Process analysis

In a seminar of the European Organization for Quality (EOQ) it was stated: "Only design of experiments [allows us] to obtain the information needed for systematic improvement of products and processes, in a reasonable time."

Clarity about influences and effects

No real manufacturing or conversion process always and exclusively does what is expected of it. If the deviations are too great for the required quality of the results, the question arises: Where does the variability come from and how can it be influenced, i.e. reduced? It is therefore a question of the internal interrelationships of the process and how they react to external intentional influences and unintentional disturbances. Only with an understanding of these are we in a position to optimize processes and keep them at their optimum.

However, this is usually not so easy, because, as the chaos researcher Arthur Koestler shows, human beings, and in particular goal-oriented human thinking, are largely subject to unconscious limit cycles (1).

That's why the designer doesn't see his own design flaws that prevent a machine from functioning properly. This is also the reason why the scientist does not doubt or even reject a cherished theory, even though it has been proven to repeatedly give false predictions for real processes.

This thinking in limit cycles was good in the African savannah, where rapid action was required in recurring situations; our ancestors also applied it successfully there. But it is usually not optimal in industrial environments where sustained response to complex problems is required. And, as Azeem, Robin Hood's Muslim companion puts it, "There are no perfect people, only perfect intentions!". (2) In order to control and, if necessary, reduce the variability of a process, we need to know the influences controlling it and their effects on the critical target variables, the results of the process.

design insight

Most of the time, the situation described here is comparable to "standing in front of a labyrinth". To gain insight into its inner workings, it is not enough to turn the familiar knobs in the hope of finding a solution. Rather, we must first ask ourselves what the overall influences are on our process and then consider all the influences identified as significant in our investigation. For experimental design, this means expanding the dimensionality of the experimental space. In the image of the labyrinth, it is sufficient to introduce the third dimension: Viewed from above, the path to the center becomes easily visible.

In the process work, it is necessary to find all settings of all essential influencing factors and to take them into account in corresponding experiments in order to be able to create a global mathematical model of the process that depicts all interesting interrelationships. With regard to the already mentioned interactions, factors whose effects are "known" must also be taken into account, and the experiments must basically be carried out according to the rule "change all factors simultaneously". How exactly this is to be done is regulated by an experiment plan, which is created with suitable software.

The intuitive procedure consists mostly of erratic probing of the multidimensional process space. While this is still feasible for two variables, it becomes confusing from the third dimension onwards. It therefore usually results in many attempts, which nevertheless do not make the inner relationships recognizable, let alone find an optimum (Figure 1).

The planned illumination of the process space, on the other hand, results in a controllable number of defined experiments and, as a result, a mathematical description of the model that can be optimized according to any criteria.

In Figure 2, the main effects of influences 1 to 6 of a real process of an existing machine are shown as scatterplots with associated approximated regression curves. The following graphs were created with the statistical program CORNERSTONE (3).

Interactions

In the contexts shown above, this is not a "faked" school example, but a more recent example from practice. It is easy to see that such complex relationships can no longer be grasped "barefoot". It should be noted that the entire data set was generated with only 38 machine settings in one shift.

As already mentioned, the main effects are unfortunately not the whole truth. Often enough, as mentioned, it is the interactions between them that contribute to the lack of understanding of the process reality to a particular extent. This circumstance is explained in more detail by means of the graph in Figure 3.

Figure 3 shows all possible interactions of the six influencing factors on target variable 1, with the larger ones highlighted in colour. The most important interactions occur between the influencing factors 1 and 6 (blue background), 2 and 6 (yellow) and 4 and 6 (green). The three curves per diagram correspond to the three settings of one partner in the diagonal boxes Max, Midpoint, Min.

The strongest interaction takes place between Influx4 and Influx6 (green). It results in an almost complete reversal of the effect on the target variable Target1! In the middle position of influencing factor 6 (Einfl6 = 3 = Midpoint[3]), the variation of Einfl4 between 3000 and 7000 (green box below) has practically no effect on the target variable Ziel1 (scale on the extreme left). This curve also corresponds essentially to the main effect shown in Figure 2 for Einfl4. In contrast, target1 varies over a wide range of values when influx6 is set to min or max - in the opposite direction!

Such a constellation may well lead to a process becoming uncontrollable if the interrelationships are not known, because depending on the initial situation, completely different, contradictory corrective measures may be necessary to achieve the desired target values.

Closing words

As incomprehensible as it may seem that process work is still carried out without test planning in many production companies today, it is gratifying to see that at least in important key industries systematic work is being done with it in research and production.

Automotive, chemistry, semiconductors work as standard with systematic methods, one of which is design of experiments. But especially for smaller companies, process difficulties are often disastrous. The procurement of a new machine to streamline a process does not automatically mean an improvement in results. Process optimization is the task of the process owner and is often inadequately supported by the manufacturer. In many cases, a joint analysis would help both parties. In practice, there are many cases in which, after months of expensive trial and error, a single planned experiment was able to solve a problem.