Design Of Experiments - GMP TRAINING-CGMP PHARMACEUTICAL TRAINING

Design Of Experiments

A process enabler tool

DOE-Primer C P Bapat 1

Design of ExperimentsA close look at evolving regulatory guidelines -

ICH Q1 to Q7 QC �� QA

• Q1 : Stability data

• Q2 : Analytical validation

• Q3 : Impurity profile

• Q4 : Pharmacopoeial text

ICH Q8 to Q11 �� QbD

• Q8 : Pharmaceutical

Development

• Q9 : Quality Risk

Management (QRM)• Q4 : Pharmacopoeial text

• Q5 : Biological products

• Q6 : Specifications

• Q7 : Good Manufg Practices

Management (QRM)

• Q10: Pharmaceutical

Quality System (PQS)

• Q11: Development and

Manufacture of Drug

Substances

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Design of Experiments• A close look at evolving regulatory guidelines ––

•• Drug regulatory guidelines clearly show an upstream focal shift, from Drug regulatory guidelines clearly show an upstream focal shift, from

product / systems monitoring to product development.product / systems monitoring to product development.

•• Focus is on science based understanding of the ‘Quality Target Focus is on science based understanding of the ‘Quality Target

Product Profile (QTPP)’ as a function of process inputs Product Profile (QTPP)’ as a function of process inputs –– ‘Material ‘Material

Attributes (MA)’ and ‘Process Parameters (PP)’Attributes (MA)’ and ‘Process Parameters (PP)’

Product Quality fn (Process, MA, PP, Environment)Product Quality fn (Process, MA, PP, Environment)Product Quality fn (Process, MA, PP, Environment)Product Quality fn (Process, MA, PP, Environment)

•• ICH guidelines Q8 to Q11 ICH guidelines Q8 to Q11 characterisecharacterise regulatory approach of regulatory approach of

engaging concepts of QTPP, Critical Quality Attributes (CQA), Quality engaging concepts of QTPP, Critical Quality Attributes (CQA), Quality

Risk Assessment/Management (QRM), Design Space, Continuous Risk Assessment/Management (QRM), Design Space, Continuous

improvement (Life cycle management) among others.improvement (Life cycle management) among others.

•• Guidelines mention use of ‘Statistical Tools’ Guidelines mention use of ‘Statistical Tools’ –– SPC and DOE.SPC and DOE.

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Design of Experiments•• Quality (r)evolution beyond Quality (r)evolution beyond PharmaPharma landscapelandscape ––

•• Post world war II consumer industry witnessed quality revolution.Post world war II consumer industry witnessed quality revolution.

•• Japan showed that quality value addition makes economic sense.Japan showed that quality value addition makes economic sense.

•• Quality circle, TQM, QFD, Kaizen and other initiatives changed outlookQuality circle, TQM, QFD, Kaizen and other initiatives changed outlook

•• Statistical experimental designs were developed by Statistical experimental designs were developed by genetistgenetist –– Fisher.Fisher.•• Statistical experimental designs were developed by Statistical experimental designs were developed by genetistgenetist –– Fisher.Fisher.

•• GenichiGenichi Taguchi gainfully used & Taguchi gainfully used & popularisedpopularised this approach this approach -- DOE.DOE.

•• Six sigma was developed by Motorola and adopted by GE and others.Six sigma was developed by Motorola and adopted by GE and others.

•• Six sigma Six sigma revolutionisedrevolutionised process approach with deployment of DOE.process approach with deployment of DOE.

Major Major pharmapharma companies have started using DOE for NCE as well as process research.companies have started using DOE for NCE as well as process research.


Design of Experiments•• Design of Experiments isDesign of Experiments is ––

•• An ‘An ‘organisedorganised’ approach for a scientific study.’ approach for a scientific study.

•• Applicable to Laboratory, Pilot & Full scale study.Applicable to Laboratory, Pilot & Full scale study.

•• Application of ‘Combinatorial Mathematics’ and ‘Statistics’ principles.Application of ‘Combinatorial Mathematics’ and ‘Statistics’ principles.

•• Adoption of Adoption of synchronisedsynchronised variation of parameters , a departure from variation of parameters , a departure from •• Adoption of Adoption of synchronisedsynchronised variation of parameters , a departure from variation of parameters , a departure from

one parameter at a time approach.one parameter at a time approach.

•• Application of mathematical treatment to extract information in data.Application of mathematical treatment to extract information in data.

•• An objective data analysis tool for ‘Robust’ process design.An objective data analysis tool for ‘Robust’ process design.

•• A force multiplier A force multiplier –– sharpens core strength of the researcher.sharpens core strength of the researcher.

•• A tool used to define ‘Design Space’ within which process can performA tool used to define ‘Design Space’ within which process can perform


Design of Experiments

Quality : A customer focused perspective -

�The traditional model for quality losses

– No losses within the specification limits!

Scrap Cost

LSL USLTarget

Cost

LSL USLTarget

� The Taguchi model for quality loss function

– The quality loss is zero only if we are on target


Design of ExperimentsTaguchi : Translation of Quality Loss to Loss in Value

L(V) = C(V/∆)2

Example: The repair cost for an engine shaft is $100. The shaft diameter is required

to be 10mm±1 micron. On average the produced shafts deviate 0.5 micron from target.

Determine the mean quality loss per shaft using the Taguchi QLF.

Solution: L(0.5) = C·(V/∆)2 = 100·(0.5/1)2 = 100·0.25 = $25 per unit

C = The unit repair cost when the deviation from target equals the maximum tolerance level

∆ = Tolerance interval (allowable parameter variation from target to SL)

T = Target value

Y = The actual metric value for a specific product

V = Deviation from target = Y-T

L(V) = Economic penalty incurred by the customer as a result of quality deviation from target (The quality loss)

Loss at 0.9 0.8 0.7 0.6 0.4 0.3 0.2 0.1

$81 $64 $49 $36 $16 $9 $4 $1


Design of ExperimentsAcurateAcurate PrecisePrecise A & PA & P

Should process chemists not use these concepts used by Should process chemists not use these concepts used by

analytical colleagues for method validation?analytical colleagues for method validation?



Design of ExperimentsProcess DevelopmentProcess Development ––• The basic philosophy is to develop processes that consistently

produce product with target attributes with minimal variation.

• To achieve this experiments are conducted in a planned manner to

study effects of parameters set at various levels.

Noise factors

SystemInput

variables

Output

responses

Control factors

(Process Parameters)


Design of ExperimentsTraditional : One factor at a Traditional : One factor at a timetime

– procedure

• Run all parameters at one condition

• Repeat experiments changing condition of one parameter and

holding others

• Hold studied parameter at optimal condition, change another

• Repeat until all factors at their optimum conditions

• Find an overall process optimum by observation


Design of ExperimentsExperimentation based on Factorial DesignsExperimentation based on Factorial Designs

� Tests are conducted at combinations of parameters

� Factorial design (Left) gives 4 results for each parameter level (Low, High) within 8 experiments.

� Conventional OFAT (Right) design will need 16 experiments for same level of information.


Design of ExperimentsDOE – Factorial array 2^3 Full Factorial -1�� Low, +1�� High

Trial xA xB xC

y1 -1 -1 -1

y2 -1 -1 +1

y3 -1 +1 -1y3 -1 +1 -1

y4 -1 +1 +1

y5 +1 -1 -1

y6 +1 -1 +1

y7 +1 +1 -1

y8 +1 +1 +1


Design of ExperimentsDOE – Factor contribution analysis

A simple regression model can be used with eight parameters.

Thus, we may represent the regression equation as

CBAABCACCACBBCBAABCCBBAA xxxpxxpxxpxxpxpxpxppy +++++++=0

The p’s are the parameter coefficients that are determined by using the “outcome”

matrix by the simultaneous solution of the following eight equations:

Y1 = P0 – PAXA – PBXB – PCXC + PABXAB + PBCXBC + PCAXCA – PABC XABC

Y2 = P0 – PAXA – PB XB+ PCXC + PABXAB – PBCXBC – PCAXCA + PABC XABC

Y3 = P0 – PAXA + PBXB – PCXC – PABXAB – PBCXBC + PCAXCA + PABC XABC

Y4 = P0 – PAXA + PBXB + PCXC – PABXAB + PBCXBC – PCAXCA – PABC XABC

Y5 = P0 + PAXA – PBXB – PCXC – PABXAB + PBCXBC – PCAXCA + PABC XABC

Y6 = P0 + PAXA – PBXB + PCXC – PABXAB – PBCXBC + PCAXCA – PABC XABC

Y7 = P0 + PAXA + PBXB – PCXC + PABXAB – PBCXBC – PCAXCA – PABC XABC

Y8 = P0 + PAXA + PBXB + PCXC + PABXAB + PBCXBC + PCAXCA+ PABC XABC


Design of ExperimentsExperimentation based on Factorial DesignsExperimentation based on Factorial Designs

� Tests are conducted at combinations of factors

� Defined arrays lend to algebraic manipulation of data

� Output as a function of input / process variables

� Y = f(x)

� Y = KK00 + K+ K11P + KP + K22T + KT + K33PTPT

� Y is an observed value like purity, yield, m/c, impurity 1, impurity � Y is an observed value like purity, yield, m/c, impurity 1, impurity

2 etc.

� X is a process variable (control variable, a factor)

� Mathematical calculations separate effect of factors and their

interaction on observed results

� Leads to predictive knowledge of a multi-factor process with

fewest possible trials

� A scientific tool for process optimisation.


Design of ExperimentsDesign space - (Example from Q11, pg19)


Design of Experiments•• Full Factorial DesignFull Factorial Design

•• An optimum can be found by conducting experiments at An optimum can be found by conducting experiments at different control levels (L) for all control variables (Factors, F)different control levels (L) for all control variables (Factors, F)

Control Variables (F)Control Variables (F) Number of settings (L)Number of settings (L)(Parameters)(Parameters) 22 33 55

22 44 99 252522 44 99 2525

33 88 2727 125125

44 1616 8181 625625

..

66 6464 729729 1562515625..

88 256 256 65616561 390625390625

..

1010 10241024 5904959049 97656259765625


Design of ExperimentsTypes of Designs -

• Number of experimental runs increase exponentially with increase

in number of parameters.

• ‘Fractional Factorial Designs’ are used to select vital few factors

(parameters) from trivial many.

• Taguchi orthogonal array, Plackette Burman, Box Behnken are few

popular designs.popular designs.

• Sequential designs build a process in a disciplined manner –

– Screening : Identify vital few factors (parameters).

– Optimisation : Evaluate parameter & interaction effects.

Evolve a compromise between conflicting goals.

– Robustness test : Ascertain process is robust to small variations in

parametric values.


Design of ExperimentsDOE Enablers -

• Enables designer to simultaneously determine individual & interaction

effects of many factors.

• Provides insight into significant factors.

• Helps understand interaction between factors and thus sensitive design

areas.

• Reveals design elements which largely affect output.

• Gives direction to reach optimal process performance.• Gives direction to reach optimal process performance.

• Enables designers to choose parameter ranges which give robust process.

• Enables derivation of predictive mathematical model.

• Enables to define design space within which manufacturing flexibility can

be exercised remaining inside regulatory boundary.

• Gives better return on investment.

Get basic initiation using MS Excel. As you move forward choice of

software is available to perform mathematical computations.



Warning!

• Bear in mind DOE works through mathematical models and chemical

knowledge should be applied in critical evaluation of the design and its

outcome.

• Domain knowledge technical expertise is used to define operating range.

• DOE will lead to an optimum in the chosen experimental region (Operating

Space).

• It is a design tool and not a design concept/creativity.• It is a design tool and not a design concept/creativity.

• It can help in discarding wrong ideas fast.

• Creative domain knowledge spark still rides high.


Design of ExperimentsReferences –

1. OPRD 1999, 3, 281-288.

2. OPRD 2001, 5, 659-664.

3. OPRD 2003, 7, 514-520.

4. OPRD 2005, 9, 18-22.

5. OPRD 2006, 10, 64-69.

6. OPRD 2007, 11, 1104-1111.

7. OPRD 2008, 12, 1188-1194.7. OPRD 2008, 12, 1188-1194.

8. OPRD 2009, 13, 54-59.

9. OPRD 2010, 14, 119-126.

10. OPRD 2010, 14, 540-548.

11. OPRD 2010, 14, 832-839.

12. OPRD 2010, 14, 1364-1372.

As can be guessed, the list is representative and not exhaustive.



This is solid science!!

Experiment !!!


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Design Of Experiments - GMP TRAINING-CGMP PHARMACEUTICAL TRAINING