Statistical investigation

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? The act or process of investigating. A careful search or examination in order to discover facts . A detailed inquiry or systematic examination . Slide No.: 3 of 51 Quality Assurance, Matoda

4. Why Investigate:…………… The Purpose To find out the Root Cause – Market complaint Out of Specification result Deviation Out of Trend drift Machine breakdown To enhance understanding – Product Process System Slide No.: 4 of 51 The reactive approach The proactive approach Quality Assurance, Matoda

5. Why Investigate:…………… The Purpose Slide No.: 5 of 51 Investigation CAPA Process Improvement Problem identification Investigation Finding Root Cause Recommendation(s) Corrective & Preventive measures Improvement Quality Assurance, Matoda

6. Why Investigate:…………… The Purpose Slide No.: 6 of 51 Quality Assurance, Matoda

7. Investigative Tools: Slide No.: 7 of 51 Quality Assurance, Matoda

8. Experience or Institution based approach Traditionally used, as it requires. No factual analysis or observations. Biased. Symptom Remedy Investigative Tools: Slide No.: 8 of 51 Quality Assurance, Matoda

9. Data based approach Scientific. Methodical. Unbiased. Symptom Root cause Remedy Investigative Tools: Slide No.: 9 of 51 Quality Assurance, Matoda

10. Investigative Tools: Slide No.: 10 of 51 Use correct tool for correct work Quality Assurance, Matoda

11. Investigative Tools:…………. Start up Slide No.: 11 of 51 Flowcharts are tools that make a process visible. Flowcharts Quality Assurance, Matoda

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. Slide No.: 12 of 51 Investigative Tools:…………. Start up Quality Assurance, Matoda

13. Flowchart of manufacturing of a Parenteral product (Lyophilized) Slide No.: 13 of 51 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 Pass Fail Pass Fail Quality Assurance, Matoda

14. Investigative Tools:…………. Data gathering Slide No.: 14 of 51 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. Quality Assurance, Matoda

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 . Slide No.: 15 of 51 Investigative Tools:…………. Data gathering Quality Assurance, Matoda

16. Brainstorming ( Mind Mapping Technique) Slide No.: 16 of 51 Broken tablets in packed bottles Broken during compression Broken during coating Broken during filling Broken during Shipment Broken during Warehousing High Hardness Low Hardness High falling Broken during handling Improper inspection High hopper vibration Excessive rolling Over dried Low LOD Fall of bottles Broken during repacking Excessive rattling Low RH exposure Incorrect complaint High speed line Investigative Tools:…………. Data gathering Quality Assurance, Matoda

17. Slide No.: 17 of 51 Investigative Tools:………… Data stratification The Cause & Effect Diagram Quality Assurance, Matoda

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. Slide No.: 18 of 51 Investigative Tools:………… Data stratification Quality Assurance, Matoda

19. The C & E Diagram for Broken tablets in bottles Slide No.: 19 of 51 Investigative Tools:………… Data stratification Quality Assurance, Matoda

20. Slide No.: 20 of 51 Investigative Tools:………… Data Trending Boxplot Boxplots summarize information about the shape , spread , and center of your data set. They can also help you to spot outliers . Quality Assurance, Matoda

21. Slide No.: 21 of 51 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 (*). Quality Assurance, Matoda

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 Data set contains 15 data. Median (Q2) = (15+1)/2 = 8 th data in set is 14.6 . 1 st Quartile (Q1) = 4 th data in set is 14.4 . 3 rd Quartile (Q3) = 12 th data in set is 14.9 . Interquartile Range (IQR) = 14.9 – 14.4 = 0.5 . Acceptable Range is Q1- (1.5 × IQR) to Q3 + (1.5 × IQR) = 13.65 to 15.65 . Outlier values are 10.2 , 15.9 and 16.4 . Lower Whisker = Lowest value ( 14.1 ) and Upper Whisker = Highest value ( 15.1 ) excluding outliers. Quality Assurance, Matoda

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 1 st Quartile (Q1) = 14.4 3 rd Quartile = 14.9 Lower Whisker = 14.1 Upper Whisker = 15.1 Outliers = 10.2, 15.9 and 16.4 Quality Assurance, Matoda

24. Slide No.: 23 of 51 Investigative Tools:………… Data Trending But not always similar.... Box Whisker Quality Assurance, Matoda

25. Slide No.: 24 of 51 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. Quality Assurance, Matoda Pareto Analysis

26. Slide No.: 25 of 51 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). Quality Assurance, Matoda

27. Slide No.: 26 of 51 Investigative Tools:………… Data Trending Pareto Analysis of Market Complaint: Quality Assurance, Matoda 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

28. Slide No.: 27 of 51 Investigative Tools:………… Data Trending Pareto Analysis of Market Complaint: Quality Assurance, Matoda 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

29. Slide No.: 28 of 51 Investigative Tools:………… Data Trending Plotting of Pareto Chart: Quality Assurance, Matoda Vital Contributors Trivial Contributors

30. Slide No.: 29 of 51 Investigative Tools:………… Experimentation This tool provides a fundamental strategy for making decisions based on some assumptions or guesses about the populations involved. Quality Assurance, Matoda Hypothesis Testing

31. Investigative Tools:………… Experimentation Slide No.: 30 of 51 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 = μ 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 Slide No.: 31 of 51 Hypothesis Testing: Null Hypothesis Alternate Hypothesis H : μ = μ H 1 : μ ≠ μ The objective Is there are enough evidence that the Null Hypothsis can be rejected? If not, then Null Hypothesis is true. Quality Assurance, Matoda

33. Slide No.: 32 of 51 Investigative Tools:………… Experimentation Quality Assurance, Matoda I AM INNOCENT HE IS GUILTY MYLORD !! THEN PROVE HE IS NOT INNOCENT TRIAL COURT

34. Investigative Tools:………… Experimentation Slide No.: 33 of 51 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 ( μ ) . 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 Quality Assurance, Matoda

35. Investigative Tools:………… Experimentation Slide No.: 34 of 51 Hypothesis Testing: Type I error (called α ): The probability of rejecting Null Hypothesis when μ = μ 0, 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 H 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 Slide No.: 35 of 51 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 Slide No.: 36 of 51 Quality Assurance, Matoda Acceptance Zone Critical Zone Critical Zone Standard Normal Curve: 0.95 H : μ = μ H 1 : μ ≠ μ H 1 : μ ≠ μ

38. Investigative Tools:………… Experimentation Slide No.: 37 of 51 Quality Assurance, Matoda Student’s Distribution Table:

39. Slide No.: 38 of 51 Quality Assurance, Matoda Design of Experiments Investigative Tools:………… Experimentation

40. Slide No.: 39 of 51 Quality 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 Slide No.: 40 of 51 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 Slide No.: 41 of 51 Design of Experiments: The 3 factors are initially selected to see the effect on dissolution. (A) W eight of tablet, (B) T hickness and (C) M/C R PM Each has their lowest and highest levels (range). Quality Assurance, Matoda 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 Slide No.: 42 of 51 Design of Experiments: Based on the case, we can construct Full Factorial design. The number of experiments would be 2 3 = 8 . Quality Assurance, Matoda 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 Slide No.: 43 of 51 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 S 2 /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 Quality Assurance, Matoda

45. Investigative Tools:………… Experimentation Slide No.: 44 of 51 Design of Experiments: Calculation of Interactions Quality Assurance, Matoda 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 Slide No.: 45 of 51 Design of Experiments: All Main Effects, Interactions and their Coefficients Quality Assurance, Matoda 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 51 Quality Assurance, Matoda Design of Experiments:

48. Investigative Tools:………… Experimentation Slide No.: 47 of 51 Quality Assurance, Matoda Design of Experiments:

49. Investigative Tools:………… Experimentation Slide No.: 48 of 51 Design of Experiments: Interpretations: The dissolution of said product largely varies with main effects of factors. The top most contribution is from Thickness followed by Machine Speed. The interactions are having negligible effect on dissolution. Effect of Machine Speed is slightly greater on higher Thickness than on lower Thickness. Effect of Thickness is slightly greater on lower tablet Weight than on higher Weight. Practically no interaction between M/C RPM and Weight. Quality Assurance, Matoda

50. Any Question ? Slide No.: 49 of 51 Quality Assurance, Matoda

51. Remember ! Slide No.: 50 of 51 Quality Assurance, Matoda

52. This is not an end……… Slide No.: 51 of 51 Quality Assurance, Matoda