Introduction to Control Charts

1. Introduction to Control Charts

2. Introduction • The science of quality control is largely statistical and Statistical quality control is a key factor in process validation and the manufacture of pharmaceutical products. • The best known application of statistics to quality control is the Shewhart control chart. • The control chart allows for judgments based on an easily comprehended graph.

3. What is Control Chart? • A statistical tool used to distinguish between process variation resulting from common causes and variation resulting from special causes. • A graph that has time or order of submission of sequential lots on X axis and the average test results on the Y axis.

4. Why Use Control Charts? • To monitor process variation over time • To differentiate between special cause and common cause variation • To assess effectiveness of changes • To communicate process performance • In preliminary research of formulation studies • In controlling and analyzing physical, chemical, analytical or biological parameters of a product, such as: • Weight variation of tablets and capsules, • Thickness of tablets, • Volume filling in a container, • The percentage of defects in parenteral products etc.

5. Types of Control Charts • There are two main categories of Control Charts: • Attribute Data: Attribute charts refer to go or no-go situations, in which only the number/percentage of articles conforming and the number/percentage of articles failing to conform to any specified requirements are counted. These “count” data may be expressed as pass/fail, yes/no, or presence/absence of a defect. • Variables Data: This category of Control Chart displays values resulting from the measurement of a continuous variable.e.g., • Weight variation of tablets • Thickness of tablets, • Volume filling in a container etc.

6. Contd… • There are three types that will work for the majority of the data analysis cases. • X-Bar and R Chart • Individual X and Moving Range Chart • for Variables Data • for Attribute Data • Other Control Chart types: • X-Bar and S Chart • u Chart • Median X and R Chart • p Chart • c Chart • np Chart

7. Control Chart Decision Tree

8. Elements of Control Charts • Each Control Chart actually consists of two graphs, an upper and a lower plotting areas. • Title. • Legend. information on how and when the data were collected. • Data Collection Section. The counts or measurements are recorded in the data collection section prior to being graphed. • Plotting Areas. A Control Chart has two areas

9. Vertical or Y-Axis. It shows • The scale of the measurement for variables data, OR • The count (frequency) or percentage of occurrence of an event for attribute data. • Horizontal or X-Axis. It displays the chronological order in which the data were collected. • Control Limits. Control limits are set at a distance of 3 sigma (Standard Deviation) above and 3 sigma (Standard Deviation) below the centerline and are calculated from actual values plotted on the Control Chart graphs. • Centerline. This line is drawn at the average or mean value of the data. The upper and lower graphs each have a separate centerline.

10. Elements of a Control Chart Title Legend Data Collection Section

11. Elements of a Control Chart upper graph Centerline Vertical Axis Control Limits Horizontal Axis lower graph

12. Steps for calculating and plotting anX-Bar and R Control Chart • Use when subgroup or sample size is between 2 and 15. • The steps for constructing of Control Chart are: • Step 1 - Determine the data to be collected. • Step 2 - Collect and enter the data by subgroup. A subgroup is made up of variables data that represent a characteristic of a product produced by a process.

13. Step 2 - Collect and enter data by subgroup

14. Step 3 - Calculate and enter the average for each subgroup. Calculate the average (mean) for each subgroup and enter it on the line labeled Average in the data collection section

15. Step 3 - Calculate and enter subgroup averages

16. Step 4 - Calculate and enter the range for each subgroup. RANGE = (Largest Value in Subgroup) - (Smallest Value in Subgroup) RANGE = (Largest Value in Subgroup) - (Smallest Value in Subgroup)

17. Step 4 - Calculate and enter subgroup ranges

18. Step 5 - Calculate the grand mean of the subgroup’s average. The grand mean of the subgroup’s average (X-Bar) becomes the centerline for the upper plot.

19. Step 6 - Calculate the average of the subgroup ranges. The average of all subgroups becomes the centerline for the lower plotting area.

20. Step 7 - Calculate the upper control limit (UCL) and lower control limit (LCL) for the averages of the subgroups. To find the X-Bar control limits, use the following formula: Use the following constants (A2) in the computation:

21. Upper and Lower Control Limits Example

22. Step 8 - Calculate the upper control limit for the ranges. To find the upper control limit for the ranges, use the formula: Use the following constants (D4) in the computation: Example = (2.114)(1.8) = 3.8052

23. Step 9 - Select the scales and plot the control limits, centerline, and data points, in each plotting area. The scales must be determined before the data points and centerline can be plotted. • Plot each subgroup average as an individual data point in the upper plotting area. Plot individual range data points in the lower plotting area

24. Step 9 - Select scales and plot

25. Step 10 - Provide the appropriate documentation. Each Control Chart should be labeled with • where the data originated, • when it was collected, • who collected it, • any identifiable equipment or work groups, • sample size, • Information about what the data describe etc.

26. When should we use an Individual X and Moving Range (XmR) Control Chart? • To assess both variables and attribute data. • For data that can not form subgroups with more than one measurement.

27. Conditions we must satisfy to use an XmR Control Chart for attribute data • The only condition to be checked for using the XmR Control Chart is that the average count per sample IS GREATER THAN ONE. • There is no variation within a subgroup since each subgroup has a sample size of 1, and the difference between successive subgroups is used as a measure of variation. This difference is called a moving range. There is a corresponding moving range value for each of the individual X values except the very first value.

28. Steps for calculating and plotting an XmR Control Chart • Step 1 - Determine the data to be collected. • Step 2 - Collect and enter the individual measurements. Enter the individual measurements in time sequence on the line labeled Individual X in the data collection section of the Control Chart.

29. Step 2 - Collect and enter individual measurements

30. STEP 3 - Calculate and enter the moving ranges. The moving range data will be plotted as individual data points in the lower plotting area.

31. Step 3 - Calculate and enter moving ranges

32. Step 4 - Calculate the overall average of the individual data points. The average of the Individual-X data becomes the centerline for the upper plot.

33. Step 5 - Calculate the average of the moving ranges. The average of all moving ranges becomes the centerline for the lower plotting area.

34. Step 6 - Calculate the upper and lower control limits for the individual X values. (for the upper plotting area) To find these control limits, use the formula:

35. Step 7 - Calculate the upper control limit for the range. (for the lower plotting area) There is no lower control limit.

36. Step 8 - Select the scales and plot the data points and centerline in each plotting area. The scales must be determined before the data points and centerline can be plotted. • Plot each Individual X value as an individual data point in the upper plotting area. Plot moving range values in the lower plotting area

37. Step 8 - Select scales and plot

38. Step 9 - Provide the appropriate documentation. Each Control Chart should be labeled to describe • Where the data originated, • When it was collected, • Who collected it, • Any identifiable equipment or work groups, • Sample size, • Clarification of what the data describe etc.

39. Step 10 - Check for inflated control limits. When either of the following conditions exists, the control limits are said to be inflated, and they must be recalculated: • If any point is outside of the upper control limit for the moving range (UCLmR) • If two-thirds or more of the moving range values are below the average of the moving ranges computed in Step 5.

40. Step 10 - Check for inflated control limits

41. Step 11 - If the control limits are inflated, calculate 3.144 times the median moving range. For example, if the median moving range is equal to 6, then (3.144)(6) = 18.864 • The centerline for the lower plotting area is now the median of all the values (vice the mean) when they are listed from smallest to largest.

42. Step 12a - Do not recompute if 3.144 times median mR is greater than 2.66 times average of moving ranges • Step 12b - Otherwise, recompute all control limits and centerlines

43. What do we need to know to interpret Control Charts? • Process stability is reflected in the relatively constant variation exhibited in Control Charts. • A point falling outside the control limits band is a signal of a special cause of variation. OR, something abnormal is occurring within your process. • The presence of unusual patterns can be evidence that your process is not in statistical control.

44. Rules for interpreting X-Bar and R Charts • RULE 1 : Whenever a single point falls outside the 3 sigma control limits, a lack of control is indicated. Since the probability of this is rather small, it is very likely not due to chance.

45. RULE 2 : Whenever at least 2 out of 3 successive values fall on the same side of the centerline and more than 2 sigma units away from the centerline (in Zone A or beyond), a lack of control is indicated.

46. RULE 3 : Whenever at least 4 out of 5 successive values fall on the same side of the centerline and more than one sigma unit away from the centerline (in Zones A or B or beyond), a lack of control is indicated.

47. RULE 4 : Whenever at least 8 successive values fall on the same side of the centerline, a lack of control is indicated.

48. Rules for interpreting XmR Control Charts • RULES FOR INTERPRETING THE X-PORTION of XmR Control Charts: Apply the four rules discussed above, EXCEPTapply them only to the upper plotting area graph. • RULE FOR INTERPRETING THE mR PORTION of XmR Control Charts for attribute data: Rule 1is the only rule used to assess signals of special causes in the lower plotting area graph.

49. When should we change the control limits? • There are only three situations appropriate to change the control limits: • When removing out-of-control data points • When replacing trial limits • When there are changes in the process, e.g., • New or modified procedures, • The use of different machines, • The overhaul of existing machines

50. References • Lachman Leon, The Theory and Practice of Industrial Pharmacy, 3rd edition, Varghesepublishing house, Bombay, Pg no.: 817 to 824 • Sanford Boulton, Pharmaceutical Statistics-Practical and Clinical Applications, 4th edition, Marcel and Dakker Inc., New York, Pg no.: 374 to 388 • “Basic Tools for Process Improvement”www.balancedscorecard.org/Portals/0/PDF/control.pdf