Use of statistical tools and methods of carrying out investigations.

1. USE OF QUALITY TOOLS & STATISTICS
IN INVESTIGATION
Prepared by: Sambhujyoti Das, Quality Assurance

2. Today we’ll discuss :
 What is an Investigation
 The purpose
 Investigative Tools
 Classification
 Start up
 Data Gathering
 Data Stratification
 Data Trending
 Experimentation
 Q & A
Quality Assurance, Matoda SLIDE NO.: 2 OF 51

3. What is an Investigation?
1. The act or process of investigating.
2. A careful search or examination in order to discover facts.
3. A detailed inquiry or systematic examination.
SLIDE NO.: 3 OF 51Quality Assurance, Matoda

4. Why Investigate:……………The Purpose
1. To find out the Root Cause –
o Market complaint
o Out of Specification result
o Deviation
o Out of Trend drift
o Machine breakdown
2. To enhance understanding –
o Product
o Process
o System
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The reactive approach
The proactive approach
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5. Why Investigate:……………The Purpose
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Investigation
CAPA
Process
Improvement
Problem identification
Investigation
Finding Root Cause
Recommendation(s)
Corrective &
Preventive measures
Improvement
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6. Why Investigate:……………The Purpose
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Root Cause
Causes
Probable Causes
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7. Investigative Tools:
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Tools
Experience /
Institution
Data based
Quality
tools
Statistical
tools
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8. Experience or Institution based approach
 Traditionally used, as it requires.
 No factual analysis or observations.
 Biased.
Symptom Remedy
Investigative Tools:
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9. Data based approach
 Scientific.
 Methodical.
 Unbiased.
Symptom Root cause Remedy
Investigative Tools:
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10. Investigative Tools:
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USE CORRECT TOOL
FOR CORRECT WORK
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11. Investigative Tools:………….Start up
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Flowcharts are tools that make a process visible.
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12. FLOWCHARTS
 Illustrate a process at a glance.
 Keep it as simple as possible.
 Rectangles represent processing steps.
 Arrows represent the flow of control.
 Circles represent start or end of process.
 Diamonds represent evaluations or decisions.
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Investigative Tools:………….Start up
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13. FLOWCHART OF MANUFACTURING OF A PARENTERAL
PRODUCT (LYOPHILIZED)
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Investigative Tools:………….Start up
Batch
Initiation
Dispensing
Bulk solution
preparation
Pre-filtration
Sterile
filtration
Filling
Half
stoppering
Lyophilization
Full stoppering Sealing Inspection Packaging
Ready for
shipment
Q.C.
analysis
Q.C.
analysis
PassFail
PassFail
Quality Assurance, Matoda

14. Investigative Tools:………….Data gathering
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Brainstorming is a simple but effective technique for
generating many ideas of a group of people within a short
span of time for finding probable causes of a problem or
its solutions.
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15. BRAINSTORMING
 Objective is to generate more & more ideas.
 Involve associated people.
 Focus on quantities not qualities.
 Record wild ideas too, avoid evaluation.
 Motivate to participate.
 Be aware of Halo effect.
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Investigative Tools:………….Data gathering
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16. BRAINSTORMING (Mind Mapping Technique)
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Broken
tablets in
packed
bottles
Broken during
compression
Broken during
coating
Broken during
filling
Broken during
Shipment
Broken during
Warehousing
High
HardnessLow Hardness
High falling
Broken during
handling
Improper
inspectionHigh hopper
vibration
Excessive
rolling
Over dried
Low LOD
Fall of bottles
Broken during
repackingExcessive
rattlingLow RH
exposure
Incorrect
complaint
High speed
line
Investigative Tools:………….Data gathering
Quality Assurance, Matoda

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Investigative Tools:…………Data stratification
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18. THE CAUSE AND EFFECT DIAGRAM (ISHIKAWA)
 Simple but useful tool for systematic grouping of causes of
a problem (Effect).
 The head of the Fish represents the problem or failure
statement.
 The primary bones are the major FACTORS.
 The secondary bones are the PROBABLE CAUSES.
 The typical categorization used in manufacturing are: 6 Ms.
 Categorization can done in any form considering the
problem.
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Investigative Tools:…………Data stratification
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19. THE C & E DIAGRAM FOR BROKEN TABLETS IN BOTTLES
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Investigative Tools:…………Data stratification
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Investigative Tools:…………Data Trending
Boxplots summarize information about the shape, spread,
and center of your data set. They can also help you to spot
outliers.
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Investigative Tools:…………Data Trending
BOXPLOT (BOX-AND-WHISKER PLOT)
 The bottom / left edge of the box represents FIRST
QUARTILE (Q1).
 The top / right edge represents THIRD QUARTILE (Q3).
 The horizontal / vertical line drawn through the box
represents the MEDIAN (Q2) of the data set.
 The lines extending from the box are called WHISKERS,
extended to lowest and highest values in data set (excluding
outliers).
 OUTLIERS, are represented by asterisks (*).
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22. SLIDE NO.: 21 OF 51
Investigative Tools:…………Data Trending
PLOTTING BOX-AND-WHISKER ON FOLLOWING DATA SET:
10.2, 14.1, 14.4, 14.4, 14.4, 14.5, 14.5, 14.6, 14.7, 14.7, 14.7, 14.9, 15.1, 15.9, 16.4
1. Data set contains 15 data.
2. Median (Q2) = (15+1)/2 = 8th data in set is 14.6.
3. 1st Quartile (Q1) = 4th data in set is 14.4.
4. 3rd Quartile (Q3) = 12th data in set is 14.9.
5. Interquartile Range (IQR) = 14.9 – 14.4 = 0.5.
6. Acceptable Range is Q1- (1.5 × IQR) to Q3 + (1.5 × IQR) = 13.65 to 15.65.
7. Outlier values are 10.2, 15.9 and 16.4.
8. Lower Whisker = Lowest value (14.1) and Upper Whisker = Highest value
(15.1) excluding outliers.
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23. SLIDE NO.: 22 OF 51
Investigative Tools:…………Data Trending
PLOTTING BOX-AND-WHISKER ON FOLLOWING DATA SET:
10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0
10.2 15.9 16.4
14.6
14.4 14.9
14.1 15.1
Median (Q2) = 14.6 1st Quartile (Q1) = 14.4 3rd Quartile = 14.9
Lower Whisker = 14.1 Upper Whisker = 15.1 Outliers = 10.2, 15.9 and 16.4
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Investigative Tools:…………Data Trending
BUT NOT ALWAYS SIMILAR....
BOX
WHISKER
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Investigative Tools:…………Data Trending
A Pareto chart ranks your data from the largest to the
smallest contributor, which can help you to prioritize the
problems.
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Pareto
Analysis

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Investigative Tools:…………Data Trending
PARETO ANALYSIS :
 Tabulate complaints and their frequencies in percentage.
 Arrange the rows in descending order of percentage.
 Add a cumulative percentage column to the table.
 Plot a bar graph with complaints on “X” axis and percent
frequency on “Y” axis (descending order).
 Plot the cumulative percentage on “Y” axis (on same graph).
 Join the above cumulative points to form a curve.
 Draw line at 80% on “Y” axis parallel to “X” axis. Then drop the
line at the point of intersection with the curve on X” axis.
 This point on the “X” axis separates the “Vital” contributors (on
the left) and “Trivial” contributors (on the right).
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27. SLIDE NO.: 26 OF 51
Investigative Tools:…………Data Trending
PARETO ANALYSIS OF MARKET COMPLAINT:
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Complaints
No. of
Complaint in
absolute term
No. of
Complaint in %
term
Order No.
Absence of product in
primary pack
5 7.2 6
Deformed pack 12 17.4 3
Missing units 17 24.6 1
Loss of integrity 8 11.6 4
Inefficacy 3 4.3 7
Extraneous Matters 14 20.3 2
Mixup 2 2.9 8
Short Supply 7 10.1 5
Counterfeit 1 1.4 9

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Investigative Tools:…………Data Trending
PARETO ANALYSIS OF MARKET COMPLAINT:
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Complaints
No. of
Complaint in
absolute term
No. of
Complaint in %
term
Cumulative %
Missing units 17 24.6 24.6
Extraneous Matters 14 20.3 44.9
Deformed pack 12 17.4 62.3
Loss of integrity 8 11.6 73.9
Short Supply 7 10.1 84.0
Absence of product in
primary pack
5 7.2 91.3
Inefficacy 3 4.3 95.6
Mixup 2 2.9 98.5
Counterfeit 1 1.4 100.0

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Investigative Tools:…………Data Trending
PLOTTING OF PARETO CHART:
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0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
Missing units Extraneous
Matters
Deformed
pack
Loss of
integrity
Short Supply Absence of
product in
primary pack
Inefficacy Mixup Counterfeit
Cumulative%
No.ofComplaintin%
Category of Complaint
Vital Contributors Trivial Contributors

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Investigative Tools:…………Experimentation
This tool provides a fundamental strategy for making
decisions based on some assumptions or guesses about
the populations involved.
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31. Investigative Tools:…………Experimentation
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HYPOTHESIS TESTING:
Hardness Testers: “Hard Tab – XP” vs “Soft Tab – Vista”
Testing Parameter: Tablet Hardness
Test Objective: Whether there is any significant difference between
two set of measurements?
Basis Data: Mean of Hardness results from Tester XP = μ0
Mean of Hardness results from Tester Vista = μ
Hypothetical Statements:
1. There is no significant hardness difference between results from
Tester Hard Tab – XP and Tester Soft Tab – Vista.
2. There is a significant difference between two results.
Quality Assurance, Matoda

32. Investigative Tools:…………Experimentation
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HYPOTHESIS TESTING:
NULL HYPOTHESIS ALTERNATE HYPOTHESIS
H0 : μ = μ0 H1 : μ ≠ μ0
THE OBJECTIVE
Is there are enough evidence that the Null Hypothsis can be rejected?
If not, then Null Hypothesis is true.
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Investigative Tools:………… Experimentation
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34. Investigative Tools:…………Experimentation
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HYPOTHESIS TESTING:
Suppose few samples from a batch of “Fortune Tablets 500 mg”
were tested on automated hardness tester “Hard Tab – XP” shows
mean hardness of 30 Kp (μ0).
20 (n) tablets from same batch were again tested on another
hardness tester “Soft Tab – Vista”. The results are:
Observed Mean ( ) = 28 Standard Deviation(s) = 11.5
The expression is
 T = - 0.78
Degrees of freedom is v = n -1  v = 20 – 1 = 19
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35. Investigative Tools:…………Experimentation
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HYPOTHESIS TESTING:
Type I error (called α):
The probability of rejecting Null Hypothesis when μ = μ0, i.e. there is
no significant difference between two hardness results.
Consider α is 0.05 (basis of area outside 95% confidence interval of
standard normal distribution curve).
Here the rejection area (critical value) is  = 0.975
quantile of Student’s t-distribution with degrees of freedom 19.
Decision Rule:
To reject H0 if the value of T (from t distribution) is greater than or
equal to 2.09 or less than equal to – 2.09.
Quality Assurance, Matoda

36. Investigative Tools:…………Experimentation
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HYPOTHESIS TESTING:
Decision:
The derived value of T is - 0.78 which is in between – 2.09 and
2.09. Hence, we can not reject the Null Hypothesis.
Inference:
There is no significant difference in hardness results obtained from
Hard Tab – XP and Soft Tab – Vista.
Quality Assurance, Matoda

37. Investigative Tools:…………Experimentation
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Acceptance ZoneCritical Zone Critical Zone
STANDARD NORMAL CURVE:
0.95
H0 : μ = μ0 H1 : μ ≠ μ0H1 : μ ≠ μ0

38. Investigative Tools:…………Experimentation
SLIDE NO.: 37 OF 51Quality Assurance, Matoda
Student’s Distribution Table:

39. SLIDE NO.: 38 OF 51Quality Assurance, Matoda
Investigative Tools:…………Experimentation

40. SLIDE NO.: 39 OF 51Quality Assurance, Matoda
Design of Experiments (DoE) enables us to determine
simultaneously the individual and interactive effects of
many factors that could affect the output results.
It helps to pin point the sensitive areas in experiments
that cause problematic results and in turns leads to
robust process.
Investigative Tools:…………Experimentation

41. Investigative Tools:…………Experimentation
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DESIGN OF EXPERIMENTS:
One fine morning Quality Control rings your phone and informed
that they recorded an OOS result on one batch of compressed
tablets due to failing in dissolution result [79% against NLT 85%].
………….and your first reaction
Quality Assurance, Matoda

42. Investigative Tools:…………Experimentation
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DESIGN OF EXPERIMENTS:
The 3 factors are initially selected to see the effect on dissolution.
(A) Weight of tablet, (B) Thickness and (C) M/C RPM
Each has their lowest and highest levels (range).
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Factors Lowest Level Code Highest Level Code
Weight (W) 120 mg -1 160 mg 1
Thickness (T) 3.50 mm -1 3.70 mm 1
Machine RPM (R) 40 -1 65 1

43. Investigative Tools:…………Experimentation
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DESIGN OF EXPERIMENTS:
Based on the case, we can construct Full Factorial design.
The number of experiments would be 23 = 8.
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Weight (W) Thickness (T) RPM (R) Dissolution Result (in %)
-1 -1 -1 75.5
1 -1 -1 80.2
-1 1 -1 84.9
1 1 -1 86.3
-1 -1 1 79.1
1 -1 1 82.4
-1 1 1 88.4
1 1 1 91.5

44. Investigative Tools:…………Experimentation
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DESIGN OF EXPERIMENTS:
Calculation of Main Effects
Extract the effect of Machine RPM (R) on the Dissolution result.
Average of dissolution results at lowest level (-1) of R = 81.725%.
Average of dissolution results at higest level (1) of R = 85.350%.
The Effect is (85.350 – 81.725) = 3.625
Coefficient (Slope) is S2/Effect = 1.8125
Like wise we can calculate the other main effects and their
coefficients.
Wight (W): Effect = 3.125 Coefficient = 1.5625
Thickness (T):Effect = 8.475 Coefficient = 4.2375
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45. Investigative Tools:…………Experimentation
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DESIGN OF EXPERIMENTS:
Calculation of Interactions
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W T R WT WR TR WTR Disso.
-1 -1 -1 1 1 1 -1 75.5
1 -1 -1 -1 -1 1 1 80.2
-1 1 -1 -1 1 -1 1 84.9
1 1 -1 1 -1 -1 -1 86.3
-1 -1 1 1 -1 -1 1 79.1
1 -1 1 -1 1 -1 -1 82.4
-1 1 1 -1 -1 1 -1 88.4
1 1 1 1 1 1 1 91.5

46. Investigative Tools:…………Experimentation
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DESIGN OF EXPERIMENTS:
All Main Effects, Interactions and their Coefficients
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Term Coefficient
Constant (Nominal) 83.5375
Weight 1.5625
Thickness 4.2375
RPM 1.8125
Weight × Thickness -0.4375
Weight × RPM 0.0375
Thickness × RPM 0.3625
Weight × Thickness × RPM 0.3875

47. Investigative Tools:…………Experimentation
SLIDE NO.: 46 OF 51Quality Assurance, Matoda
DESIGN OF EXPERIMENTS:

48. Investigative Tools:…………Experimentation
SLIDE NO.: 47 OF 51Quality Assurance, Matoda
DESIGN OF EXPERIMENTS:

49. Investigative Tools:…………Experimentation
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DESIGN OF EXPERIMENTS:
Interpretations:
1. The dissolution of said product largely varies with main effects
of factors.
2. The top most contribution is from Thickness followed by
Machine Speed.
3. The interactions are having negligible effect on dissolution.
4. Effect of Machine Speed is slightly greater on higher Thickness
than on lower Thickness.
5. Effect of Thickness is slightly greater on lower tablet Weight
than on higher Weight.
6. Practically no interaction between M/C RPM and Weight.
Quality Assurance, Matoda

50. Any Question ?
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51. Remember !
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52. This is not an end………
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