Transcript Document

Statistical Basis for
Quality by Design
Lynn Torbeck
Evanston, IL
1
Overview
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2.
3.
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6.
7.
Evolution of QbD
Statistical basis for QbD
Controlled Experiments
Cause and Effect
Design Space
Three case studies
Modeling
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• “The only thing new in the world
may be the history we don’t
know.”
• “All models are incorrect, but
some are useful.” G. E. P. Box
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Getting to Quality by Design
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5.
Quality Control
Quality Assurance
Statistical Quality Control
Statistical Process Control
Quality by Design
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Quality Control
• Def #1: Sampling or 100% inspection, test
and accept, reject, rework or scrap. The
focus is on the product after is has been
made. No statistics.
• Def #2: The technical activities of a quality
department working with other departments
to achieve quality. No statistics.
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Quality Assurance
• Management activities needed to run a
quality control department and provide
oversight. This includes organization,
planning, policies, procedures,
documentation, training, suppliers and
working with other departments.
• No statistics
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Statistical Quality Control
• Specific statistical techniques used for end
product quality control including
probability, basic statistics, sampling plans,
statistical metrology, repeatability and
reproducibility studies, as well as tabulating
and reporting defects, rejects and costs.
• A passive descriptive approach.
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Statistical Process Control
• Specific statistical techniques used to
monitor, improve and control the
manufacturing process itself. These
include probability, basic statistics,
graphics, statistical control charts, process
capability studies and designed experiments
for improvement and optimization.
• An active approach for the process
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Quality by Design
• A broad life-cycle approach to development
that uses statistics but is not limited to
statistics. Statistical techniques include,
basic statistics, inferential statistics,
graphics, experimental design and statistical
model building using contour plots and
response surfaces. An active approach to
product and process development.
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Statistical Basis for QbD
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Correct data collection
Define the reportable result or value
Find summary statistics, average, S
Do controlled experiments
Develop mathematical models
Infer to the larger population
Maintain control of the product / process
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Controlled Experiments
1. Success / Failure
2. One-Factor-at-a-Time
3. Multiple-Factors-at-a-Time, DOE
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2.
3.
4.
Full Factorials
Fractional Factorials
Plackett – Burman designs
Central Composite designs
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The Genius
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Sir Ronald A. Fisher
Born 1890
Died 1962
Graduated college in 1913, math, genetics
1919 joined Rothamsted Experimental
Station in Harpenden, England
• The right person in the right place.
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13
In The Beginning
• 1926, “The Arrangements of Field
Experiments.” Journal of the Ministry of
Agriculture of Great Britain. Fisher.
• 1935, The Design of Experiments, Oliver &
Boyd, London. Fisher.
• 1946, “The Design of Optimum Multifactor
Experiments,” Plackett and Burman.
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More Beginning
• 1951, “On the Experimental Attainment of
Optimum Conditions,” Box and Wilson.
• “… determining optimum conditions in
chemical investigations, …”
• Finding the effect of quantitative factors on
a measured response.
• Thus, factor space and response space.
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Industrial Applications
• 1954, The Design and Analysis of Industrial
Experiments, Davies, editor.
• “In this field [chemical industries] statistical
methods have a major contribution to make to
industrial research, because the use of such
methods enables clear and unambiguous
conclusions to be drawn from the minimum
number of experiments and therefore for the
minimum cost.”
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“The Book” on DOE
• 1978, Statistics for Experimenters, Box,
Hunter and Hunter.
• This is the text that popularized DOE.
• “Scientific research is a process of guided
learning. The object of statistical methods is
to make that process as efficient as
possible.”
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• “If the experimental design is poorly chosen, so
that the resultant data do not contain much
information, not much can be extracted, no
matter how thorough or sophisticated the
analysis. On the other hand, if the experimental
design is wisely chosen, a great deal of
information in readily extractable form is usually
available, and no elaborate analysis may be
necessary. In fact, in many happy situations all
the important conclusions are evident from
visual examination of the data.”
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Basic Science
Cause
?
Effect
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Classic Fishbone
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R=
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6.
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Terminology - Cause
Causes =
Input variables = “X” variables
Independent Variables =
Factors = Factor Space
Critical Parameters for materials, processes
and products or CP
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Terminology - Effect
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Effects =
Output variables = “Y” variables
Dependent Variables =
Responses = Response Space
Critical Quality Attributes for processes and
products or CQAs
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Design Space
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FACTOR SPACE
N dimension X’s
X1
X2
X3
X4
X5
XN
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RESPONSE SPACE
M dimension Y’s
Y1
Y2
Y3
Y4
Y5
YM
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Design space
Independent
Factor
Space
f(x)=?
Dependent
Response
Space
“Linkage”
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More Terminology
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Univariable = One variable at a time
Multivariable = More than one variable
Empirical #1 = Not using DOE, Trial/Error
Empirical #2 = DOE & generic equations
Systematic = DOE & generic equations
Mechanistic = DOE and theory equation
E=MC2
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Perturbation Study of Dissolution
Apparatus Variables
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Eaton, J.; Deng, G. and Hauck, W., et all.
Dissolution Technologies, February 2007
USP dissolution apparatus 2
USP Prednisone Reference tablets
Response is mean percent dissolved & S
9 variables, each at two levels.
A 46 run resolution V design was used.
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Nine Multifactor Variables
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Temperature
Shaft wobble
Rotation speed
Vessel centering
Vessel tilt
Paddle height
Base plate levelness
Vessel types
Level of deaeration
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What They Found
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For the mean percent dissolved
Three statistically significant variables:
Level of deaeration
Vessel type
Rotation speed
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Designing in a Vacuum
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James Dyson of Dyson Ltd.
Invented the Dyson vacuum cleaner
Experimented with cardboard and tape
“I made hundreds of cyclones, then
thousands of them.”
• Hand built 5,127 prototypes
• He claims using the “Edisonian” process
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Prototyping
• “When you develop a prototype, you have
to change one thing at a time. If you make
several changes simultaneously, how do
you know which change has improved the
object and which hasn’t?”
• “You have to be very patient, testing and
retesting and building a series of results.”
• United’s Hemispheres Magazine, November 2005, p86
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1954 Example
• Box, G. E. P. “The Exploration and
Exploitation of Response Surfaces,”
Biometrics, 10, 16, 1954
• “The object of this paper is to discuss and to
illustrate with examples certain ideas which
have arisen from the [prior] work and which
it is believed may be of value in a wider
field than that of chemical research.”
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5-1
2
A
-1
1
-1
1
-1
1
-1
1
-1
1
-1
1
-1
1
-1
1
B
-1
-1
1
1
-1
-1
1
1
-1
-1
1
1
-1
-1
1
1
Fractional Factorial
C
-1
-1
-1
-1
1
1
1
1
-1
-1
-1
-1
1
1
1
1
D
-1
-1
-1
-1
-1
-1
-1
-1
1
1
1
1
1
1
1
1
E
1
-1
-1
1
-1
1
1
-1
-1
1
1
-1
1
-1
-1
1
Yield %
49.8
51.2
50.4
52.4
49.2
67.1
59.6
67.9
59.3
70.4
69.6
64
53.1
63.2
58.4
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64.3
B
B
+1
+1
50.40
52.40
59.60
69.60
67.90
-1
49.80
58.40
51.20
A
64.30
-1
59.30
-1
70.40
-1
-1
-1
49.20
C
64.00
67.10
+1
53.10
C
Left Cube is D = LOW
E = HIGH
63.20
+1
Right Cube is D = HIGH
E = LOW
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A
+1
One Factor
Design-Expert® Software
Yield
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X1 = A: A
65.5
Yield
Actual Factors
B: B = 0.00
C: C = 0.00
D: D = 0.00
E: E = 0.00
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54.5
49
-1.00
-0.50
0.00
A: A
0.50
1.00
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Interaction
Design-Expert® Software
D: D
Yield
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D- -1.000
D+ 1.000
X1 = C: C
X2 = D: D
Yield
Actual Factors
A: A = 1.00
B: B = 0.00
E: E = 0.00
67
61
55
49
-1.00
-0.50
0.00
C: C
0.50
1.00
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Yield
Design-Expert® Software
1.00
Yield
70.4
66.5396
49.2
0.50
64.0604
Actual Factors
A: A = 1.00
B: B = 0.00
E: E = 0.00
D: D
X1 = C: C
X2 = D: D
0.00
61.5812
-0.50
59.1021
56.6229
-1.00
-1.00
-0.50
0.00
C: C
0.50
1.00
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Design-Expert® Software
Yield
70.4
49.2
70
X1 = C: C
X2 = D: D
Actual Factors
A: A = 1.00
B: B = -1.00
E: E = 0.97
Yield
66
62
58
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1.00
1.00
0.50
0.50
0.00
D: D
0.00
-0.50
-0.50
-1.00
-1.00
C: C
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Model Evaluation
• Coefficient of Determination
• R Squared or R2
• The percent of variability in the data that is
explained by the proposed model equation.
• R2 ranges from zero to one hundred %
• R2 needs to be large, say greater than 90%
and preferably 95% to 99%.
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Robustness
• “… a measure of its capacity to remain
unaffected by small but deliberate variations
in method parameters and provides an
indication of its reliability during normal
usage.”
• Reliability is consistency over time
• “The evaluation of robustness should be
considered during the development phase.”
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Ruggedness
• “… the degree of reproducibility of test
results obtained by the analysis of the same
samples under a variety of normal test
conditions …”
• See Torbeck, L. “Ruggedness and Robustness with
Designed Experiments,” Pharmaceutical Technology,
March 1996.
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Flat Line Variables
• “An input variable or process parameter
need not be included in the design space if it
has no effect on delivering CQAs when the
input variable or parameter is varied over
the full potential range of operation.”
• A graph would show a flat horizontal line
• Changing X has no effect on the value of Y
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Mechanistic Models
• Box, G. E. P. and Youle, P. V.
• “Exploration and Exploitation of Response
Surfaces. An Example of the Link Between
the Fitted Surface and the Basic Mechanism
of the System.”
• Biometric, 1955
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“Mechanistic Understanding”
• “The present article shows how study of the
form of the empirical surface can throw
important light on the basic mechanism
operating and can thus make possible
developments in the fundamental theory of
a process.”
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A Theoretical Surface
• “A theoretical surface, based on reaction
kinetics is now derived, rate constants are
estimated from the data and the theoretical
surface is compared with the empirical
surface previously obtained.”
• Called Mechanistic Model Building.
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Process Reengineering
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Also called Reverse Quality by Design
Work on an existing or legacy product
Use historical and validation data
Use designed experiments to find the cause
and effect relationships between the process
parameters, factors, and the quality
attributes, the responses.
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Chemometrics
• From Wikipedia, the free encyclopedia
• Chemometrics is the application of mathematical or statistical
methods to chemical data. The International Chemometrics Society
(ICS) offers the following definition:
• Chemometrics is the science of relating measurements made on a
chemical system or process to the state of the system via application of
mathematical or statistical methods.
• Chemometric research spans a wide area of different methods which
can be applied in chemistry. There are techniques for collecting good
data (optimization of experimental parameters, design of experiments,
calibration, signal processing) and for getting information from these
data.
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Chemometrics’ Tools
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Multivariate data acquisition
Principal Component Analysis
Classical Least Squares regression analysis
Multiple Linear Regression
Principal components Regression
Partial Lease Squares
Discriminant Analysis
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Take Home Points
• The statistical basis for QbD was first
published in 1951 by Box and Wilson.
• Mechanistic model concepts were first
published in 1955 by Box and Youle.
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A Last Thought
• “Statistical thinking will one
day be as necessary for
efficient citizenship as the
ability to read and write.”
• H. G. Wells
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Historical Articles
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1926, R. Fisher, “The Arrangements of Field Experiments,” J of the Ministry of
Agriculture, England, Vol. 33, 1926, pp 503-513.
1937, F. Yates, “Design and Analysis of Factorial Experiments,” Commonwealth
Bureau of Soil Science, Technical Communication No. 35, 1937.
1946, “The Design of Optimum Multifactorial Experiments,” Biometrika, Vol. 33,
1946, pp 305-325.
1951, G. Box and K. Wilson, “On the Experimental Attainment of Optimum
Conditions,” J of the Royal Statistical Society, Series B, Vol. XII, No. 1, 1951.
1954, G. Box, “The Exploration and Exploitation of Response Surfaces: Some
Considerations and Examples,” Biometrics, 10: 16, 1954.
1955, G. Box and P. Youle, “The Exploration and Exploitation of Response
Surfaces: An Example of the Link Between the Fitted Surface and the Basic
Mechanism of the System,” Biometrics, Vol. 11, pp 287-323, 1955.
1957, G. Box and S. Hunter, “Multi-Factor Experimental Designs for Exploring
Response Surfaces,” Ann Math Statistics, 28, pp 195-241.
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Historical Books
• 1935, R. Fisher, The Design of Experiments, Oliver &
Boyd, Edinburgh, 1935.
• 1949, K. Brownlee, Industrial Experimentation, Chemical
Publishing Co., 1949.
• 1950, Experimental Design,, W. Cochran and G. Cox, John
Wiley & Sons, 1950.
• 1954, O. Davies, Ed, The Design and Analysis of
Industrial Experiments, Longman Group, London, 1954
• 1954, Statistical Analysis In Chemistry and the Chemical
Industry, C. Bennett and N. Franklin, John Wiley & Sons,
1954.
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A Few of Many Articles
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L. Torbeck, “Ruggedness and Robustness with Designed Experiments,”
Pharm Tech, March 1996.
L. Torbeck and R. Branning, “Designed Experiments – A Vital Role in
Validation” Pharm Tech, June 1996.
C. Chen and C. Moore, CDER/FDA, “Role of Statistics In Pharmaceutical
Development Using Quality by Design Approach – An FDA Perspective,
FDA/Industry Statistics Workshop, Washington, DC, September 27-29, 2006
X. Castells, et all, “Application of Quality by Design Knowledge From Site
Transfers to Commercial Operations Already in Progress, Process Analytical
Technology, Vol. 3, No. 1, Jan/Feb 2006.
J. Eaton, et all, “Perturbation Study of Dissolution Apparatus Variables – A
Design of Experiment Approach, Dissolution Technologies, February 2007, pp
20-26.
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Recommended Books
1.
2.
3.
4.
5.
6.
R. Gunst, and R. Mason, How to Construct Fractional Factorial
Experiments, ASQ Quality Press, Vol. 14, 1991.
J. Cornell, How to Apply Response Surface Methodology, ASQ Quality
Press, Vol. 8, 1984.
L. Torbeck, Ed, Pharmaceutical and Medical Device Validation by
Experimental Design, Informa Healthcare, 2007. Source of case studies
G. Lewis, D. Mathieu and R. Phan-Tan-Luu, Pharmaceutical Experimental
Design, Marcel Dekker, 1999.
P. Mathews, Design of Experiments with Minitab, ASQ Quality Press,
2005.
G. Box, J. Hunter and W. Hunter, Statistics for Experimenters, John Wiley
and Sons, 2005.
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References - Software
• Design-Expert,
http://www.statease.com/
• Minitab, http://www.minitab.com/
• JMP, http://www.jmp.com/
• MODDE,
http://www.umetrics.com/default.asp/p
agename/software_modde/c/2
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References - Internet
• NIST,
http://www.itl.nist.gov/div898/handbook/in
dex.htm
• http://www.sixsigmafirst.com/Templates/do
e1.htm
• http://www.umetrics.com/default.asp/pagen
ame/software_modde/c/2
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How to Get Started
1. Buy Gunst and Mason’s book from ASQ.
Read it and the internet information
2. Do simple full factorials or fractional
factorials by hand. Learn from them.
3. Buy a software package and do more
experiments, gaining in expertise.
4. Take a formal training course.
5. “There is no instant pudding.” Deming
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THANK YOU
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