Statistical Investigation - NS

USE OF QUALITY TOOLS & STATISTICS IN INVESTIGATIONPrepared by: Neeraj Shrivastava, Quality Assurance

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 SLIDE NO.: 2 OF 51

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 51 Quality Assurance

Why Investigate:……………The Purpose1. To find out the Root Cause –

o Market complainto Out of Specification resulto Deviationo Out of Trend drifto Machine breakdown

2. To enhance understanding –o Producto Processo System

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The reactive approach

The proactive approach

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Why Investigate:……………The Purpose

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Investigation

CAPA

Process Improvem

ent

Problem identification

Investigation

Finding Root Cause

Recommendation(s)

Corrective & Preventive measures

Improvement

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Why Investigate:……………The Purpose

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Root Cause

Causes

Probable Causes

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Investigative Tools:

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Tools

Experience /

InstitutionData based

Quality tools

Statistical tools

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Experience or Institution based approach Traditionally used, as it requires. No factual analysis or observations. Biased.

Symptom Remedy



Data based approach Scientific. Methodical. Unbiased.

Symptom Root cause Remedy




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USE CORRECT TOOL FOR CORRECT WORK

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Investigative Tools:………….Start up

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Flowcharts are tools that make a process visible.

Flowcharts

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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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Quality Assurance

FLOWCHART OF MANUFACTURING OF A PARENTERAL PRODUCT (LYOPHILIZED)

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Batch Initiatio

nDispensing

Bulk solution

preparation

Pre-filtration

Sterile filtrationFillingHalf

stopperingLyophilizati

on

Full stoppering Sealing Inspection Packaging

Ready for

shipment

Q.C. analy

sis

Q.C. analy

sisPass

Fail

Pass

Fail

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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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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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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


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Investigative Tools:…………Data stratification

The Cause & Effect Diagram

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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.SLIDE NO.: 18

OF 51


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THE C & E DIAGRAM FOR BROKEN TABLETS IN BOTTLES

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Investigative Tools:…………Data Trending

Boxplot

Boxplots summarize information about the shape, spread, and center of your data set. They can also help you spot outliers.

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Investigative Tools:…………Data TrendingBOXPLOT (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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Investigative Tools:…………Data TrendingPLOTTING 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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Investigative Tools:…………Data TrendingPLOTTING 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 TrendingBUT NOT ALWAYS SIMILAR....

BOX

WHISKERQuality Assurance

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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 TrendingPARETO 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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Investigative Tools:…………Data TrendingPARETO ANALYSIS OF MARKET COMPLAINT:

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ComplaintsNo. of

Complaint in absolute

term

No. of Complaint in

% termOrder No.

Absence of product in primary pack 5 7.2 6

Deformed pack 12 17.4 3Missing units 17 24.6 1Loss of integrity 8 11.6 4Inefficacy 3 4.3 7Extraneous Matters 14 20.3 2Mixup 2 2.9 8Short Supply 7 10.1 5Counterfeit 1 1.4 9

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Investigative Tools:…………Data TrendingPARETO ANALYSIS OF MARKET COMPLAINT:

Quality Assurance

ComplaintsNo. of

Complaint in absolute

term

No. of Complaint in

% termCumulative

%

Missing units 17 24.6 24.6Extraneous Matters 14 20.3 44.9Deformed pack 12 17.4 62.3Loss of integrity 8 11.6 73.9Short Supply 7 10.1 84.0Absence of product in primary pack 5 7.2 91.3

Inefficacy 3 4.3 95.6Mixup 2 2.9 98.5Counterfeit 1 1.4 100.0

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Investigative Tools:…………Data TrendingPLOTTING OF PARETO CHART:

Quality Assurance

Missing units

Ex-traneous Matters

Deformed pack

Loss of integrity

Short Supply

Absence of product in primary

pack

Inefficacy Mixup Coun-terfeit

0

10

20

30

40

50

60

70

0

10

20

30

40

50

60

70

80

90

100

Category of Complaint

No.

of C

ompl

aint

in %

Cum

ulat

ive

%

Vital Contributors

Trivial Contributors

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Investigative Tools:…………Experimentation

This tool provide a fundamental strategy for making decisions based on some assumptions or guesses about the populations involved.Quality Assurance


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HYPOTHESIS TESTING:Hardness Testers: “Hard Tab – XP” vs “Soft Tab – Vista”Testing Parameter: Tablet HardnessTest Objective: Whether there is any significant difference between two set of measurements?Basis Data: Mean of Hardness results from Tester A = μ0

Mean of Hardness results from Tester B = μHypothetical Statements: 1. There is no significant hardness difference between

results from Tester A and Tester B.2. There is a significant difference between two results.

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HYPOTHESIS TESTING:NULL HYPOTHESIS ALTERNATE HYPOTHESISH0 : μ = μ0 H1 : μ ≠ μ0

THE OBJECTIVEIs 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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I AM INNOCENT

HE IS GUILTY MYLORD !!

THEN PROVE HE

IS NOT INNOCENT

TRIAL COURT


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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) =

11.5The expression is

T = - 0.78

Degrees of freedom is v = n -1 v = 20 – 1 = 19

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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.

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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.

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Acceptance ZoneCritical Zone

Critical Zone

STANDARD NORMAL CURVE:

0.95

H0 : μ = μ0 H1 : μ ≠ μ0H1 : μ ≠ μ0



Student’s Distribution Table:


Design of

Experiments



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.



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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

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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 RPMEach has their lowest and highest levels (range).

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Factors Lowest Level Code Highest Level Cod

e

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


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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 75.51 -1 -1 80.2-1 1 -1 84.91 1 -1 86.3-1 -1 1 79.11 -1 1 82.4-1 1 1 88.41 1 1 91.5


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DESIGN OF EXPERIMENTS:Calculation of Main EffectsExtract 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) = 3.625Coefficient (Slope) is S2/Effect = 1.8125Like wise we can calculate the other main effects and their coefficients.Wight (W): Effect = 3.125 Coefficient = 1.5625Thickness (T):Effect = 8.475 Coefficient = 4.2375

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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 75.51 -1 -1 -1 -1 1 1 80.2-1 1 -1 -1 1 -1 1 84.91 1 -1 1 -1 -1 -1 86.3-1 -1 1 1 -1 -1 1 79.11 -1 1 -1 1 -1 -1 82.4-1 1 1 -1 -1 1 -1 88.41 1 1 1 1 1 1 91.5


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DESIGN OF EXPERIMENTS:All Main Effects, Interactions and their Coefficients

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Term CoefficientConstant (Nominal) 83.5375Weight 1.5625Thickness 4.2375RPM 1.8125Weight × Thickness -0.4375Weight × RPM 0.0375Thickness × RPM 0.3625Weight × Thickness × RPM 0.3875



DESIGN OF EXPERIMENTS:



DESIGN OF EXPERIMENTS:


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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.

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Statistical Investigation - NS