This presentation from IVT's 2nd Annual Validation Week Canada covers the 2011 FDA Process validation and the subsequent statistical processes. Statistics in process validation is introduced as well as the integration with six sigma and solutions to common mistakes.
4. PV GUIDELINES
• statistical tools to be used in • Emphasis on process design
the analysis of data elements, and maintaining
• the number of process runs process control based on
carried out and observations knowledge gained throughout
made should be sufficient to commercialization
allow the normal extent of • Emphasize to have good
variation and trends to be knowledge to detect and to
established to provide control variability through use
sufficient data for evaluation. of statistical analysis
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5. PROCESS VALIDATION LIFE CYCLE
Variation analysis, capability,
Stage 2: Process
stability analysis
Qualification
Stage 1: Process
Design
Statistics to
analyze and
optimize
results (DOE,
variation
analysis, etc)
Process Capability
Stage 3: Process Monitoring Control Charts
and Improvement
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6. PROCESS UNDERSTANDING
Testing the final
product and passing
specifications does
not give knowledge
of the process
Variation at each production
stage
Knowledge of stability and
capability
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7. PROCESS UNDERSTANDING – KNOW VARIATION
“Understanding variation is the key to success in
quality and business” W. Edwards Deming (Father of
Modern Process Control)
The customers “feel” variation and lack of
consistency in a product much more so than the
“average” (Jack Welch)
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8. FDA PV GUIDANCE RECOMMENDATIONS
INTEGRATED TEAM APPROACH
industrial
pharmacy
Recommended that a statistician quality or
process assurance
person with adequate training in
engineering
and statistical process control technique
manufacturing analytical
develop the data collection plan and
chemistry
statistical methods and procedures
used in measuring and evaluating
microbiology
process stability and process
capability. statistics
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9. DESCRIPTIVE VS INFERENTIAL
STATISTICS
This distinction is based on
what you’re trying to do with The Division Between
your data Descriptive and
Inferential Statistics
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10. DESCRIPTIVE STATISTICS
• Summarizing or displaying the facts
Mean = Sum of all observations/ # of
observations
Range = Max - Min
Standard Deviation
Variance = std dev2
Relative Standard Deviation or CV = std
dev*100/mean
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11. RELATIVE STANDARD DEVIATION
Example 1: Example 2:
Group Size Avg St Dev RSD Group Size Avg St Dev RSD
1 10 80 0.8 1.0 1 10 80 1.0 1.4
2 10 90 0.9 1.0 2 10 90 1.0 1.1
3 10 100 1.0 1.0 3 10 100 1.0 1.0
4 10 110 1.1 1.0 4 10 110 1.0 0.9
5 10 120 1.2 1.0 5 10 120 1.0 0.8
Standard deviation is proportional to the %RSD is changing because the average is
average and the %RSD is unchanged changing, not the standard deviation
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16. INFERENTIAL STATISTICS
• A decision about the batch is based on a relative
small sample taken since it is not realistic to test the
entire batch.
• To confirm that the data is representative of the
batch, inference statistics (confidence and tolerance
intervals) can be used to predict the true mean.
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17. CONFIDENCE INTERVAL
• A confidence interval is an interval within which
it is believed the true mean lies
CI = ±
where is sample mean, s is sample standard
deviation, N is the sample size, and t value is a
constant obtained from t-distribution tables
based on the level of confidence.
Note the value of t should correspond to N-1.
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18. TOLERANCE INTERVAL
• A tolerance interval is an interval within which
it is believed the individual values lie,
TI = ± k*s
where is sample mean, s is sample
standard deviation, N is the sample size, and
k value is a constant obtained from factors for
two-sided tolerance limits for normal
distributions table believed the true mean lies.
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19. EXAMPLE
A batch of tablets was tested for
content uniformity. The mean
value of 10 tablets tested was
99.1% and a standard deviation
was 2.6%.
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21. EXAMPLE: Confidence Interval
• CI = ± = 99.1 ± =96.4 to 101.8
• Then we can say that we are 99% certain that
the true batch mean will be between 96.4%
and 101.8 %.
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23. EXAMPLE: TOLERANCE INTERVAL
• N=10, mean=99.1, s =2.6, k =5.594
TI = ± k*s
• Probability of 99% covering 99% of
data:
TI =99.1 ± (5.594*2.6)
TI = 84.6% to 113.6%
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24. EXAMPLE: Confidence and Tolerance
Interval
• If a sample has the mean value of 10 tablets
at 99.1% and a standard deviation at 2.6%.
• Then we can say that we are 99% certain that
99% of the tablet content uniformity lies
between 80.6 and 117.6% and we are 99%
certain that the true batch mean will be
between 96.4 and 101.8 %.
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26. SAMPLING
• The cGMPs mention samples, sampling plans,
or sampling methods repeatedly.
• Firms are expected:
– To use a sampling plan that utilizes basic elements
of statistical analysis
– Provide a scientific rationale for sampling that
would vary the amount of samples taken
according to the lot size
– Define a confidence limit to ensure an accurate
and representative sampling of the product
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27. WARNING LETTER EXAMPLE
211.165 - Testing and release for distribution:
(d) Acceptance criteria for the sampling and testing conducted by the
quality control unit shall be adequate to assure that batches of drug
products meet each appropriate specification and appropriate
statistical quality control criteria as a condition for their approval and
release. The statistical quality control criteria shall include appropriate
acceptance levels and/or appropriate rejection levels.
“For example, your firm's finished product sampling plan product A is
not representative of the batch produced. A total of 13 units are
sampled per lot, with 3 tested for bacterial endotoxin and 10 tested for
bioburden. This sampling of 13 units is irrespective of lot size, which
may vary from X to Z units (vials) per lot”
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30. SAMPLING RISK
DISPOSITION IMPACT IF LOT IMPACT IF LOT BAD
GOOD
Lot is accepted Correct Decision Incorrect Decision
(Type II or
Consumer’s risk)
Lot is rejected Incorrect Decision Correct Decision
(Type I or Producer’s
risk)
Expressed as Acceptable Quality Level (AQL): maximum average percent
defective that is acceptable for the product being evaluated.
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31. ACCEPTANCE SAMPLING
Acceptance Sampling is a form of inspection applied to lots or
batches of items before or after a process to judge
conformance to predetermined standards.
Sampling Plans specify the lot size, sample size, number of
samples and acceptance/rejection criteria.
Lot Random sample 31
32. OPERATING CHARACTERISTIC CURVE
• The operating-characteristic (OC) curve measures the
performance of an acceptance-sampling plan.
• The OC curve plots the probability of accepting the lot
versus the lot fraction defective.
• The OC curve shows the probability that a lot
submitted with a certain fraction defective will be
either accepted or rejected.
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33. OC CURVES
Ideal OC Curve
Reject all lots with more than 2.5%
defective and accept all lots with less
than 2.5% defective
The only way to assure is 100%
inspection
100
90
acceptance (%)
80
Probability of
70
60
50
40
30
20
10
1 1.5 2 2.5 3 3.5
Percent defective (%) 33
34. OCCs for Single Sampling Plans
An Operating Characteristic Curve (OCC) is a probability curve for a sampling plan that
shows the probabilities of accepting lots with various lot quality levels (% defectives).
1
0.9 Under this sampling plan, if the lot has 3% defective
Probability of accepting lot
the probability of accepting the lot is 90%
0.8
the probability of rejecting the lot is 10%
0.7
0.6
0.5 If the lot has 20% defective
0.4 it has a small probability (5%) of being accepted
0.3 the probability of rejecting the lot is 95%
0.2
0.1
0
0 .05 .10 .15 .20 Lot quality (% defective)
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35. SAMPLING PLANS
Sampling plans involve:
Single sampling
Double sampling
Multiple sampling
Provisions for each type of sampling plan include
1. Normal inspection
2. Tightened inspection
3. Reduced inspection
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36. SWITCHING RULES
“and” conditions: 2 out of 5
Production Steady Start
consecutive
10 consecutive lots lots rejected
accepted
Approved by
responsibility
authority
Tightened
Reduced Normal
5
consecutive
“or” conditions: lots
accepted 10 consecutive
Lot rejected
lots remain on
Irregular production
tightened
A lot meets neither
inspection
the accept nor the
reject criteria
Other conditions Discontinue
warrant return to inspection
normal inspection
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37. SAMPLING BY ATTRIBUTES: ANSI Z1.4 2008
• The acceptable quality level (AQL) is a primary
focal point of the standard
• The AQL is generally specified in the contract or
by the authority responsible for sampling.
• Different AQLs may be designated for different
types of defects (critical, major, minor).
• Tables for the standard provided are used to
determine the appropriate sampling scheme.
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38. ANSI Z1.4 2008
PROCEDURE:
1. Choose the AQL
2. Choose the inspection level
3. Determine the lot size
4. Find the appropriate sample size code
letter from Table I-Sample Size Code Letters
5. Determine the appropriate type of
sampling plan to use (single, double,
multiple)
6. Check the appropriate table to find the
acceptance criteria.
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39. SAMPLE SIZE DETERMINATION
Table I - Sample Size Letter Codes
Special Inspection Levels General Inspection Levels
Lot or Batch Size S-1 S-2 S-3 S-4 I II III
2 to 8 A A A A A A B
9 to 15 A A A A A B C
16 to 25 A A B B B C D
26 to 50 A B B C C D E
51 to 90 B B C C C E F
91 to 150 B B C D D F G
151 to 280 B C D E E G H
281 to 500 B C D E F H J
501 to 1200 C C E F G J K
1201 to 3200 C D E G H K L
3201 to 10000 C D F G J L M
10001 to 35000 C D F H K M N
35001 to 150000 D E G J L N P
150001 to 500000 D E G J M P Q
500001 to over D E H K N Q R
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41. SINGLE SAMPLING PLAN - EXAMPLE
Defect: any color except of red
N = lot size = 25 apples
From Sample Size Code Letters:
Lot or batch size General Inspection
Level
16-25 B
From Normal Single Level Inspection
Sampling Sample Size AQL 0.010
Size Code
Letter
B 3 0/1 Scenario 1: Scenario 2:
0 defects 2 defects
n = sample size =3 Accept Reject
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C=acceptance number = 0 Accept/1 Reject
42. SINGLE SAMPLING PLAN - EXAMPLE
N = lot size = 120,000
From Sample Size Code Letters:
Lot or batch size General Inspection
Level
35,001-150,000 N
Normal Inspection
From Normal Single Level Inspection
Sampling Size Sample Critical Major Minor
Code Letter Size AQL 0.010 AQL 0.65 AQL 4.0
N 500 ACC 0 / REJ 1 ACC 7/ REJ 8 ACC 21 / REJ 22
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43. STATISTICAL PROCESS CONTROL
• The principle of SPC analysis is to understand
the process and detect the process change.
• Statistical Process Control (SPC) charts are
used to detect process variation.
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44. STATISTICAL PROCESS CONTROL
• The Current Good Manufacturing Practices for
Process Validation published by the FDA in
January 2011 states "homogeneity within a
batch and consistency between batches are
goals of process validation activities." Control
charts explicitly compare the variation within
subgroups to the variation between
subgroups, making them very suitable tools
for understanding processes over time
(stability).
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45. VARIABLE CONTROL CHARTS
n=1 2<n<9 n is ‘small’ n is ‘large’
median 3<n<5 n > 10
X & Rm X&R X&R X&S
Used for measured data
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46. CONTROL CHART SELECTION: ATTRIBUTE DATA
Defect or Defective Data
Nonconformity Data
Constant Variable Constant Variable
Sample Size Sample Size n > 50 n > 50
C chart u chart p or np chart p chart
Used for count (attribute) data 46
47. Stable and Unstable Processes
A stable (or “in
control”) process is UCL
one in which the
key process
responses show no
signs of special LCL
causes.
An unstable (or UCL
“out of control”)
process has both
common and
special causes LCL
present.
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48. CONTROL CHART
Tablet Weight
305
UCL
303.7
302
300 mean
298.0
296.3 LCL
285
280
1 hr 30 2hr 30
0 min 30 min 1 hr min 2 hr min
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49. PROCESS CAPABILITY
• Is the process capable of consistently
delivering quality products?
• Is the process design confirmed as being
capable of reproducible commercial
manufacturing?
• Process capability is expressed as a ratio of
specifications/process variability
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51. PROCESS CAPABILITY
Accurate and precise Accurate but not precise Precise but not accurate
Desired Desired
Desired Current
Current Situation
Situation
LSL T USL LSL T USL LSL T USL
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52. PROCESS CAPABILITY INDECES
• Short-term (Cp and Cpk) and/or long term (Pp
and Ppk) are commonly used to evaluate
process performance.
• Cpk attempts to answer the question "does
my current production sample meet
specification?"
• Ppk attempts to answer the question "does
my process in the long run meet
specification?"
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54. PROCESS CAPABILITY
• At a minimum, 50 individual values or 25
subgroups for sub-grouped data are required
to calculate process capability; and 100
individual values provide a stronger basis for
the assessment.
• Use SPC charts to check if the process is stable
• Check the distribution (normal vs not normal)
• Use the Cpk value which represents the
process under consideration
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55. PROCESS CAPABILITY EXAMPLE
• A client had to meet Cpk requirement of ≥
1.20.
• When data was assumed to be normally
distributed, the Cpk =0.8
• When the non-normal behavior was
accounted for, the Cpk = 1.22
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56. SIX SIGMA AND PROCESS VALIDATON
• Six Sigma and Process
Validation
• Use the process
knowledge to make
improvements
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57. SIX SIGMA AND PROCESS VALIDATON
Six Sigma – process improvement methodology
DMAIC
Define Objective To improve compression
process
Measure Measure hardness during PV
Analyze Statistical analysis, calculate Cp/Cpk
Improve Decrease variation
Control Control variation
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59. COMMON MISTAKES
• Incorrect use of statistical tools:
– ANSI Attribute Sampling for measurement data
(pH)
– Incorrect sampling size
– Distribution is not checked
– Process in not stable
– Incorrect uses of Cpk (equivalency between
equipment, large specification limits, etc)
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60. WARNING LETTER: EQUIPMENT
COMPARABILITY AND CAPABILITY
• The firm referenced the Cpk values for processes using a double-sided
tablet press and the single-sided tablet press to demonstrate statistical
equivalence.
• FDA evaluation :
– The Cpk value alone was not appropriate metric to demonstrate
statistical equivalence. Cpk analysis requires a normal underlying
distribution and a demonstrated state of statistical process control.
– Statistical equivalence between the two processes could have been
shown by using either parametric or non-parametric (based on
distribution analysis) approaches and comparing means and variances.
– Firm did not use the proper analysis to support their conclusion that
no significant differences existed between the two compression
processes.
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61. STATISTICAL EVALUATION
• Is required by statute
• Is an expectation of the regulatory inspector
during inspection of the firm as it relates to
process validation of products
• Use statistical tools that are meaningful and
useful to understand the baseline
performance of the process
• Is invaluable as a troubleshooting tool post
validation
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