WELCOME

INTRODUCTION TO STATISTICAL VALIDATION

JIJO PAUL K

APPROACHES TO VALIDATION

Statistical or Retrospective Validation – Based on

historical data .

Experimental Validation – Based on plant trials data

STATISTICAL VALIDATION

To be done before carrying out experimental validation.

Retrospective validation is an approach based on analysis of historical data.

More the no of trials better will be the statistical validation results.

The results will indicate that whether the process is under control or not.

STATISTICAL TOOLS CONSIDERED FOR VALIDATION

Control charts

Capability study

Scatter diagrams

STATISTICAL TERMS : Standard Deviation – Sigma ( s ) Mean - µ Slope - b Y Intercept - a Upper Standard Limit - USL Lower Standard Limit - LSL Process capability index - Cp Process performance index upper - Cp K upper

Process performance index lower - Cp K lower

Correlation Coefficient – r Coefficient of determination - R2

Regression line y = a + bx Control Ratio - CR

+3

-3Time

CONTROL CHARTS - APPLICATIONS

“Early Warning”

Assures that Process is Working

Provides Information on “Process Capability”

Distinguishes between common and spl cause problems

CAPABILITY STUDYCAPABILITY STUDY

Capability studies are performed to evaluate the ability of a process to consistently meet a specification.

Cp = (allowable range)/6s = (USL - LSL)/6s. Where Cp is the capability index.

Cpk = min[ (USL - m)/3s, (m - LSL)/3s ].Where Cpk is the process performance index.

CR = (UCL-LCL)/(USL-LSL). Where CR is control ratio.

+3-3

-3 +3

Good

Poor

CPK>1

CPK<1

PROCESS CAPABILITYPROCESS CAPABILITY

Cp > 1

Cp < 1

CR < 1

CR > 1

LSL USL

LSL USL

EXAMPLES for Control Charts

TRIAL DATA For Control chart 1:    

         

Trial NoRM active ingredient

%Mean ( X - M ) ( X - M )2

1 8.63 8.539 0.091 0.008

2 8.52 8.539 -0.019 0.000

3 8.76 8.539 0.221 0.049

4 8.35 8.539 -0.189 0.036

5 8.45 8.539 -0.089 0.008

6 8.81 8.539 0.271 0.073

7 8.23 8.539 -0.309 0.095

8 8.65 8.539 0.111 0.012

9 8.46 8.539 -0.079 0.006

10 8.53 8.539 -0.009 0.000

Mean 8.539

Std deviation

0.18

.+1s 8.72

.-1s 8.36

.+2s 8.90

.-2s 8.18

.+3s 9.08

.-3s 8.00

LSL 7.80

USL 9.00

Cp 1.12

Cpk1 1.38

Cpk2 0.86

CR 0.90

Mean+/- 1S+/- 2S+/- 3S

TRIAL DATA for control chart 2 :      

         

Trial No Efficiency Mean ( X - M ) ( X - M )2

1 72.3 70.26 2.04 4.16

2 70.5 70.26 0.24 0.06

3 68.6 70.26 -1.66 2.76

4 73.2 70.26 2.94 8.64

5 69.5 70.26 -0.76 0.58

6 72.8 70.26 2.54 6.45

7 67.9 70.26 -2.36 5.57

8 69.3 70.26 -0.96 0.92

9 70.5 70.26 0.24 0.06

10 68.9 70.26 -1.36 1.85

mean 70.26

std dev 1.86

.+1s 72.12

.-1s 68.40

.+2s 73.97

.-2s 66.55

.+3s 75.83

.-3s 64.69

LSL 63.000

USL 75.000

Cp 1.077

Cpk1 1.303

Cpk2 0.851

CR 0.929

Mean+/- 1S+/- 2S+/- 3S

SCATTER DIAGRAMSSCATTER DIAGRAMS

Scatter Diagrams are used to study and identify the possible relationship between the changes observed in two different sets of variables.

SCATTER DIAGRAMS

The coefficient of determination ranges from 0 to 1.

An R2 of 0 means that the dependent variable cannot be predicted from the independent variable.

An R2 of 1 means the dependent variable can be predicted without error from the independent variable.

The quantity r, called the linear correlation coefficient, measures the strength and the direction of a linear relationship between two variables.

Importance of correlation coefficient The value of r is such that -1 < r < +1.  The + and – signs are used

for positive linear correlations and negative linear correlations respectively

A correlation greater than 0.8 is generally described as strong,

whereas a correlation less than 0.5 is generally described as weak.  The coefficient of determination, r 2, is useful because it gives the

proportion of the variance (fluctuation) of one variable that is predictable from the other variable.

EXAMPLE for Scatter Diagramme

           

TRIAL DATA FOR SCATTER CHART    

EFFICIENCY Vs RM Active ingredient %    

           

Trial NoEfficiency

( X)

RM active

ingredient % (Y)

XY X2 Y2

1 73.5 8.63 634.3 5402.3 74.5

2 71.8 8.52 611.7 5155.2 72.6

3 74 8.76 648.2 5476.0 76.7

4 66 8.35 551.1 4356.0 69.7

5 68.6 8.45 579.7 4706.0 71.4

6 74.2 8.81 653.7 5505.6 77.6

7 64 8.23 526.7 4096.0 67.7

8 71 8.65 614.2 5041.0 74.8

9 71 8.46 600.7 5041.0 71.6

10 72.4 8.53 617.6 5241.8 72.8

           

Σ 706.5 85.39 6037.9 50020.9 729.4

RESULTS

R 0.910  

R2 0.829  

Slope (b) 0.047  

Y intercept (a) 5.192  

Equation y = 5.192 + 0.047x

             

               

               

               

               

               

               

               

               

               

               

               

               

               

               

               

               

               

               

               

               

 

EXPERIMENTAL VALIDATION

To be done once statistical validation is completed and found to be satisfactory.

Run full process according to SOP n times.

Record all required data in the batch process records (BPR).

Deviations to the procedures must be recorded on the data record forms.

Relevant samples to be given (as per sampling plan) to the QC and results to be recorded in the BPR.

Perform the routine tests associated with the process according to the SOP. Test results must be approved by QC.

EXPERIMENTAL VALIDATION

Attach all data record forms and charts.

Perform all necessary calculations and statistical analysis (pre-determined).

Compare to acceptance criteria.

Prepare deviation report – Justification if any on acceptance and impact of process.

Prepare a process validation report including all relevant data.

The Process must meet all specifications for three consecutive runs. If failed, then validation has to be repeated.

Submit the Document to QA for review and approval.

Thank you