## DoE Flow Chart

We have seen that the DoE is a integral part of any QbD studies however, we seldom apply it properly during developmental stage. I have seen scientist afraid of using it because, they think that DoE means  more experiments. But in reality what I have seen that they end-up in doing more experiments than that suggested by DoE. To give you an idea, scientist would perform 40-50 experiments if they are investigating 4-5 variables whereas, DoE con do that job in 15-20 experiments. This is because, when DoE experiments proposes 15-20 experiments in a single go, it appears more for the developmental team. Other issue is that the lack of knowledge on how to exploit the DoE using fractional factorial designs, Plackett-Burma or D-optimal etc.

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## Sequence of Events While Performing Design of Experiments (DoE) & QbD

As a chemist I was always in a hurry to perform a DoE for optimizing a chemical reaction. More often I failed and gradually I learned that it can’t be done in a hurry, we need to do some homework before that.

Basic concept behind QbD is the Juran’s concept of “building/designing quality into the product”[i] rather than “complying product with the quality”. Designing quality into the product could be achieved by having better control on the process and this can be achieved by proper understanding of the relationship between the CQAs (y) and CPPs/CMAs (x) as shown in Figure 4 and 7. This concept of building quality into the product is based on the quality risk management[ii] where one needs to assess the risk of each PPs/MAs on CQAs. Basic outline of QbD in process development is shown in Figure 9. It involves following steps

For a successful DoE, we need to divide the whole process into two phases

Phase-1: Preparing for DoE

It deals with the preliminary homework, like

what quality parameters we want to study & why?

What are the process parameters and material attributes that can affect the selected quality parameters?

Phase-2: Performing DoE and analysis followed by proposing the control strategy

Once quality parameters and most probable process parameters and material attributes are identified, its time for performing DoE to establish cause and effect relationship between the two.

Based on the DoE study, CPPs and CMAs are identified and a design space is generated within which CPPs & CMAs could be varied to keep CQAs under control.

Finally, before commercialization, a control strategy is proposed to keep CPPs/CMAs under specified range, either by proposing a engineering or manual control.

DoE: Design of Experiment

CQA: Critical quality attribute —these qualities of the product is critical for the customers

CPP: critical process parameters — these process parameters affects CQAs

CMA: Critical Material Attributes — These are input material attributes affecting the CQAs.

[i]. Juran on Quality by Design: The New Steps for Planning Quality Into Goods and Services, J. M. Juran, Simon and Schuster, 1992

[ii]. José Rodríguez-Pérez, Quality Risk Management in FDA-Regulated Industry, ASQ Quality Press, Milwaukee, 2012.

## Concept of Process Robustness — 2

Earlier we have seen that robustness is inversely related to the slope of the main effect. We dealt with the linear relationship in those cases.

But some time effects could be of higher order like quadratic, cubic etc.  In such cases principle remains same i.e. select the region with least slope for least variability — at the tip of the parabola.

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Concept of Process Robustness — 1

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## Concept of Process Robustness — 1

Before we understand the concept of robustness, we must understand “How Variance Gets Transmitted To The Out-put (y)?”

Let’s have three scenarios where we are measuring the effect of factor A on the response.

We can see that as we increase the factor A there is a increase in response Y in all cases. Also in all three cases factor-A got fluctuated by an amount = A2-A1.

Case-1: A small fluctuation in  factor A (denoted by A1 to A2) which could be possible at commercial scale can result in ΔY1 fluctuation in response. This ΔY1 fluctuation is depends on the slope of response. Since the slope in case-1 is least, therefore fluctuation in ΔY1 because of the factor-A fluctuation is least.

As the slope increases from case-1 to case-2, the fluctuation (variance) that is transmitted to response Y (denoted by ΔY2) increases, even though the variation in factor A remains constant (A2-A1).

Matter becomes worst as the slope further increases (case-3).

If we are looking for a robust process during commercialization, we should focus not only on the output of the DoE but also the slope of the response.

Suppose we are optimizing a reaction at two different temperatures as shown below

Even though temperature-1 can give me better yield if we keep on increasing A, I would prefer to take a hit on yield and commercialize the process at temperature-2 because the slope of the response is negligible and hence the yield of the process would be consistent at commercial scale.

Summary

1. A small change (deviation) in input can cause huge fluctuations in the response depending on the slope
2. Higher the slope of response, more is the fluctuation in response due to slight change in reaction parameter

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