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Introduction to
     Statistical
     Applications for
     Process
     Validation
Eugenie Khlebnikova
Sr. Validation Specialist, CQE
McNeil Consumer Healthcare

                                 1
AGENDA
    Regulatory
    Expectations for
    Statistical Analysis

    Statistical Tools

    Six Sigma and Process
    Validation

    Common Mistakes to
    Avoid
                            2
REGULATORY EXPECTATIONS




                          3
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



                                                                          4
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
                                                                              5
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

                                                 6
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)



                                                 7
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

                                                                    8
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




                                                         9
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
                                                                  10
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




                                                                                     11
EXAMPLE: BLEND UNIFORMITY
  Tote     Batch 1   Batch 2   Batch 3
Location                                 Specification:
   1        101       100       102      90-110%
                                         RSD ≤ 5.0%
   2         98        99       104
   3         99       101        99
   4        100       103        97
   5        103        97       101
   6        102       102       100
   7        101       100       102
   8        100       101        98
   9        102       102       103
  10        104        99       102


                                                          12
EXAMPLE: BLEND UNIFORMITY
  Tote     Batch 1   Batch 2   Batch 3   Minitab Output:
Location                                 Descriptive Statistics: Batch 1, Batch 2, Batch 3
   1        101       100       102
                                         Variable Mean StDev     CoefVar Minimum Maximum
   2         98        99       104      Batch 1 101.00 1.83     1.81 98.00 104.00
                                         Batch 2 100.40 1.78     1.77 97.00 103.00
   3         99       101        99      Batch 3 100.80 2.25     2.23 97.00 104.00

   4        100       103        97

   5        103        97       101

   6        102       102       100

   7        101       100       102

   8        100       101        98

   9        102       102       103

  10        104        99       102




                                                                                             13
EXAMPLE: BLEND UNIFORMITY




                            14
INFERENTIAL STATISTICS




                         15
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.




                                                             16
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.

                                                      17
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.
                                                 18
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%.


                                    19
EXAMPLE: Confidence Interval

• t from a
  table
• N-1=10-1=9
• t=3.25
• probability of
  99% covering
  99% of data


                                      20
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 %.




                                                 21
EXAMPLE: TOLERANCE INTERVAL

N=10,
k =5.594
probability
of 99%
covering
99% of data



                                 22
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%
                                       23
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 %.

                                                 24
SAMPLING




           25
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
                                                      26
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”


                                                                          27
CHOOSING SAMPLES


           Sampling
           Method:
             •Simple Random
             •Convenience
             •Systematic
             •Cluster
             •Stratified

                              28
SAMPLING METHODS

SIMPLE RANDOM                      SYSTEMATIC




                       0 min            30 min          1 hr

CONVENIENCE            CLUSTER                   STRATIFIED
                                 top


              middle
                               bottom
                                                               29
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.

                                                                        30
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
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.


                                                           32
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
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)
                                                                                                          34
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



                                                    35
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

                                                                        36
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.


                                                        37
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.
                                                  38
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
                                                                                   39
SAMPLE SIZE DETERMINATION




                            40
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
                                                                      41
C=acceptance number = 0 Accept/1 Reject
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




                                                                              42
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.




                                                   43
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).
                                                 44
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



                                                             45
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
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.

                                   47
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
                                                                        48
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


                                                  49
PROCESS CAPABILITY INDECES
                                       Lower                  Cust. Tolerance                  Upper
                                       Spec.                                                   Spec.
                               0 .4
                                       Limit                                                   Limit

                               0 .3


                               0 .2


                                0 .1


                               0 .0
                                       -5.33   -4.0   -2.67    -1.33   0   1.33   2.67   4.0    5.33


                                       Lower                                                   Upper
                                       Spec.                  Cust. Tolerance                  Spec.
                               0 .4    Limit                                                   Limit

                               0 .3



Cpk < 1 - not capable          0 .2



Cpk = 1 - marginally capable   0 .1


                               0 .0
Cpk > 1 - capable                      -5.33   -4.0   -2.67    -1.33   0   1.33   2.67   4.0    5.33
                                                                                                       50
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


                                                                                    51
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?"

                                             52
EXAMPLE: PROCESS CAPABILITY
                                            Process Capability Sixpack of Hardness
                                            Xbar Chart                                           Capabilit y Hist ogram
                                                                                          LSL                                        USL
                                                                          UC L=20.239
                    20.0                                                                                                                   Specifications
Sample Mean




                                                                          _                                                                  LSL    16
                                                                          _
                                                                          X=19.599                                                           USL    23
                    19.5


                    19.0                                                  LC L=18.959
                           1   2   3    4     5    6     7   8   9   10                   16     17    18    19   20     21     22   23

                                             S Chart                                                         Normal Prob Plot
                     1.2                                                                                      AD: 0.304, P: 0.564
                                                                          UC L=1.126
     Sample StDev




                     0.8                                                  _
                                                                          S=0.656

                     0.4
                                                                          LC L=0.186
                           1   2   3    4     5    6     7   8   9   10                               18.0             19.5            21.0           22.5

                                       Last 10 Subgroups                                                      Capabilit y Plot
                    21.0                                                                        Within                 Within             Overall
                                                                                        StDev     0.674453                           StDev  0.673974
Values




                                                                                        Cp        1.73                               Pp     1.73
                    19.5                                                                                           Overall
                                                                                        Cpk       1.68                               Ppk    1.68
                                                                                                                                     Cpm    *
                    18.0
                                                                                                                       Specs
                               2        4          6         8       10
                                              Sample




                                                                                                                                                       53
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
                                                 54
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



                                              55
SIX SIGMA AND PROCESS VALIDATON
• Six Sigma and Process
  Validation
• Use the process
  knowledge to make
  improvements




                              56
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


                                                   57
Cpk and Sigma
Sigma 1,
Cpk =
0.33          Sigma 3,
                                    Sigma 5,
              Cpk = 1
                                    Cpk =
                                    1.67
   Sigma 2,
                         Sigma 4,
   Cpk =
                         Cpk =
   0.67
                         1.33
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)


                                                    59
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.
                                                                                60
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
                                                   61
QUESTIONS




            62

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Introduction to Statistical Applications for Process Validation

  • 1. Introduction to Statistical Applications for Process Validation Eugenie Khlebnikova Sr. Validation Specialist, CQE McNeil Consumer Healthcare 1
  • 2. AGENDA Regulatory Expectations for Statistical Analysis Statistical Tools Six Sigma and Process Validation Common Mistakes to Avoid 2
  • 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 4
  • 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 5
  • 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 6
  • 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) 7
  • 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 8
  • 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 9
  • 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 10
  • 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 11
  • 12. EXAMPLE: BLEND UNIFORMITY Tote Batch 1 Batch 2 Batch 3 Location Specification: 1 101 100 102 90-110% RSD ≤ 5.0% 2 98 99 104 3 99 101 99 4 100 103 97 5 103 97 101 6 102 102 100 7 101 100 102 8 100 101 98 9 102 102 103 10 104 99 102 12
  • 13. EXAMPLE: BLEND UNIFORMITY Tote Batch 1 Batch 2 Batch 3 Minitab Output: Location Descriptive Statistics: Batch 1, Batch 2, Batch 3 1 101 100 102 Variable Mean StDev CoefVar Minimum Maximum 2 98 99 104 Batch 1 101.00 1.83 1.81 98.00 104.00 Batch 2 100.40 1.78 1.77 97.00 103.00 3 99 101 99 Batch 3 100.80 2.25 2.23 97.00 104.00 4 100 103 97 5 103 97 101 6 102 102 100 7 101 100 102 8 100 101 98 9 102 102 103 10 104 99 102 13
  • 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. 16
  • 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. 17
  • 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. 18
  • 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%. 19
  • 20. EXAMPLE: Confidence Interval • t from a table • N-1=10-1=9 • t=3.25 • probability of 99% covering 99% of data 20
  • 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 %. 21
  • 22. EXAMPLE: TOLERANCE INTERVAL N=10, k =5.594 probability of 99% covering 99% of data 22
  • 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% 23
  • 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 %. 24
  • 25. SAMPLING 25
  • 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 26
  • 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” 27
  • 28. CHOOSING SAMPLES Sampling Method: •Simple Random •Convenience •Systematic •Cluster •Stratified 28
  • 29. SAMPLING METHODS SIMPLE RANDOM SYSTEMATIC 0 min 30 min 1 hr CONVENIENCE CLUSTER STRATIFIED top middle bottom 29
  • 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. 30
  • 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. 32
  • 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) 34
  • 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 35
  • 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 36
  • 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. 37
  • 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. 38
  • 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 39
  • 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 41 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 42
  • 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. 43
  • 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). 44
  • 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 45
  • 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. 47
  • 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 48
  • 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 49
  • 50. PROCESS CAPABILITY INDECES Lower Cust. Tolerance Upper Spec. Spec. 0 .4 Limit Limit 0 .3 0 .2 0 .1 0 .0 -5.33 -4.0 -2.67 -1.33 0 1.33 2.67 4.0 5.33 Lower Upper Spec. Cust. Tolerance Spec. 0 .4 Limit Limit 0 .3 Cpk < 1 - not capable 0 .2 Cpk = 1 - marginally capable 0 .1 0 .0 Cpk > 1 - capable -5.33 -4.0 -2.67 -1.33 0 1.33 2.67 4.0 5.33 50
  • 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 51
  • 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?" 52
  • 53. EXAMPLE: PROCESS CAPABILITY Process Capability Sixpack of Hardness Xbar Chart Capabilit y Hist ogram LSL USL UC L=20.239 20.0 Specifications Sample Mean _ LSL 16 _ X=19.599 USL 23 19.5 19.0 LC L=18.959 1 2 3 4 5 6 7 8 9 10 16 17 18 19 20 21 22 23 S Chart Normal Prob Plot 1.2 AD: 0.304, P: 0.564 UC L=1.126 Sample StDev 0.8 _ S=0.656 0.4 LC L=0.186 1 2 3 4 5 6 7 8 9 10 18.0 19.5 21.0 22.5 Last 10 Subgroups Capabilit y Plot 21.0 Within Within Overall StDev 0.674453 StDev 0.673974 Values Cp 1.73 Pp 1.73 19.5 Overall Cpk 1.68 Ppk 1.68 Cpm * 18.0 Specs 2 4 6 8 10 Sample 53
  • 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 54
  • 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 55
  • 56. SIX SIGMA AND PROCESS VALIDATON • Six Sigma and Process Validation • Use the process knowledge to make improvements 56
  • 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 57
  • 58. Cpk and Sigma Sigma 1, Cpk = 0.33 Sigma 3, Sigma 5, Cpk = 1 Cpk = 1.67 Sigma 2, Sigma 4, Cpk = Cpk = 0.67 1.33
  • 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) 59
  • 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. 60
  • 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 61
  • 62. QUESTIONS 62