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The EVOP plans of experiments are interesting because they allow, by successive small changes of influence factors, to optimise our results.

## Introduction

The EVOP method, Evolutionary Operation, is a method of optimizing process-type experiments, introduced by George Box in 1957. It can be used in all cases and allows to include as many variables as you wish, but in a pragmatic way, it is limited to 3 variable at 2 levels and preferences on high volume productions.

The advantage of this method is that by working through small parameter changes, you will most often be able to do the experiments without using line stops or complex planning.

## The principle

After selecting 2 or 3 parameters, they are changed one by one and see what the results are. We will then test their effects with regard to the error of the effects. As long as the effect of the factors is greater than the error of the effects, new tests are redone to optimise our model.

In other words, if the effects of the factors are greater than the standard deviation of the results, then our model can still be optimized.

## Step 1: Define the factors and their levels

As a first step, we define the factors on which we will ” play ” to optimize the result. of a maximum number of 3 for simple use, these factors must meet some prerogatives:

• Easy to control
• Simple to modify
• Having a strong effect on the result

Once the factors are chosen, we will identify for each of them 2 possible levels. These levels must be within the acceptable limits. In the first stage, we choose the ” standard ” levels that we used to use.

Example:

We are a manufacturer of cream. The viscosity of our product is essential to our customers. To optimize it, knowing that we do not want to play on the recipe, we have two essential process factors: the speed of rotation of our mixer and the mixing time. namely that for reasons of cost, we wish the time of mixing as short as possible allowing us to have a significant viscosity.

## Step 2: Identify experiences

As part of these experiments, the same test matrices are used as for the complete factorial plans for screening. It’s even based on the Hadamard matrix.

As part of our example, we get the following test matrix:

 Test 1 Test 2 Test 3 Test 4 Factor 1 – + – + Factor 2 – – + +

## Step 3: Perform 2 test cycles

EVOP plans operating on the basis of the error of our factors, we need at minimum 2 cycles of tests to carry out our test of significance.

## Step 4: Calculate the effects

Here we calculate the effect of the factors in a slightly different way than for the traditional experience plans because here we do not take into account the interactions. In our case, it gives us:

## Step 5: Calculate the error of the tests

The error of the effect represents the probability of getting our results. We understand, at the most the standard deviation of our results is great, at least we can have confidence in getting these. The formula for the error is as follows

K: the number of factors

A : the number of times the test has been repeated (cycle number).

P: The number of test where the factor is in its high position.

Taking our example, we get the following result:

## Step 6: Concluding on the situation

The value of our factor effects is compared with the value of the factor error. We’re going to be in two cases:

 Result Statistical Conclusion Practical Conclusion Effect of effects < error factor The effect is not significant The effect is not a priori influencing the result. We have to redo a test cycle under the same conditions. If after 10 test cycles, the factor is still not significant, then this is ” optimized “. Effect of effects > error factor The effect is significant The effect is influencing our outcome. We can change it wisely in the desired direction of our result and move on to a new test phase.

In resuming our case, we identify that the 2 factors are significant in this first phase. What’s more, having a positive sign, they therefore have a positive effect on our result: in clear, at the most they increase, at the most the viscosity increases. We decide to change the parameters by increasing our values.

We reproduce this process repeatedly. From Phase 4, we observe that at 30 mn of mixing time, the effect is no longer the significant mixing time. Which is good for us, because it’s time to go. On the other hand, the speed factor does not have as much influence as before. We decide to increase it but in a less pronounced way.

We decide to continue our tests with a phase 5 where we no longer increase the mixing time, but only the mixing speed. We observe that despite 10 cycles, the speed factor no longer has a significant influence. We can therefore consider that at this stage we have identified the optimized values that are 3600 for the speed and 30mn for the mixing time, which would allow us to have on average a viscosity of 61.8 (you will find all the calculations and result in the Excel file attached).