Transcript ISPE OFFICE SPACE ANALYSIS

Mark Varney
Statistics Program Manager
Abbott Quality and Regulatory
Abbott Park, IL
FDA Process Validation Guidance, Jan 2011
• Statistics mention 15 times
• “statistical”
• “statistics”
• “statistically”
• “statistician” – as a suggested team member
• Clear that FDA expects more statistical thinking in validation
• Some statisticians asked to be a team member may not be
familiar with Quality Assurance applications and jargon
• Acceptance Sampling
• Statistical Process Control (SPC)
• Process Capability
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FDA Process Validation Guidance Overview
Process Validation: The collection and evaluation of data, from
the process design stage through commercial production,
which establishes scientific evidence that a process is
capable of consistently delivering quality product.
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FDA Process Validation Guidance Overview
The new Guidance specifies a lifecycle approach:
• Stage 1 – Process Design
• Statistically designed experiments (DOE)
• Stage 2 – Process Qualification
• Design of facility and equipment/utilities qualification
• Process Performance Qualification (PPQ)
• SPC; Variance components; Acceptance Sampling; CUDAL, etc.
• Number of lots required is no longer specified as three
• Must complete Stage 2 before commercial distribution
• Stage 3 – Continued Process Verification (CPV)
• Continual assurance the process is operating in a state of control
• Data trending, SPC, Acceptance Sampling, etc.
• Guidance recommends scrutiny of intra- and inter-batch variation
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Statistical Acceptance Criteria for Validation
Provide X% confidence that the
requirement has been met
Requirements: Process performance to consistently meet attributes
related to identity, strength, quality, purity, and potency
Statistical confidence required may be based on…
• Risk
• Scientific knowledge
• Criticality of attribute (AQL, etc.)
• Prior / historical knowledge
• Stage 1 knowledge
• Revalidation
• Is test an abuse test?
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Three Common Situations
Provide statistical confidence that…
1. A high percent of the population is within specification
2. A population parameter is within specification
- Mean; Standard Deviation; RSD; Cpk/Ppk
3. A standard test (UDU, Dissolution, etc.) will pass
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Assure a High % of Population in Spec
“90% confidence at least 99% of population meets spec”
“90% confidence nonconformance rate <1%”
“90% confidence for 99% reliability”
Common statistical methods
• Continuous data: Normal Tolerance Interval
• Discrete data: High Confidence Binomial Sampling Plan
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A Word about Confidence…
Which sampling plan provides more confidence?
1. n=90,
accept=0, reject=1 99% confidence ≥95% conforming
2. n=300, accept=0, reject=1 95% confidence ≥99% conforming
3. n=2300, accept=0, reject=1 90% confidence ≥99.9% conforming
What you want to be confident of
is usually more important than
how confident you want to be
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Validation: High Degree of Assurance
• Phrase “high degree of assurance” mentioned four times
• “…the PPQ study needs to be completed successfully and
a high degree of assurance in the process achieved
before commercial distribution of a product.”
ICH Q7A GMP for APIs:
• “A documented program that provides a high degree of
assurance that a specific process, method, or system will
consistently produce a result meeting pre-determined
acceptance criteria.”
• Suggest 90% or 95% confidence is acceptable
• This confidence is more related to Type II error and Power
• Although α=0.05 / 95% confidence is common for Type I error, it is
not as common for power, where 80% and 90% also common.
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Assure a High % is Within Spec
Variables data: Normal Tolerance Interval*
• Example: Show with 90% confidence that at least 99.6%
of powdered drug fill weights meet spec of 505-535mg.
• Test n=50 bottles; 1 every 5 minutes for 4 hrs
• Acceptance criterion: 90% confidence ≥99.6% meet spec
• Variables data with average, s.d.: use tolerance interval method
• Mean  ks must be within specification limits
• Why 99.6%? Production AQL is 0.4% for fill weight.
*other methods may be used, such as variables sampling; may give lower Type I error
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Fill Weight Example
F ill e r V a li da tio n R un
I C ha r t
C a pa bility H isto gr a m
I n d iv id u a l Va lu e
530
UC L = 529.10
L SL
U SL
S p e cifica tio n s
_
X = 519.31
520
510
6
11
16
21
26
31
36
41
46
508 512 516 520
M o v ing R a nge C ha r t
535
524 528 532
No r m a l P r o b P lo t
A D : 0 .4 6 4 , P : 0 .2 4 5
UC L = 12.03
M o v in g R a n g e
505
USL
L C L = 509.52
1
10
__
M R = 3.68
5
0
LC L= 0
1
6
11
16
21
26
31
36
41
46
510
515
L a st 5 0 O bse r v a tio ns
520
522
516
510
W ith in
10
20
30
40
50
O b se rv a tio n
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11
O v e ra ll
S tD e v
3 .2 6 3 8 6
S tD e v
3.24963
Cp
1 .5 3
Pp
1.54
C pk
1 .4 6
P pk
1.47
C pm
*
O v e ra ll
S p e cs
0
525
C a pa bility P lo t
W ith in
Va lu e s
LS L
Fill Weight Example
• Process is in statistical control, normality not rejected
• 90% confidence / 99.6% coverage tolerance interval:
x  ks  519 . 31  3 . 35  3 . 25
 ( 508 . 4  530 . 2 )
• Pass: Tolerance interval lies within spec of 505 - 535
• We can be 90% confident ≥99.6% of containers meet spec
• Will be able to pass in-process 0.4% AQL sampling
• If process is stable, 90% confidence ≥95% of lots will pass
• Engineer friendly: tables or software can be used
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2-Sided Normal Tolerance Interval Factors
Two-Sided Normal Tolerance Limit k-Factors
90% Confidence
95% Confidence
% Coverage
% Coverage
n 95% 99% 99.6% 99.9%
n 95% 99% 99.6% 99.9%
20 2.56 3.37 3.76 4.30
20 2.75 3.62 4.04 4.61
30 2.41 3.17 3.55 4.05
30 2.55 3.35 3.74 4.28
40 2.33 3.07 3.43 3.92
40 2.45 3.21 3.59 4.10
50 2.28 3.00 3.35 3.83
50 2.38 3.13 3.49 3.99
60 2.25 2.96 3.30 3.77
60 2.33 3.07 3.43 3.92
70 2.22 2.92 3.27 3.73
70 2.30 3.02 3.38 3.86
80 2.20 2.89 3.24 3.70
80 2.27 2.99 3.34 3.81
90 2.19 2.87 3.21 3.67
90 2.25 2.96 3.31 3.78
100 2.17 2.85 3.19 3.65
100 2.23 2.93 3.28 3.75
Mean ± 3.35s must be within spec limits
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1-Sided Normal Tolerance Interval Factors
One-Sided Normal Tolerance Limit k-Factors
90% Confidence
95% Confidence
% Coverage
% Coverage
n 95% 99% 99.6% 99.9%
n 95% 99% 99.6% 99.9%
20 2.21 3.05 3.46 4.01
20 2.40 3.30 3.73 4.32
30 2.08 2.88 3.27 3.79
30 2.22 3.06 3.47 4.02
40 2.01 2.79 3.17 3.68
40 2.13 2.94 3.33 3.87
50 1.97 2.73 3.11 3.60
50 2.07 2.86 3.25 3.77
60 1.93 2.69 3.06 3.55
60 2.02 2.81 3.19 3.70
70 1.91 2.66 3.02 3.51
70 1.99 2.77 3.14 3.64
80 1.89 2.64 3.00 3.48
80 1.96 2.73 3.10 3.60
90 1.87 2.62 2.97 3.46
90 1.94 2.71 3.07 3.57
100 1.86 2.60 2.96 3.44
100 1.93 2.68 3.05 3.54
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A problem with most normality tests
•
•
Need to check for normality to use normal tolerance interval
Process quality data is often rounded
•
•
•
Or data is “granular”
Most normality tests will interpret rounding as non-normality
Example: n=100 from N(100,1.52)
Unrounded
100.071
98.238
99.122
99.190
100.623
Rounded
100
98
99
99
101
… , n=100
… , n=100
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A problem with most normality tests
N o rm a l P ro b a b ility P lo t o f U n ro u n d ed
P e rc e n t
99.9
M ean
99.78
99
StD e v
1.502
95
90
80
70
60
50
40
30
20
10
5
N
100
AD
0.379
P-V a lue
0.400
1
0.1
9 5 .0
9 7 .5
1 0 0 .0
1 0 2 .5
1 0 5 .0
Un rou n de d
Unrounded data: normality not rejected by Anderson-Darling test
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A problem with most normality tests
n = 1 0 0 , N ( 1 0 0 , 1 .5 ^ 2 ) R o u n d ed to 0 D ec im a ls
30
Fre q u e n c y
25
M ean
99.84
StD e v
1.536
N
20
15
10
5
0
96
98
100
102
R ou n de d
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104
100
A problem with most normality tests
• Rounding data causes most normality tests to fail
• SAS 9.2 Proc Univariate Tests:
Unrounded Data
Test
Shapiro-Wilk
Kolmogorov-Smirnov
Cramer-von Mises
Anderson-Darling
--Statistic--W
0.98874
D
0.063184
W-Sq
0.06213
A-Sq 0.378299
-----p Value-----Pr < W
0.5643
Pr > D
>0.1500
Pr > W-Sq >0.2500
Pr > A-Sq >0.2500
Rounded Data (to whole numbers)
Test
--Statistic--Shapiro-Wilk
W
0.956808
Kolmogorov-Smirnov
D
0.148507
Cramer-von Mises
W-Sq 0.358655
Anderson-Darling
A-Sq 1.926991
-----p Value-----Pr < W
0.0024
Pr > D
<0.0100
Pr > W-Sq <0.0050
Pr > A-Sq <0.0050
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OK
Reject
normality
A problem with most normality tests
• Two normality tests not substantially affected by granularity
• Ryan-Joiner test (Minitab 16)
• Omnibus skewness/kurtosis test
P ro ba b ility P lo t o f R o u n d e d a n d R ya n - Jo in e r T e st
P e rc e n t
99.9
M ean
99.84
99
StD e v
1.536
95
90
N
80
70
60
50
40
30
20
P-V a lue
RJ
100
0.999
> 0.100
10
5
1
0.1
95.0
97.5
100.0
102.5
105.0
R ou n de d
For more information, see Seier, E. “Comparison of Tests for Univariate Normality.”
http://interstat.statjournals.net/YEAR/2002/articles/0201001.pdf
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Confidence for Conformance Proportion
•
Usual 2-sided normal tolerance interval controls both tails
•
This can present a problem for an uncentered process
2-Sided Normal Tol Int for 99% Coverage Will Fail
Both tails controlled to 0.5%, half of the non-coverage
LSL
USL
0.6%
94
95
96
97
98
99
100
101
20
20
102
103
104
105
Estimation for Conformance Proportion
Example: Removal Torque, Spec = 5.0 – 10.0 in-lbs
95% conf / 99% coverage tolerance interval: (4.85, 8.62) FAILS
T o r que : 9 5 % C o nfide nc e / 9 9 % C o v e r a ge T o le r a nc e Inte r v a l
5
10
St a t ist ics
N
5 .0
5 .5
6 .0
6 .5
7 .0
7 .5
8 .0
8 .5
9 .0
9 .5
30
Me a n
6.738
St De v
0.561
No rma l
1 0 .0
T o l_I n t
Lo w e r
4.852
.
Upper
8.623
5
6
7
8
9
10
No rm a l P ro b a b ilit y P lo t
99
P e r ce nt
90
50
10
1
5.5
6.0
6.5
7.0
7.5
8.0
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8.5
No rma lit y Te st
AD
0.281
P -Va lue
0.617
Estimation for Conformance Proportion
•
Usual 2-sided normal tolerance interval controls both tails
•
•
This can present a problem for an uncentered process
Can use estimation for proportion conforming
•
•
•
Also called bilateral conformance proportion
Reduce probability of failing for uncentered processes
Similar method used by ANSI Z1.9 for routine production sampling
Let Y be the quality characteri stic with specificat ion [ A , B ]
The bilateral conformanc e proportion   Pr( A  Y  B )
Pass if upper C . I . for  is  acceptance value ( usually the AQL )
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Estimation for Conformance Proportion
Estimation for Conformance Proportion for Removal Torque:
95% confidence ≥ 99.07% conforming: PASS
Torque
No Transformation (Normal Distribution)
Sample Size =
Average =
Standard Deviation =
Skewness =
Excess Kurtosis =
30
6.737513
0.561204
0.47
0.72
Test of Fit: p-value =
(SK All)
Decision =
(SK Spec) Decision =
0.2808
Pass
Pass
Pp =
Ppk =
Est. % In Spec. =
1.48
1.03
99.901940%
LSL = 5
USL = 10
5.5723100 6.87139008.1704700
With 95% confidence more than 99% of the values are between 4.8576399 and 8.6173854
With 95% confidence more than 99.0666% of the values are in spec.
Lee, H., and Liao, C. “Estimation for Conformance Proportions in a Normal Variance Components
Mode.” Journal of Quality Technology, Jan., 2012.
Taylor, W. Distribution Analyzer, version 1.2.
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Random Effects Process Tolerance Limits
• Overall process tolerance limits may be constructed to take
between-lot variation into account
• Example: Impurities
Lot 1
Lot 2
Lot 3
n Mean
20 0.047
20 0.054
20 0.050
StDev
0.0113
0.0055
0.0087
Min
0.018
0.046
0.035
Max
0.069
0.065
0.068
• Approx 90% confidence / 95% coverage tolerance interval1:
x ..  t k 1 (  1 , )
ss 
k ( k  1) n
 0 . 12
Appears conservative
• Usual 90/95% tolerance interval for all data combined: 0.07
1Krishnamoorthy,
K. and Mathew, T. “One-Sided Tolerance Limits in Balanced and Unbalanced One-Way
Random Models Based on Generalized Confidence Intervals.” Technometrics, Vol. 46, No. 1, Feb. 2004.
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What is an AQL?
• AQL = "Acceptance Quality Limit“
• The quality level that would usually (95% of the time) be
accepted by the sampling plan
• RQL = "Rejection Quality Limit“
• The quality level that will usually (90% of the time) be rejected
by the sampling plan
• Also called LTPD (Lot Tolerance Percent Defective)
• Also called LQ (Limiting Quality)
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AQL / RQL
AQL: Pr(accept)=0.95
RQL: Pr(accept)=0.10
AQL and RQL (LTPD) for n=50, a=1
1.0
Probability of Acceptance
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
1
2
3
4
5
6
7
8
9
10
Percent Defective
RQL = 7.56%
AQL = 0.72%
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What is an AQL?
Can be cast as a hypothesis test or confidence interval
For routine acceptance sampling…
Ho: p ≤ Assigned AQL
H1: p > Assigned AQL
α=0.05, “accept” lot if Ho not rejected
But for validation…
Ho: p > Assigned AQL
H1: p ≤ Assigned AQL or desired performance level
α =1-confidence; i.e., 1-.90 = .10 for 90% confidence
Pass validation if Ho rejected
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Typical AQLs in Pharma / Medical Devices
Product Attribute
Typical Assigned AQLs
Critical
0.04%, 0.065%, 0.1%, 0.15%, 0.25%
Major Functional
0.25%, 0.4%, 0.65%, 1.0%
Minor Functional
0.65%, 1.0%, 1.5%
Cosmetic Visual
1.5%, 2.5%, 4%, 6.5%
• For validation, suggest 90% confidence that process ≤ assigned AQL
• Why 90%?
• Traditional probability used for RQL/LTPD/LQ
• This means for validation the assigned AQL is treated as an RQL
• If nonconforming rate is at AQL, will fail validation 90% of the time
• Selection of the AQL more important than confidence selected
• Much tighter than ANZI Z1.4/Z1.9 tightened (10-20% confidence)
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Assure high % within spec: attributes data
Conforming
99.9%
99.6%
99.0%
97.5%
95.0%
90% Confidence 95% Confidence
n
a
n
a
2300
0
3000
0
3890
1
4745
1
5320
2
6295
2
575
0
750
0
970
1
1185
1
1330
2
1575
2
230
0
300
0
390
1
475
1
530
2
630
2
90
0
120
0
155
1
190
1
210
2
250
2
45
0
29
0
77
1
45
1
105
2
60
2
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Attributes data is
binomial pass/fail data
Example:
n=230, a=0 provides
90% confidence ≥ 99%
conforming;
90% confidence ≤1%
nonconforming
Attributes Example for AQL: Fill Volume PPQ
• Production assigned AQL is 1.0%
• AQL = “Acceptance Quality Limit”
• Assigned based on risk assessment
• If process is better than AQL, almost all mfg lots will be accepted
• Validation: Show with 90% confidence that the process
produces ≤1.0% nonconforming units
• Multi-head filler; we know data are non-normal
• 90% confidence ≥99% are in spec
• Medical devices: 90% confidence for 99% “reliability”
• Assures that future AQL production sampling can be passed
• If process is at the AQL, ~95% of lots will pass AQL sampling
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Example: Fill Volume
• Attributes plans: 90% confidence ≤1.0% nonconforming
Sampling Plan
RQL0.10
n=230, acc=0, rej=1
1.0%
n=390, acc=1, rej=2
1.0%
n1=250, a1=0, r1=2
n2=250, a2=1, r2=2
1.0%
Z1.4 normal: n=80, acc=2
Z1.4 tightened: n=80, acc=1
• If the validation sampling plan passes…
• We have 90% confidence the nonconforming rate is ≤1.0%
• ANSI Z1.4 plans provide far less than 90% confidence
• Normal sampling: typically about 5% confidence
• Tightened: typically about 15% confidence
• Note: RQL=“Rejection Quality Limit”
• Also called LTPD (Lot Tolerance Pct Defective) or LQ (Limiting Quality)
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PV Acceptance Criteria for Attribute Types
Attribute type
Comment
AQL attributes
• Fill volume
• Tablet defects
• Extraneous matter, etc.
≥90% confidence that
• Nonconformance rate ≤ assigned AQL
Non-AQL attributes
• Dissolution / UDU / Batch Assay
• Other tests
≥90% confidence that…
• USP test will be met ≥95% of the time
• ≥99% of results in spec (critical)
• ≥95% of results in spec (non-critical)
Statistical Parameters
• Mean / sigma / RSD(CV)
• Cpk, Ppk
≥90% confidence that…
• Mean / sigma / RSD in spec
• Ppk ≥1.0, 1.33 or related to % coverage
No within batch variation expected
• pH of a solution
• Label copy text
Statistics not usually necessary
• May consider 3X-10X testing
• Assess between lot variation
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Show Population Parameter Meets Spec
• Show confidence interval for parameter in spec
• Example: API mean potency; spec of 98.0-102.0
• n=30 test results (3 from each of 10 drums)
• 95% C.I. for mean is traditional
S umma r y fo r A P I
A n d e rso n -D a rlin g N o rm a lity T e st
A -S q u a re d
P -V a lu e
M ean
S tD e v
V a ria n ce
S k e w n e ss
K u rto sis
N
M in im u m
100.0
100.4
100.8
101.2
0 .7 0
0 .0 5 9
1 0 0 .4 0
0 .3 7
0 .1 4
0 .4 4 0 5 6 5
-0 .9 9 7 4 8 0
30
9 9 .8 4
1 st Q u a rtile
1 0 0 .0 8
M e d ia n
1 0 0 .2 9
3 rd Q u a rtile
1 0 0 .7 5
M a xim u m
1 0 1 .1 3
9 5 % C o n fid e n ce I n te rv a l fo r M e a n
1 0 0 .2 6
1 0 0 .5 4
9 5 % C o n fid e n ce I n te rv a l fo r M e d ia n
1 0 0 .1 4
1 0 0 .6 2
9 5 % C o n fid e n ce I n te rv a l fo r S tD e v
9 5 % C o n f id e n c e I n t e r v a ls
0 .3 0
M ean
M edian
100.1
100.2
100.3
100.4
100.5
100.6
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95% C.I. for mean is
100.26 – 100.54; pass.
0 .5 0
Also need to analyze
data across drums!
Process Capability/Performance Statistic Ppk
Measures process capability of meeting the specifications
P pk
 USL  x x  LSL 
 Min 
,

3

3

LT
LT


σLT is long-term sd, usual formula,
includes variation over time;
Cpk uses short-term estimate of sd
USL
105
104
103
102
101
100
99
98
97
96
LSL
95
Ppk=2.0
Ppk=1.0
Ppk=1.0
Ppk=1.33
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Ppk=0.9
Ppk vs Percent Nonconforming
Ppk
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.5
2.0
Percent
Nonconforming
7.2%
3.6%
1.6%
0.69%
0.27%
0.10%
0.03%
0.01%
0.0007%
0.0000002%
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•
•
•
•
In statistical control
Normally distributed
Centered in spec
If1-sided: half % shown
Example: Show Ppk Meets Requirement
• Provide 90% confidence process Ppk≥1.3
• n=15 assay tests were obtained across each of 3 PPQ lots
• No significant difference in mean/variance in the 3 lots; pool data?
P r o c e s s C a pa bility o f A s s a y R e s ult
(us ing 9 0.0 % co nfide nce )
LS L
USL
P ro ce ss D a ta
LS L
95
T a rg e t
*
USL
105
S a m p le M e a n
1 0 1 .2 9 8
S a m p le N
45
S tD e v (W ith in )
0 .6 3 7 1 4 7
W ith in
O v er all
P o te n tia l (W ith in ) C a p a b ility
S tD e v (O v e ra ll) 0 .7 6 0 4 2 1
Cp
2 .6 2
Lo w e r C L
2 .2 4
C PL
3 .3 0
C PU
1 .9 4
C pk
1 .9 4
Lo w e r C L
1 .6 6
O v e ra ll C a p a b ility
9 6 .0
O b se rv e d P e rfo rm a n ce
9 7 .5
E xp . W ith in P e rfo rm a n ce
9 9 .0
1 0 0 .5 1 0 2 .0 1 0 3 .5 1 0 5 .0
E xp . O v e ra ll P e rfo rm a n ce
% < LS L
0 .0 0
% < LS L
0 .0 0
% < LS L
0 .0 0
% > USL
0 .0 0
% > USL
0 .0 0
% > USL
0 .0 0
% T o ta l
0 .0 0
% T o ta l
0 .0 0
% T o ta l
0 .0 0
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Pp
2 .1 9
Lo w e r C L
1 .8 8
PPL
2 .7 6
PPU
1 .6 2
P pk
1 .6 2
Lo w e r C L
1 .3 9
C pm
*
Lo w e r C L
*
Pass
Pooling OK if Process in Statistical Control
Total Variation
Within batch
105
104
103
102
101
100
99
98
97
96
95
Batch 1 Batch 2 Batch 3 Batch 4 Batch 5
Total process variation
Process in Classical Statistical Control
Common Cause Variation Only
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Intra-batch and Inter-batch Variation
105
104
103
99
98
Total Variation
100
Between batch
101
Within batch
102
97
96
95
Batch 1 Batch 2
Batch 3 Batch 4 Batch 5
Total process variation
Variance Components Model
Intra=Within batch: σw
Inter=Between batch: σb
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Special Cause Variation
105
104
103
102
101
99
98
Within lot
100
?
97
96
95
Batch 1 Batch 2 Batch 3 Batch 4 Batch 5
Total process over time
Process not in Statistical Control - Special Cause Variation
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Ppk if Process is Not in Statistical Control
• Use of Ppk is controversial if process not in statistical control1
•
•
•
•
“Ppk has no meaningful interpretation”
“statistical properties are not determinable”
“a waste of engineering and management effort”
Note: between-batch variation means not in classic statistical control
• If variance components model holds, estimate Ppk with σw and σb
• Usual confidence intervals from standards/software not applicable
• Confidence interval must take degrees of freedom for σb into account
• Difficulty in proving variance components model assumptions with
small number of lots
1
Montgomery, Introduction to Statistical Quality Control 6th edition, p 363
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Potential problems with Ppk over multiple lots
• Usual Ppk confidence interval assumes normal distribution
and process stable / in statistical control
• Any changes/trends within or between lots invalidates assumption
• Often differences in mean between batches
• Usual Ppk C.I. does not consider variance components
• Example: 30 samples from each of 5 lots
• (30-1)x5 = 145 degrees of freedom for within lot variation
• (5-1) = 4 degrees of freedom for between lot variation
• ASTM reference E2281 does not address this
• Alternative: Show Ppk for each lot meets requirement for
• 3 lots: ~87% overall confidence median process Ppk meets spec
• 4 lots: ~94% confidence
• 5 lots: ~97% confidence
Or calculate a modified Ppk based on variance components C.I.
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Example: Ppk if process not in statistical control
P r o c e s s C a pa bil ity fo r V a lida tio n
X ba r C ha r t
S a m p le M e a n
C a pa bility H isto gr a m
1
101
L SL
U SL
1
S p e cifica tio n s
UC
_
_ L = 100.342
X = 100.037
100
LS L
USL
L C L = 99.733
95
105
1
99
1
1
2
3
4
5
9 6 .0
9 7 .6
S C ha r t
1 0 0 .8 1 0 2 .4 1 0 4 .0
No r m a l P r o b P lo t
0.8
S a m p le S tD e v
9 9 .2
A D : 0 .5 1 2 , P : 0 .1 9 2
UC L = 0.7689
_
S= 0.5509
0.6
0.4
L C L = 0.3330
1
2
3
4
5
98
L a st 5 Subgr o ups
W i th i n
100
2
3
104
W ith in
4
O ve r a l l
S tD e v
0 .5 5 5 7
S tD e v
0 .9 3 2 1
Cp
3 .0 0
Pp
1 .7 9
Cp k
2 .9 8
Ppk
1 .7 7
PPM
0 .0 0
Cp m
*
PPM
0 .0 8
O v er all
98
1
102
C a pa bility P lo t
102
Va lu e s
100
S p ec s
5
S a m p le
Ppk=1.77; lower 95% C.I. for Ppk using Minitab is 1.60.
But should PPQ pass? Scientific understanding of trend?
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Plot
your
data!
Assure a Standard Test will Pass
• Example: Uniformity of Dosage Units (Content Uniformity)
• Requirement: Pass USP‹905› Uniformity of Dosage Units
• ≥90% confidence USP test would be passed ≥95% of the
time (coverage)
•
•
•
•
See Bergum1 for specifics to determine acceptance criteria
Why 90% confidence? Comparable to RQL probability.
Why 95% coverage? Comparable to AQL probability for single test.
Bayesian approach also available2
1Bergum,
J. and Li, H. “Acceptance Limits for the New ICH USP 29 Content-Uniformity Test”,
Pharmaceutical Technology , Oct 2, 2007
2Leblond,
D., and Mockus, L. “Posterior Probability of Passing a Compendial Test.” Presented
at Bayes-Pharma 2012, Aachen, Germany.
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