Quality by Design (QbD) Space for Pharmaceuticals and Beyond...Quality by Design “QbD” Design...

6/25/2013

Copyright © 2013 Stat-Ease, Inc. Do not copy or redistribute in any form. 1

Quality by Design (QbD) Space for Pharmaceuticals and Beyond

*Presentation is posted at www.statease.com/webinar.html

There are 250+ attendees today! To avoid disrupting the Voice over Internet Protocol (VoIP) system, I will mute all. Please use Questions feature on GotoWebinar. Trygve will answer selected questions. Feel free to

By Wayne F. Adams, MS, Applied Stats.Stat-Ease, Inc., Minneapolis, MN

[email protected]

email questions to [email protected] which we will answer off-line. -- Wayne

1

Quality by Design It’s Not Just For Pharmaceuticals

*Presentation is posted at www.statease.com/webinar.html

There are 250+ attendees today! To avoid disrupting the Voice over Internet Protocol (VoIP) system, I will mute all. Please use Questions feature on GotoWebinar. Trygve will answer selected questions. Feel free to

By Wayne F. Adams, MS, Applied Stats.Stat-Ease, Inc., Minneapolis, MN

[email protected] 2

email questions to [email protected] which we will answer off-line. -- Wayne

http://www.statease.com/webinar.html

mailto:[email protected]





6/25/2013


Getting Started: Stat-Ease Resources

New to Design of Experiments?

Take advantage of all the free resources available to you!g y

On the statease.com website:

• Beginner resources: http://www.statease.com/beginner.html

• Webinars: http://www.statease.com/webinar.html

Articles: http://www statease com/articles html• Articles: http://www.statease.com/articles.html

• Software Tutorials: http://www.statease.com/dx8_man.html

3June 2013 Webinar

Getting Started: Other Resources

New to Design of Experiments?

Take advantage of all the free resources available to you!g y

LinkedIn Groups:

• The Design of Experiment (DOE) Group – great place to post general questions about DOE’s

• ASQ Statistics Division – more general statistics and DOEQ g

• The Stat-Ease Professional Network – friends and clients of Stat-Ease

4June 2013 Webinar

http://www.statease.com/beginner.html


http://www.statease.com/articles.html

http://www.statease.com/dx8_man.html

6/25/2013


Agenda Transition

Quality by Design – QbD Wh t i QbD What is QbD

(FDA references) Finding the design space with DOE

(tableting process)

Proving the control space (extrusion-spheronization)

5June 2013 Webinar

Quality by DesignFDA View on QbD1

Quality by Design is:

Scientific, risk-based, holistic and proactive approach toScientific, risk based, holistic and proactive approach to product development

Deliberate design effort from product conception through commercialization

Full understanding of how product attributes and process relate to product performance

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Quality by DesignFDA View on QbD2

QbD involves the following key elements:

Target the product profile.g p p

Determine critical quality attributes (CQAs).

Link raw material attributes, formulation and process parameters to CQAs and perform risk assessment.

Develop a design space.

Design and implement a control strategy.g p gy

Manage product life cycle, including continual improvement.

7June 2013 Webinar

Develop a Design SpaceStatistically Designed Experiments

1. First-principles approach Combine experimental data and mechanistic knowledge to

model and predict performancemodel and predict performance.

2. Statistically designed experiments (DOEs) Efficient method for determining impact of

multiple parameters and their interactions.

3. Scale-up correlations A semi-empirical approach to translate operating conditions

between different scales or pieces of equipmentbetween different scales or pieces of equipment.

4. Combinations of the above

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Quality by Design “QbD”Design Space Determination

1. A region where quality product is produced.

2. Includes product formulation and/or process parameters.

3. Arrived at by iterative application of risk assessment and experimental design to knowledge space.

4. Includes evaluation of scale and equipment.

ICH guidelines Q8 (on Pharmaceutical Development), Q9 (on Quality Risk Management), and Q10 (on Pharmaceutical Quality System) provide some assistance for manufacturers to implement Quality by Design into their own operations.

9June 2013 Webinar

Design Space DeterminationQuality by Design

FDA defines design space in its Guidance for Industry Q8: Pharmaceutical Development, as:

“The multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality. Working within the design space is not considered as a change. Movement out of the design space is considered to be a change and would normally initiate a regulatory post approval change process.

Design space is proposed by the applicant and is subject to regulatory assessment and approval.”

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Quality by DesignVerification of Specifications

Confirmation:

Simple confirmation

KnownFactors

UnknownFactors

Screening

One or several runs at optimal conditions compared to prediction from the “Confirmation” node.

Verification (QbD)Size design for tolerance intervals and use them to yes

Factor effectsand interactions

R

Curvature?

Screening

no

Trivialmany

Vital fewCharacterization

Optimizationback off from specifications. Response

SurfaceMethods

Confirm? Backup

Celebrate!

no

yes

Optimization

Confirmation

11June 2013 Webinar

Using DOE with Tolerance Intervals to Verify Specifications

Objective:

Define an operating window in process factor space where we have 95% confidence that 99% of the population meet (or exceed) specifications.

Tools:

Use empirical DOE to model the responses as functions of the process factors.

Use a tolerance interval to “back off” (provide a buffer) fromUse a tolerance interval to back off (provide a buffer) from the specifications.

Size the DOE for required half-width of tolerance interval.

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Agenda Transition


(FDA references)

Finding the design space with DOE(tableting process)


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Illustrative ExampleTableting Process

This case study illustrates how DOE and tolerance intervals can be used to set an operating window where specifications are

i t tl tconsistently met.

An optimal design is run on two process parameters (granulation time and lubrification time) in a tableting process.

Three responses (dissolution, friability and hardness) are measured.

The specifications are:The specifications are:

• Dissolution ≥ 75%

• Friability ≤ 0.5%

• Hardness ≥ 10 kP

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Initial Operating WindowSpecifications as Bounds

y1 = Dissolution %8.00

Specifications on Graphical Overlay

(specification ≥ 75%)

y2 = Friability %(specification ≤ 0.5%)

y3 = Hardness kP(specification ≥ 10 kP) 4.00

5.00

6.00

7.00

B: L

ub

rific

atio

n

Dissolution: 75.00

Friability: 0.50

3.00 4.00 5.00 6.00 7.00

2.00

3.00

A: Granulation

Hardness: 10.00

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Uncertainty is a BIG ProblemSpecifications as Bounds

If the tableting process is operated on a boundary, then 50% of tablets

d d f ll t id thproduced fall outside the specification.

Specification

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Gaining confidence that individuals are within specifications.

If we want more confidence that individual units are within specifications:

Then we should back off using a tolerance interval rather than a confidence interval.

Specify the confidence level; e.g. 95%.

Specify the portion of the population to be within specifications; e.g. 99%.

Note:Note:

A confidence interval pads our design space to give us confidence that the process mean is within boundaries.

A tolerance interval gives us confidence that a stated proportion of the population is within specifications.

17June 2013 Webinar

Tolerance IntervalDefinition

Tolerance Interval: An interval that covers a fixed proportion of outcomes from the population with a pre-determined confidence level for estimating the population mean andconfidence level for estimating the population mean and standard deviation.

( ) ( )

( )2 2

2

d i th h lf idth f th t l i t l

y k s P% of population y k s

TI y k s

TI y d

− ≤ ≤ +

= ±

= ±

d is the half width of the tolerance interval

y ULTILLTI

P% of population

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Interval CalculationsSingle Sample & Normal Distribution

Confidence Interval

sy t

± 2

Tolerance Interval

y k s±

df t α=0.05 k2 α=0.05, P=0.95

1 12.706 37.674

Note:

TI multipliers are larger than those for a CI; especially for small samples.

As the sample size increases:

• CIs shrink towards zero.

y tn

±

2y2 4.303 9.916

3 3.182 6.370

4 2.776 5.079

5 2.571 4.414

10 2.228 3.259

25 2.060 2.612

50 2.009 2.375

• TIs tend towards a fixed value: Z(s).

Larger sample sizes are needed for TIs than CIs.

100 1.984 2.232

∞ 1.960 1.960

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Tolerance IntervalCalculation for a DOE

ˆTI y

TI cal

d

culation for a DOE *

= ±

( ) ( )1T T 1 n ps t X X Pd

− − −+ Φ

Standarddeviation

Design Matrix“sample size”

Position inDOE space

Proportionof population

Confidence

0

0

TI y d

d fn(s, X, x , P, )

= ±= α

( ) ( )( )

( ) ( ) ( )

,df 0 0 2

,df

s t x X X x Pn p,1

d

d

s t TI multiplier

α

α

+ Φχ − − α

=

=

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TI Interval MultipliersSingle Sample versus Two-Factor DOE

Comparison:

single sample k2(α= 0.05, P=99%)df k2 α=0.05, P=0.99 (t)(TIM*)

10 4 277 5 013versus

(tα=0.05,df)(TI multiplierα= 0.05, P=99%)

Note: The tolerance intervals that cover the design volume are wider than those at a single point in space.

10 4.277 5.013

11 4.150 4.860

12 4.044 4.739

13 3.955 4.636

14 3.878 4.532

15 3.812 4.460

20 3.577 4.155

25 3 432 3 966

* Basis is average TI multiplier for a two-factor unconstrained IV optimal design for a quadratic model with 6+ model points, 5 lack of fit points and 5 replicates.

25 3.432 3.966

30 3.344 3.826

50 3.121 3.518

100 2.933 3.224

*TIM = TI multiplier

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Interval Multipliers for “s”TI DOE, TI sample and CI sample

t*TIM

KK2

t*(1/sqrt(n))

start at 10 df

degrees of freedom

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Back off from SpecificationOne-Sided tolerance interval (TI)

One-sided TI calculation for DOE

0 0

d is the off set for the tolerance interval

One-sided TI calculation for DOE

ˆ ˆTI y d or TI y d= + = −

TI Specificationnew boundary

d

23June 2013 Webinar

Picking a TI Off-SetThe Lower bound for “d”

A tolerance interval that covers the design volume is approximately 20% wider thanapproximately 20% wider than that at a single point in space.

Therefore, d must be greater than (1.2)(K1)(s):

d > (1.2)(K1(α=5%, P=99%, n=20))(s)

need to guess “n”

d (1 2)(3 295)( )

TI Specificationnew boundary

dd > (1.2)(3.295)(s)

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RSM DOE Process (1 of 2)

Tableting Process

1. Identify opportunity and define objective.Define an operating window in process factor space where we have 95% confidence that 99% of the population meets (or exceeds)95% confidence that 99% of the population meets (or exceeds) specifications.

2. State objective in terms of measurable responses.

a. Define the precision that is required for each response.Tolerance interval (α=0.05, P=99%) half-width (d):dissolution d = 9, friability d = 0.3, hardness d = 0.7

b. Estimate experimental error (σ) for each response.b. Estimate experimental error (σ) for each response.dissolution s = 2, friability s = 0.03, hardness s = 0.14

c. Use fraction of design space (FDS) to quantify precision.

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RSM DOE Process (2 of 2)

Tableting Process

3. Select the input factors and ranges to study.(Consider both your region of interest and region of operability.)

A = Granulation time: 3 7 minutesA = Granulation time: 3 – 7 minutesB = Lubrification time: 2 – 8 minutes

7 ≤ total mixing time ≤ 12

4. Choose a polynomial to estimate: quadratic

5. Select a design and:

Size design for precision needed

Examine the design layout to ensure all the factor combinations are Examine the design layout to ensure all the factor combinations are safe to run and are likely to result in meaningful information (no disasters).

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7

Two Component MixThe solid center line is the fitted model;is the expected value or mean

prediction.y

Fraction of Design Space Review

4

5

6

R1 y δ±

The curved dotted lines are the computer generated confidence limits, or the actual precision.

δ Is the half-width of the desired confidence interval, or the desired precision. It is used to create the outer straight lines.

27

Note: The actual precision of the fitted value depends on where we are predicting.

3

0

1

0.25

0.75

0.5

0.5

0.75

0.25

1

0

Actual A

Actual B


Only 53% of the design space is precise enough to predict the mean within ± 0.64.

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53% of the design space h h d i d i i

7

Two Component Mix

53%has the desired precision, i.e. is inside the solid straight (red) lines.

4

5

6

R1 y δ±

53%

29

3

0

1

0.25

0.75

0.5

0.5

0.75

0.25

1

0

Actual A

Actual B

Whitcomb & Oehlert, “Sizing Mixture (RSM) Designs for Adequate Precision via Fraction of Design Space (FDS)”, htt // t t / bi /11 07 i i i (RSM) df

For More Details on Sizing DOEsfrom our past webinars

Sizing Mixture (RSM) Designsfor Adequate Precision via

Fraction of Design Space (FDS)

http://www.statease.com/webinars/11-07_sizing_mix(RSM).pdf

30

Pat WhitcombStat-Ease, Inc.612.746.2036

fax [email protected]

Gary W. OehlertSchool of Statistics

University of Minnesota612.625.1557

[email protected]

http://www.statease.com/webinars/11-07_sizing_mix%28RSM%29.pdf



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DOE with Tolerance IntervalsSizing for Precision Requirements

Define the precision required as the half-width of a Tolerance Interval that contains 99% of the population with 95% confidence:Interval that contains 99% of the population with 95% confidence:

Response Desired d sLower bound

on d*d/s

dissolution 9.0 2.00 7.9 4.5

friability 0.2 0.03 0.12 6.7

hardness 0.7 0.14 0.55 5

Size the DOE to the smallest (d/s) ratio.

*(1.2)(3.3)s is a lower bound on d. Since the desired d is higher thanthe lower bound on d, we can achieve a precise enough design

31June 2013 Webinar

FDS Graph

Sizing for Precision RequirementsDOE Sizing (page 1 of 3)

The default design has 16 runs (6 model, 5 lack of fit, 5 replicates) FDS = 0%

TI M

ultip

lier

2.000

3.000

4.000

d = 9s = 2a = 0.05P= 0 99

Design too small!

Ti M

ulti

plie

r

Fraction of Design Space

0.00 0.20 0.40 0.60 0.80 1.00

0.000

1.000

P 0.99


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FDS Graph


23 runs (13 model, 5 lack of fit, 5 replicates) FDS = 93%

TI M

ultip

lier

2.000

3.000

4.000

d = 9s = 2a = 0.05P= 0 99

Much better!

Ti M

ulti

plie

r


0.00 0.20 0.40 0.60 0.80 1.00

0.000

1.000P 0.99


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Re-build the design with increase the number of model points with 7 additional points to request 13 model points.

(13 model, 5 lack of fit, 5 replicates) 23 total runs

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Tableting ProcessResults

Analyze responses, aim for:

Dissolution ≥ 75%

Friability ≤ 0 5%

5.00

6.00

7.00

8.00Friability

ubri

ficat

ion

0.500

0.600

0.800

2 3

2 2

5.00

6.00

7.00

8.00Dissolution

ubri

ficat

ion

90.02 3

2 2

5.00

6.00

7.00

8.00Hardness

ubri

ficat

ion 12.00

13.00

2 3

2 2

Friability ≤ 0.5%

Hardness ≥ 10 kP

3.00 4.00 5.00 6.00 7.00

2.00

3.00

4.00

A: Granulation

B: L

u

3 3

3

3.00 4.00 5.00 6.00 7.00

2.00

3.00

4.00

A: Granulation

B: L

u

75.0

80.0

3 3

3

3.00 4.00 5.00 6.00 7.00

2.00

3.00

4.00

A: Granulation

B: L

u

10.00

11.00

3 3

3

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Final Operating WindowTolerance Intervals as Bounds

Set Graphical Optimization intervals and criteriafor each responsefor each response.

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Final Operating WindowTolerance Intervals as Bounds

y1 = Dissolution %8.00

Tolerance Intervals (α = 5%, P = 99%)

(specification ≥ 75%)

y2 = Friability %(specification ≤ 0.5%)

y3 = Hardness kP(specification ≥ 10 kP) 4.00

5.00

6.00

7.00

B: L

ub

rific

atio

n

Dissolution: 75.00

Dissolution TI: 75.00

Friability: 0.50

Friability TI: 0.50

3.00 4.00 5.00 6.00 7.00

2.00

3.00

A: Granulation

Hardness: 10.00

Hardness TI: 10.00

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7.00

8.00

Knowledge Space

Design Space

Quality by Design “QbD”Design Space Determination

4.00

5.00

6.00

Design Space

Control Space

3.00 4.00 5.00 6.00 7.00

2.00

3.00

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Agenda Transition


(FDA references)

Finding the design space with DOE(tableting process)


39June 2013 Webinar

QbD – New vs Existing Process

Implementation of DOE as a QbD tool depends on your current state of knowledge about the process:

New Process Optimization

Use RSM to simultaneously model the influencing factors and focus in on where to operate.

Use Tolerance Intervals to define the design space.

Existing Process

Design space is assumed to be known from pre existing Design space is assumed to be known from pre-existing production data.

Use factorial DOE with Tolerance Intervals to verify design space, that is, demonstrate that no large effects will occur.

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Extrusion-SpheronizationGeneral Process Background

The extrusion-spheronizationi l d i thprocess is commonly used in the

pharmaceutical industry to make uniformly sized spheroids.

It is especially useful for making dense granules for controlled-release solid dosage oral forms.

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Extrusion-SpheronizationQbD Background Info

Previous study of this process showed that four factors are the key drivers of sphere size. Based on experience we believe that

ithi th i th d ll t ithwithin the ranges given the process produces pellets with a mean size of 750 µm and within specifications; 700 to 800 µm.

Name Units Low High

Kneading time sec 200 300

Extruder speed rpm 60 80

Spheronizer time sec 700 800

Gather data to submit for QbD design space.

Spheronizer time sec 700 800

Spheronizer speed rpm 800 1000

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Extrusion-SpheronizationBuild the Design (page 1 of 3)

1. Build a four factor full factorial design:

Add 4 center points

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2. Enter the factor information:

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3. Enter the response name and units:

Leave the signal and noise blank,

ill i th d i f t l i t l i FDSwe will size the design for tolerance intervals via FDS.

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Extrusion-SpheronizationSize the Design (page 1 of 2)

1. Go to Evaluation and change the model order to “Mean”:

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Extrusion-SpheronizationSize the Design (page 2 of 2)

2. Go to the FDS graph “Tolerance Interval” and enter “d = 50” and “s = 14”:

The design is not precise enough: the black line (the capability of the design) is above the blue line d = 50(what is required by d and s).s = 14

a = 0.05P= 0.99

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Rebuild the design: “Yes” to “Use previous design info?”:

Extrusion-SpheronizationAugment the Design

2 Replicates, 2 Blocks, 3 Center points

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Extrusion-SpheronizationCheck Precision

Check precision of augmented design:

The design is precise enough: the black line (the capability of the design) is below the blue line (what is required by d and s).

d = 50s = 14a = 0.05P= 0.99

49June 2013 Webinar

Extrusion-SpheronizationQbD Illustration #1: Mean Model

Evaluate capability relative to the pellet size specifications: 700 to 800 µm.

Two responses are provided.

Response 1 shows the results if the process is stable over the range tested.

Response 2 shows the results if there are small effects.

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Extrusion-SpheronizationQbD Illustration #1: Mean Model

Design-Expert® SoftwareFactor Coding: ActualPellet size

CI BandsTI BandsDesign Points

820Warning! Factor not in model.

One Factor

Design Points

X1 = A: Kneading time

Actual FactorsB: Extruder speed = 70.00C: Spheronizer time = 750.00D: Spheronizer speed = 900.00

Pel

let s

ize

720

740

760

780

800

200.00 225.00 250.00 275.00 300.00

A: Kneading time

700

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Extrusion-SpheronizationQbD Illustration #2: Linear Model

820 820

linea

r ef

fect

s

700

720

740

760

780

800

linea

r ef

fect

s

700

720

740

760

780

800

200.00 225.00 250.00 275.00 300.00

A: Kneading time

680

700.00 725.00 750.00 775.00 800.00

C: Spheronizer time

680

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Design-Expert® SoftwareFactor Coding: ActualOverlay Plot

linear effectsTI Low

800.00Overlay Plot

TI Low TI High

Design Points

X1 = A: Kneading timeX2 = C: Spheronizer time

Actual FactorsB: Extruder speed = 70.00D: Spheronizer speed = 900.00

725.00

750.00

775.00

C:

Sp

he

ron

ize

r tim

e

linear effects TI: 700.000

linear effects TI: 800.000

6

200.00 225.00 250.00 275.00 300.00

700.00

A: Kneading time

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Agenda Transition


(FDA references)

Finding the design space (tableting process)


S mmar Summary

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Verification for SpecificationsSummary

1. Size your DOE appropriately for its propose: Functional design – size via confidence intervals.

A confidence interval pads our design space to give us confidence that the process mean is within boundaries.

Verify specifications – size via tolerance intervals.A tolerance interval give us confidence that a stated portion of the population is within specifications.

2. TI multipliers are larger than those for a CI. As the sample size increases: As the sample size increases:

• CIs shrink towards zero.• TIs tend towards a fixed value.

3. Tolerance intervals require a large design (sample size).

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Quality by DesignDesign Space Determination

Summary:

Design space determination is a key aspect of QbD “Quality by Design”.

Design space is the multidimensional combination and interaction of input variables that have been demonstrated to provide assurance of quality.

DOE is a means to determine the design space:• Scope out initial formulation and/or process design.• CharacterizationCharacterization• RSM and numeric optimization• Determine design space (graphic optimization)• Verification

57June 2013 Webinar

QbD – New vs Existing Process

Implementation of DOE as a QbD tool depends on your current state of knowledge about the process:

New Process

Use DOE to simultaneously gain knowledge about the influencing factors and interactions, and learn where to operate.

Use Tolerance Intervals to define the design space.

Existing Process

Design space is assumed to be known Design space is assumed to be known. (pre-existing production data)

Use DOE with Tolerance Intervals to verify design space. (show no large effects present).

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ReferencesFDS, and TI

1. Alyaa R. Zahran, Christine M. Anderson-Cook and Raymond H. Myers, “Fraction of Design Space to Assess Prediction”, Journal of Quality Technology, Vol. 35, No. 4, October 2003.

2. Heidi B. Goldfarb, Christine M. Anderson-Cook, Connie M. Borror and Douglas C. Montgomery, “Fraction of Design Space plots for Assessing Mixture and Mixture-Process Designs”, Journal of Quality Technology, Vol. 36, No. 2, October 2004.

3. Steven DE Gryze, Ivan Langhans and Martina Vandebroek, “Using the Intervals for Prediction: A Tutorial on Tolerance Intervals for Ordinary Least-Squares Regression”, Chemometrics and Intelligent Laboratory Systems, 87 (2007) 147 – 154.

4. Gerald J. Hahn and William Q. Meeker, Statistical Intervals; A Guide for Practitioners, (1991) John Wiley and Sons Inc(1991) John Wiley and Sons, Inc,

5. Gary Oehlert and Patrick Whitcomb (2001), Sizing Fixed Effects for Computing Power in Experimental Designs, Quality and Reliability Engineering International, July 27, 2001.

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If we were unable to answer your questions l d th t bi @ t tplease send them to [email protected].

We will reply as soon as possible.

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Half-Normal Plot

Select signif icant terms - see Tips

30

50

70

80

90

95

99

Hal

f-N

orm

al %

Pro

babi

lity

g p

0.00 3.34 6.68 10.02 13.36

01020

|Standardized Ef f ect|

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Adjusted UnadjustedModel Model

F-value p-value F-value p-value

Model

Curvature 0.069 0.7943

Lack of Fit

0.33 0.9685 0.32 0.9723Fit

0.33 0.9685 0.32 0.9723

62June 2013 Webinar

Quality by Design (QbD) Space for Pharmaceuticals and Beyond...Quality by Design “QbD” Design...

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Transcript of Quality by Design (QbD) Space for Pharmaceuticals and Beyond...Quality by Design “QbD” Design...