 |
| 5 | 12 | Block1 | -1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | 1 | 1 |
| 16 | 13 | Block2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 10 | 14 | Block2 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 |
| 9 | 15 | Block1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 |
| 2 | 16 | Block1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 |
| 12 | 2 | Block1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 |
| 1 | 3 | Block2 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 |
| 11 | 4 | Block2 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 |
| 13 | 5 | Block2 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 |
| 6 | 6 | Block2 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 |
| 3 | 7 | Block1 | -1 | 1 | -1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | 1 | -1 | 1 |
| 4 | 8 | Block2 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 |
| 14 | 9 | Block1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 |