1. Lynn Torbeck Torbeck and Assoc. Evanston, IL
Trend Data
Lynn Torbeck
Torbeck and Assoc.
Evanston, IL
June 28, 2007

2. Overview OOT vs. OOS Why trend? How to get started
Types of trends with examples
OOT is relative
Graphical tools
Tend limits
June 28, 2007

3. Why Trend Data? Good business practice.
Early warning of possible Out Of Specification (OOS) results.
Gain process understanding.
Minimize risk of potential failures of product in the market.
Find the “gold in the hills” for process improvements.
June 28, 2007

4. Regulatory Basis for Trending
No specific regulation requirement
(e) Annual Reviews
FDA Form 483 for observations
Establishment Inspection Reports
Warning letters
FDA presentations at conferences
June 28, 2007

5. OOS Guidance Footnote
“Although the subject of this document is OOS results, much of the guidance may be useful for examining results that are out of trend (OOT).”
How is OOT different than OOS?
How is OOT the same as OOS?
June 28, 2007

6. Out Of Specification - OOS
OOS is the comparison of one result versus a predetermined specification criteria.
OOS investigations focus on determining the truth about that one value.
Is the OOS result confirmed or not?
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7. Out Of Trend - OOT
OOT is the comparison of many historical data values versus time.
OOT investigations focus on understanding non-random changes.
Is the non-random change confirmed or not?
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8. OOS Guidance
Taking into account the differences between OOS and OOT, the guidance does provide a framework for OOT investigations:
Responsibilities
Philosophical basis
General principles of investigations
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9. 1. How to get started Select the variable to be studied: Potency Yield
Impurities
Hardness
Bioburden
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10. 2. How to get started Select a time period:
At least one year if possible.
More than two preferred.
Do not go past a major change in the process. Use process knowledge to advantage.
Use the reportable result, the value compared to the specifications.
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11. 3. How to get started Enter the data into analysis software: Excel
Minitab
Sigma Plot
JMP
StatGraphics
Northwest Analytical
SAS
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12. 4. How to get started Plot the data vs. time or lot sequence.
Look for non-random changes over time.
Determine if they are of practical importance.
Statistical significance is insufficient.
Do an impact and risk assessment.
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13. What is Trending? The several activities of: Collecting data,
Recording it,
Documenting it,
Storing it,
Monitoring it,
Fitting models to it
Evaluating it, and
Reporting it.
June 28, 2007

14. What is a trend? Any non-random pattern.
Short and long term patterns in data over time that are of practical importance.
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15. Beneficial Trends Desirable patterns in the data series. Examples:
A move toward the target or center of the specification.
More consistent with less variation.
Less likelihood of an OOS value.
A benefit to SSQuIP.
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16. Beneficial Trend
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17. No Trend Easier to define what a trend is not. Random data Noise
Stationary
No ups, no downs
No cycles
No outliers
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18. Neutral or No Trend Neither beneficial or adverse Examples:
Results that are always the same.
Stability data with a slope of zero.
Data in a state of “statistical control” on a control chart.
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19. Process Control Statistical Process Control, SPC
Normal random data over time
Due to common causes only
Engineering Process Control, EPC
Estimate departures from target
Feedback to control point
Physical changes to the process
June 28, 2007

20. Adverse Trends Undesirable patterns in the data series. Examples:
A movement away from the target.
Increased variability.
Increased probability of OOS.
An unexplained change to a beneficial trend.
A challenge to SSQuIP.
June 28, 2007

21. Out-of-Trend (OOT)
A change from an established pattern that has the potential of an adverse effect on SSQuIP or of becoming OOS.
Must be large enough to be of practical significance.
Statistical significance is insufficient to determine OOT.
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22. Long Term Change Not stationary around a fixed value
Increasing or decreasing average.
Apparently will continue to get worse (or better) unless action is taken.
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23. The Aberrant Outlier
Stationary and random but with one very large value that could be a statistical outlier.
Generally assumed to be due to a “special cause.”
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24. Shift in the Average
Here the mean has increased from 100 to 104 at sample 51.
No other changes were made.
Variability is the same.
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25. Variation Change This is stationary around a fixed mean of 100%.
But, the standard deviation increased from 1.0 to 4.0.
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26. Cycles A reoccurring cycle. Stationary about a fixed mean.
The data are not independent.
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27. Autocorrelated Data are correlated with the previous data.
Not stationary.
Check different time lags, 1,2, ….
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28. OOT is Relative
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29. OOT is Relative
The importance of a trend is its size relative to the specification criteria.
A state of Statistical Control is desired but not necessary.
A state of Engineering Control is necessary to meet specifications.
Success is a marriage of the two.
June 28, 2007

30. A Little Humor (Very Little)
Lottery: A tax on the statistically-challenged.
If you want three opinions, just ask two statisticians.
Statistics means never having to say you're certain.
June 28, 2007

31. Trend Fitting
“The general process of representing the trend component of a time series.”
A Dictionary of Statistical Terms. Marriott
Depends very much on the type of data and the subject matter being studied.
Need to adapt the tools and techniques to our specific data and issues.
June 28, 2007

32. Tools of Trending Summary statistics Graphical plots
Averages, Medians
Ranges, Standard Deviations, %RSD
Graphical plots
Distribution analysis - Histograms
Outlier determination
Regression analysis
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33. Graphic Tools Line Plots vs. time. Shewhart Control Charts.
Histograms.
Sector chart
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34. Line Plots vs. Time Response on the vertical axis.
Time or batch # on the horizontal axis.
Usually connect the data points with a line, but optional.
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35. Control Chart Add ‘natural process limits’ to the line plot.  ± 3 
A chart for the response.
A chart for the variability.
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36. Control Chart Family Individuals Averages Medians Standard deviations
Ranges
Number of defectives
Fraction defectives
Defects per units
Number of defects
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37. Variation Change A control chart will detect change in the variation.
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38. The Outlier
A control chart finds values outside the natural limits of the data.
The value is larger than would be expected by chance alone.
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39. “Western Electric” Rules
One value outside 3 S limits.
Nine values in a row on one side of the average.
Six values in a row all increasing or decreasing.
14 values in a row alternating up and down.
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40. “Western Electric” Rules
Two of three values greater than 2 S from the average.
Four of five values greater than 1 S from the average.
15 values in a row within 1 S of the average.
Eight values in a row greater than 1 S.
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41. Histogram Show the ‘shape’ of the distribution of data.
In this case it is Normally distributed.
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42. The Outlier The outlier is clearly seen in the histogram.
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43. Outlier Determination
Reference:
USP 30 NF 25
Chapter <1010>
“Analytical Data – Interpretation and Treatment”
Page 392 “Outlying Results”
Appendix C: Examples of Outlier Tests for Analytical Data.
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44. Regression Analysis
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45. Trend Limits
Numeric (or non-numeric) criteria, that if exceeded, indicates that an out-of-trend change has occurred.
Usually the ‘natural process’ variation
AKA “Alert limits”
Use Statistical Tolerance Limits
See USP <1010> Appendix E
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46. Here, Trend This
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47. A New Engineering Chart
Brings together for the first time:
Comparison to the specification limits in place of the probability limits
Divides the specification range into equal zones in place of 1, 2, & 3 sigma areas
Uses cumulative scores
Pharmaceutical Technology, April 2005
June 28, 2007

48. The New “Sector Chart”
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49. The New “Sector Chart” Rules
The first batch tally takes the weight of the sector it is in.
Subsequent batches have a cumulative tally of the previous tally plus the current sector weight.
If the tally reaches a value of, say, 10, an alert is given.
If the batch enters the A or B sectors, the tally is reset to zero.
June 28, 2007

50. The New “Sector Chart” Rules
Sectors A and B cover the center 50% of the specification range.
Sector F is outside the current specification.
Other weights can be set to fit the process and the degree of sensitivity needed.
June 28, 2007

51. Advantages of Sector Chart
No minimum sample size. Can start with one data point.
No assumptions about the data at all.
Identifies beneficial and adverse trends.
Weights and tally total are selected by scientific and empirical knowledge.
A decision is made with each new point.
Alerts quickly if a problem exists.
June 28, 2007

52. Justification for Sector Chart
If the process is well inside the specification, it need not be in a state of statistical control.
The focus is on OOT and SSQuIP not being out of “statistical” control.
Sensitivity of the chart is adjustable.
Can be use in parallel with other charts.
June 28, 2007

53. That’s All Folks Summary Points: OOT is not OOS
OOT is non-random changes over time
OOT is a statistical and graphical issue
OOT is relative. Statistical significance is not sufficient.
Trend limits = Natural Limits
June 28, 2007

54. References Graphics: Statistics http://www.edwardtufte.com/tufte/
Statistics
June 28, 2007

55. Software References http://www.minitab.com/
June 28, 2007