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Introduction to

StatisticalApplications forProcess

ValidationEugenie KhlebnikovaSr. Validation Specialist, CQEMcNeil Consumer Healthcare

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AGENDA

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RegulatoryExpectations forStatistical Analysis

Statistical Tools

Six Sigma and ProcessValidation

Common Mistakes toAvoid


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REGULATORY EXPECTATIONS

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PV GUIDELINES

Emphasis on process designelements , and maintainingprocess control based onknowledge gained throughoutcommercialization

Emphasize to have goodknowledge to detect and tocontrol variability through useof statistical analysis

statistical tools to be used inthe analysis of data the number of process runs

carried out and observationsmade should be sufficient toallow the normal extent ofvariation and trends to beestablished to providesufficient data for evaluation.

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PROCESS VALIDATION LIFE CYCLE

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Statistics toanalyze andoptimizeresults (DOE,variationanalysis, etc)

Variation analysis, capability,stability analysis

Process CapabilityControl Charts

Stage 1: ProcessDesign

Stage 2: ProcessQualification

Stage 3: Process Monitoringand Improvement


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PROCESS UNDERSTANDING

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Testing the finalproduct and passingspecifications doesnot give knowledge

of the process

Variation at each productionstage

Knowledge of stability andcapability


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PROCESS UNDERSTANDING KNOW VARIATION

Understanding variation is the key to success inquality and business W. Edwards Deming (Father of

Modern Process Control)

The customers feel variation and lack ofconsistency in a product much more so than theaverage (Jack Welch)

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FDA PV GUIDANCE RECOMMENDATIONS

INTEGRATED TEAM APPROACH

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processengineeringandmanufacturing analytical

chemistry

microbiology

industrialpharmacy

quality

assurance

statistics

Recommended that a statistician orperson with adequate training instatistical process control techniquedevelop the data collection plan andstatistical methods and proceduresused in measuring and evaluatingprocess stability and processcapability .


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DESCRIPTIVE VS INFERENTIALSTATISTICS

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The Division BetweenDescriptive andInferential Statistics

This distinction is based onwhat youre trying to do with

your data


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DESCRIPTIVE STATISTICS

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Summarizing or displaying the factsMean = Sum of all observations/ # ofobservations

Range = Max - Min

Standard DeviationVariance = std dev 2

Relative Standard Deviation or CV = stddev*100/mean


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RELATIVE STANDARD DEVIATION

Example 1:Group Size Avg St Dev RSD

1 10 80 0.8 1.0

2 10 90 0.9 1.0

3 10 100 1.0 1.0

4 10 110 1.1 1.0

5 10 120 1.2 1.0

Example 2:

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Group Size Avg St Dev RSD

1 10 80 1.0 1.4

2 10 90 1.0 1.13 10 100 1.0 1.0

4 10 110 1.0 0.9

5 10 120 1.0 0.8

Standard deviation is proportional to theaverage and the %RSD is unchanged

%RSD is changing because the average ischanging, not the standard deviation


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EXAMPLE: BLEND UNIFORMITY

ToteLocation

Batch 1 Batch 2 Batch 3

1 101 100 102

2 98 99 104

3 99 101 99

4 100 103 97

5 103 97 101

6 102 102 100

7 101 100 1028 100 101 98

9 102 102 103

10 104 99 102

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Specification:90-110%RSD 5.0%


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EXAMPLE: BLEND UNIFORMITY

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INFERENTIAL STATISTICS

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INFERENTIAL STATISTICS

A decision about the batch is based on a relativesmall sample taken since it is not realistic to test theentire batch.

To confirm that the data is representative of thebatch, inference statistics (confidence and toleranceintervals) can be used to predict the true mean.

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CONFIDENCE INTERVAL

A confidence interval is an interval within whichit is believed the true mean lies

where is sample mean , s is sample standarddeviation , N is the sample size , and t value is a

constant obtained from t-distribution tablesbased on the level of confidence.Note the value of t should correspond to N-1.

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CI =


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TOLERANCE INTERVAL

A tolerance interval is an interval within whichit is believed the individual values lie,

TI = k*swhere is sample mean , s is samplestandard deviation , N is the sample size , and

k value is a constant obtained from factors fortwo-sided tolerance limits for normaldistributions table believed the true mean lies.

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EXAMPLE

A batch of tablets was tested forcontent uniformity. The meanvalue of 10 tablets tested was99.1% and a standard deviation

was 2.6% .

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EXAMPLE: Confidence Interval

t from atable

N-1=10-1=9 t=3.25 probability of

99% covering99% of data

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EXAMPLE: Confidence Interval

CI = = 99.1 =96.4 to 101.8

Then we can say that we are 99% certain thatthe true batch mean will be between 96.4%and 101.8 % .

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EXAMPLE: TOLERANCE INTERVAL

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N=10,k =5.594

probabilityof 99%covering99% of data


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EXAMPLE: TOLERANCE INTERVAL

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N=10, mean=99.1, s =2.6, k =5.594TI = k*s

Probability of 99% covering 99% ofdata:

TI =99.1 (5.594*2.6)TI = 84.6% to 113.6%


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EXAMPLE: Confidence and ToleranceInterval

If a sample has the mean value of 10 tabletsat 99.1% and a standard deviation at 2.6% .

Then we can say that we are 99% certain that99% of the tablet content uniformity liesbetween 80.6 and 117.6% and we are 99%certain that the true batch mean will bebetween 96.4 and 101.8 % .

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SAMPLING

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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 takenaccording to the lot size

Define a confidence limit to ensure an accurateand representative sampling of the product

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WARNING LETTER EXAMPLE

211.165 - Testing and release for distribution:

(d) Acceptance criteria for the sampling and testing conducted by thequality control unit shall be adequate to assure that batches of drugproducts meet each appropriate specification and appropriate

statistical quality control criteria as a condition for their approval andrelease. The statistical quality control criteria shall include appropriateacceptance levels and/or appropriate rejection levels .

For example, your firm's finished product sampling plan product A isnot representative of the batch produced . A total of 13 units aresampled per lot, with 3 tested for bacterial endotoxin and 10 tested forbioburden. This sampling of 13 units is irrespective of lot size, whichmay vary from X to Z units (vials) per lot

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CHOOSING SAMPLES

SamplingMethod:

Simple Random Convenience

Systematic Cluster Stratified

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SAMPLING METHODS

SYSTEMATIC

CONVENIENCE

SIMPLE RANDOM

0 min 30 min 1 hr

CLUSTER

top

bottom

middle

STRATIFIED

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SAMPLING RISK

DISPOSITION IMPACT IF LOTGOOD

IMPACT IF LOT BAD

Lot is accepted Correct Decision Incorrect Decision

(Type II orConsumers risk)

Lot is rejected Incorrect Decision(Type I or Producers

risk)

Correct Decision

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Expressed as Acceptable Quality Level (AQL): maximum average percentdefective that is acceptable for the product being evaluated.


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ACCEPTANCE SAMPLING

Acceptance Sampling is a form of inspection applied to lots orbatches of items before or after a process to judgeconformance to predetermined standards.

Sampling Plans specify the lot size , sample size , number ofsamples and acceptance/rejection criteria .

Random sampleLot 31


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OPERATING CHARACTERISTIC CURVE

The operating-characteristic (OC) curve measures theperformance of an acceptance-sampling plan.

The OC curve plots the probability of accepting the lotversus the lot fraction defective .

The OC curve shows the probability that a lotsubmitted with a certain fraction defective will beeither accepted or rejected.

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OC CURVES

Ideal OC Curve

100908070

605040302010

1 1.5 2 2.5 3 3.5

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Reject all lots with more than 2.5%defective and accept all lots with lessthan 2.5% defectiveThe only way to assure is 100%inspection

P r o

b a

b i l i t y o

f

a c c e p t a n c e

( % )

Percent defective (%)


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An Operating Characteristic Curve (OCC) is a probability curve for a sampling plan thatshows the probabilities of accepting lots with various lot quality levels (% defectives).

00.1

0.20.3

0.40.5

0.60.7

0.80.9

1

0 .05 .10 .15 .20

P r o

b a

b i l i t y o

f a c c e p

t i n g

l o t

Lot quality(% defective)

Under this sampling plan, if the lot has 3% defectivethe probability of accepting the lot is 90%

the probability of rejecting the lot is 10%

If the lot has 20% defectiveit has a small probability (5%) of being accepted

the probability of rejecting the lot is 95%

OCCs for Single Sampling Plans

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SAMPLING PLANS

Sampling plans involve:Single samplingDouble sampling

Multiple sampling

Provisions for each type of sampling plan include1. Normal inspection

2. Tightened inspection3. Reduced inspection

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SWITCHING RULES

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Reduced

TightenedNormal

and conditions:Production Steady10 consecutive lots

acceptedApproved byresponsibility

authority

or conditions:Lot rejected

Irregular productionA lot meets neitherthe accept nor the

reject criteriaOther conditionswarrant return tonormal inspection

2 out of 5consecutivelots rejected

5consecutive

lotsaccepted 10 consecutive

lots remain on

tightenedinspection

Start

Discontinueinspection


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SAMPLING BY ATTRIBUTES: ANSI Z1.4 2008

The acceptable quality level (AQL) is a primaryfocal point of the standard

The AQL is generally specified in the contract orby the authority responsible for sampling.

Different AQLs may be designated for differenttypes of defects (critical, major, minor).

Tables for the standard provided are used todetermine the appropriate sampling scheme.

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ANSI Z1.4 2008

PROCEDURE:1. Choose the AQL2. Choose the inspection level

3. Determine the lot size4. Find the appropriate sample size codeletter from Table I-Sample Size Code Letters

5. Determine the appropriate type ofsampling plan to use (single, double,multiple)

6. Check the appropriate table to find theacceptance criteria .

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SAMPLE SIZE DETERMINATION

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Table I - Sample Size Letter CodesSpecial Inspection Levels General Inspection Levels

Lot or Batch Size S-1 S-2 S-3 S-4 I II III2 to 8 A A A A A A B9 to 15 A A A A A B C

16 to 25 A A B B B C D26 to 50 A B B C C D E51 to 90 B B C C C E F91 to 150 B B C D D F G

151 to 280 B C D E E G H281 to 500 B C D E F H J501 to 1200 C C E F G J K

1201 to 3200 C D E G H K L3201 to 10000 C D F G J L M

10001 to 35000 C D F H K M N35001 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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SAMPLE SIZE DETERMINATION

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SINGLE SAMPLING PLAN - EXAMPLE

Defect: any color except of redN = lot size = 25 apples

From Sample Size Code Letters:

From Normal Single Level Inspection

n = sample size =3

C=acceptance number = 0 Accept/1 Reject

Lot or batch size General Inspection

Level16-25 B

SamplingSize Code

Letter

Sample Size AQL 0.010

B 3 0/1 Scenario 1:0 defectsAccept

Scenario 2:2 defectsReject

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SINGLE SAMPLING PLAN - EXAMPLE

N = lot size = 120,000

From Sample Size Code Letters:

Normal Inspection

From Normal Single Level Inspection

Lot or batch size General InspectionLevel

35,001-150,000 N

Sampling SizeCode Letter

SampleSize

CriticalAQL 0.010

MajorAQL 0.65

MinorAQL 4.0

N 500 ACC 0 / REJ 1 ACC 7/ REJ 8 ACC 21 / REJ 22

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STATISTICAL PROCESS CONTROL

The principle of SPC analysis is to understandthe process and detect the process change .

Statistical Process Control (SPC) charts areused to detect process variation.

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STATISTICAL PROCESS CONTROL

The Current Good Manufacturing Practices forProcess Validation published by the FDA inJanuary 2011 states " homogeneity within a

batch and consistency between batches aregoals of process validation activities." Controlcharts explicitly compare the variation withinsubgroups to the variation betweensubgroups, making them very suitable toolsfor understanding processes over time(stability) .

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http://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM070336.pdfhttp://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM070336.pdfhttp://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM070336.pdfhttp://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM070336.pdf


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n = 1 2 < n < 9median

n is small3 < n < 5

n is largen > 10

X & Rm X & R X & R X & S

VARIABLE CONTROL CHARTS

Used for measured data

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CONTROL CHART SELECTION: ATTRIBUTE DATA

Defect orNonconformity Data

Defective Data

Variablen > 50

Constantn > 50

ConstantSample Size

VariableSample Size

C chart u chart p or np chart p chart

Used for count (attribute) data 46


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Stable and Unstable Processes

A stable (or incontrol) process isone in which thekey processresponses show nosigns of specialcauses.

An unstable (orout of control)process has bothcommon andspecial causespresent.

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UCL

LCL

UCL

LCL


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CONTROL CHART

305

303.7

302

300

298.0

296.3

285280

0 min 30 min 1 hr1 hr 30

min 2 hr2hr 30

min

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mean

UCL

LCL

Tablet Weight


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PROCESS CAPABILITY

Is the process capable of consistentlydelivering quality products?

Is the process design confirmed as beingcapable of reproducible commercialmanufacturing?

Process capability is expressed as a ratio ofspecifications/process variability

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PROCESS CAPABILITY INDECES

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5.334.02.671.33-1.33-2.67-4.0-5.33 0

0 .4

0 .3

0 .2

0 .1

0 .0

LowerSpec.Limit

UpperSpec.Limit

Cust. Tolerance

0

0 .4

0 .3

0 .2

0 .1

0 .0

5.334.02.671.33-1.33-2.67-4.0-5.33

LowerSpec.Limit

UpperSpec.Limit

Cust. Tolerance

Cpk < 1 - not capableCpk = 1 - marginally capableC

pk> 1 - capable


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PROCESS CAPABILITY

Accurate and precise Accurate but not precise Precise but not accurate

Desired

CurrentSituation

LSL USLT LSL USLT

CurrentSituation

DesiredDesired

LSL USLT

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EXAMPLE: PROCESS CAPABILITY

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10987654321

20.0

19.5

19.0 S a m p l e M e a n

_ _ X=19.599

UC L=20.239

LC L=18.959

10987654321

1.2

0.8

0.4 S a m p l e S t D e v

_ S=0.656

UC L=1.126

LC L=0.186

108642

21.0

19.5

18.0

Sample

V a l u e s

2322212019181716

LSL USL

LSL 16USL 23

Specifications

22.521.019.518.0

Within

Overall

Specs

StDev 0.674453Cp 1.73Cpk 1.68

WithinStDev 0.673974Pp 1.73Ppk 1.68Cpm *

Overall

Process Capability Sixpack of Hardness Xbar Chart

S Chart

Last 10 Subgroups

Capability Histogram

Normal Prob Plot AD: 0.304, P: 0.564

Capability Plot


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PROCESS CAPABILITY

At a minimum, 50 individual values or 25subgroups for sub-grouped data are requiredto calculate process capability; and 100

individual values provide a stronger basis forthe 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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PROCESS CAPABILITY EXAMPLE

A client had to meet Cpk requirement of 1.20.

When data was assumed to be normallydistributed, the Cpk =0.8

When the non-normal behavior wasaccounted for, the Cpk = 1.22

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SIX SIGMA AND PROCESS VALIDATON

Six Sigma and ProcessValidation

Use the process

knowledge to makeimprovements

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SIX SIGMA AND PROCESS VALIDATON

Six Sigma process improvement methodologyDMAICDefine Objective To improve compression

processMeasure Measure hardness during PVAnalyze Statistical analysis, calculate Cp/Cpk

Improve Decrease variationControl Control variation

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Cpk and SigmaSigma 1,Cpk =0.33

Sigma 2,Cpk =0.67

Sigma 3,Cpk = 1

Sigma 5,Cpk =1.67

Sigma 4,Cpk =1.33


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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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WARNING LETTER EQUIPMENT


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WARNING LETTER: EQUIPMENTCOMPARABILITY AND CAPABILITY

The firm referenced the Cpk values for processes using a double-sidedtablet press and the single-sided tablet press to demonstrate statisticalequivalence .

FDA evaluation : The Cpk value alone was not appropriate metric to demonstrate

statistical equivalence . Cpk analysis requires a normal underlyingdistribution and a demonstrated state of statistical process control .

Statistical equivalence between the two processes could have beenshown by using either parametric or non-parametric (based ondistribution analysis) approaches and comparing means and variances.

Firm did not use the proper analysis to support their conclusion thatno significant differences existed between the two compressionprocesses.

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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 baselineperformance of the process

Is invaluable as a troubleshooting tool postvalidation

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QUESTIONS

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