1. ©2005 LUDECA, INC. Understanding Standard Deviation

2. ©2005 LUDECA, INC. www.ludeca.com Unbiased Standard Deviation intimidated Are you intimidated yet? The whole point of this presentation is to unintimidate you regarding this excellent feature of the Rotalign® Ultra.

3. ©2005 LUDECA, INC. www.ludeca.com Here you see alignment results in the Measure screen, after readings have been taken, without Standard Deviation information. [Please click] Now you see the Standard Deviation Result in the same screen. You can enable or disable the appearance of this information at will. However, we recommend that you do enable it. This is a critically important and very powerful feature that only your Ultra has, and it can make the difference in achieving certain critical alignments.

4. ©2005 LUDECA, INC. www.ludeca.com To turn on the SD display, go to the Global Menu and select Units. [Please click.] Then select Show on Measurement screen in the Showing SD value window.

5. ©2005 LUDECA, INC. www.ludeca.com Even if you have SD turned off in the main Measure Screen, you can still see the SD value in the Measurement Table. Just scroll to the right a little.

6. ©2005 LUDECA, INC. www.ludeca.com Understanding Standard Deviation So then, what is Standard Deviation? Standard Deviation is the mean of the means. It describes how closely a group of data points are clustered around the average of those data points. It is a measure of measurement quality. The smaller the SD, the better the quality of the data you collected.

7. ©2005 LUDECA, INC. www.ludeca.com Understanding Standard Deviation really sure On a very critical alignment, or where you have a lot of vibration, or couldnt turn the shafts, just getting the results may not be good enough. Of course, a repeatability check is essential, but even if you pumped up the averaging of the readings in Multipoint, are you really sure the data is good?? With Standard Deviation display, the need for a repeatability check disappears, which can save you time under difficult conditions.

8. ©2005 LUDECA, INC. www.ludeca.com Understanding Standard Deviation average The alignment results you get are the average of all the data points collected. Why is this average of the data, by itself, not good enough, even if it is repeatable? [Please click] Look at the ages: scattered all the way from 2 to 20. Ask yourself: How successful is my party going to be if I plan it around activities suitable for age 10? Suppose youre planning a party for a group of kids. All you are told is: the average age of the group is 10.

9. ©2005 LUDECA, INC. www.ludeca.com Understanding Standard Deviation Obviously, your party will be a bomb. Lets look at the distribu- tion of ages again: [Please click] If you had been told the standard deviation of the group, youd know you were in trouble. [Please click]

10. ©2005 LUDECA, INC. www.ludeca.com Understanding Standard Deviation Now suppose you had this group instead: All the kids are much closer in age to the average, so your party will be a hit! Look at the Standard Deviation: [Please click] Much better! As you can see, if all youre told is the average of the data, it doesnt tell you anything about the quality of the data.

11. ©2005 LUDECA, INC. www.ludeca.com Understanding Standard Deviation average In perfect alignment, the laser beam describes a dot on the sen- sor that never moves as you rotate the shafts. But when misalignment exists, the beam will move in an ever changing arc. Each dot repre- sents a reading taken somewhere on this arc. The dots are not all positioned perfectly upon the arc. Some fall above or below it. If we average out all their positions, we get a curved path that represents the average trajectory of all the dots. Eventually, over a full rota- tion of the shafts, this averaged beam track describes an ellipse.

12. ©2005 LUDECA, INC. www.ludeca.com Understanding Standard Deviation However, just looking at this average is not good enough, because, like the ages of the kids, it doesnt really tell us much about how good the data is, or how far above or below the average trajectory the points fall. Clearly, if we are deriving the trajectory of the arc from the average, and some points are widely scattered, that average will be greatly affected, and it would be good to know that.

13. ©2005 LUDECA, INC. www.ludeca.com Understanding Standard Deviation If we take the ellipse, cut it, and lay it out flat, we get the deviation dia- gram shown here. This is called Broken Ellipse view in the Ultra. Notice that one point seems to be way out of the pattern or average track of the others. Clearly, this particular point represents an aberration of some sort.

14. ©2005 LUDECA, INC. www.ludeca.com Understanding Standard Deviation Taking the aberrant point into considera- tion will affect the calculated results harm- fully. It would skew the aver- age. It should be deleted from consideration. How would you ever know this is happening? A high Standard Deviation value would immediately alert you.

15. ©2005 LUDECA, INC. www.ludeca.com This is the result of a set of Multipoint readings taken on a large gas turbine. While ta- king the readings, the result values were stable and looked great, but all of a sudden the numbers changed and the SD value jumped up. Since rotating the shafts was very difficult, it was not convenient to start over again. Since the numbers had been good up to that point, it was decided to continue since there was nothing to indicate that the laser or receiver had been bumped, or had hit anything. After 33 points were taken the rotation of the shafts was finally completed and readings were stopped. Clearly, with an SD of 53, something had gone seriously wrong, yet the prospect taking another set of readings was to be dreaded. To see what went wrong with the readings, we went to the Menu and... Using Standard Deviation

16. ©2005 LUDECA, INC. www.ludeca.com Using Standard Deviation... selected Edit points. [Please click]

17. ©2005 LUDECA, INC. www.ludeca.com Using Standard Deviation Broken Ellipse view is selected. Note the deviation diagram in this screen. Clearly, at least one of those 33 readings was very bad. Next, instead of scrolling to it, just press Menu again and...

18. ©2005 LUDECA, INC. www.ludeca.com Using Standard Deviation...select Max point. This will automatically select the point with the highest deviation in the group when you press the key. [Please click]

19. ©2005 LUDECA, INC. www.ludeca.com Using Standard Deviation Simply press the key to disable the point. Next, youll see what happened when the worst point was disabled.

20. ©2005 LUDECA, INC. www.ludeca.com Using Standard Deviation The SD dropped all the way down to 2.19! You can continue disabling points the same way until you are satisfied that your SD value is low enough that you can rely on the quality of the remaining data.

21. ©2005 LUDECA, INC. www.ludeca.com One important thing to look at in deciding whe- ther or not to disable a point is how far away from the trajectory or average it lies. Look at the Delta value. If this number is fairly high, chances are great youll improve the SD. Also make sure that you dont disable too many points. It is important that the number of remaining active points be sufficient to still render your data meaningful. (By the way, the aberrant worst point was caused by taking that point just as the laser beam barely clipped the chain fall cable that was being used to turn the shafts. When disabling the nine points with the highest deviations we worked with the best data and lowered the SD to just 0.8 mils!) Using Standard Deviation.

22. ©2005 LUDECA, INC. www.ludeca.com Here we see the laser and receiver at about the 12 oclock position. Note that the beam is shot through the coupling bolt hole. After the shafts were turned, the laser beam just barely clipped the chainfall cable at that one point, located at about 10 oclock. This can be seen in the Edit Points screen that we saw earlier. [Please click]

23. ©2005 LUDECA, INC. www.ludeca.com So... When should I disable a point?? The red point is clearly not on the standard track of the others. It is an aberrant point and should be disabled. The Standard Deviation will improve significantly.

24. ©2005 LUDECA, INC. www.ludeca.com The red point has the largest absolute de- viation, but, ask your- self, is it really fur- thest away from the average track of the others? Would a straight line average track really represent what these points are collectively trying to tell us? No! Here the So... When should I disable a point?? sinusoidal track appears to be a more accurate representative of reality. Disabling this point will not significantly change the Standard Deviation! This illustrates that the average itself, and the absolute deviation from the average mean little, whereas the Standard Deviation is very significant. You should not disable this point.

25. ©2005 LUDECA, INC. www.ludeca.com So... When should I disable a point?? not reduce the Standard Deviation much. Since the data is quite rough, more points are what is needed to ensure good reliable data. Collectively, the Standard Deviation of all of those points may not be that bad. Again, choose not to disable the max point in this case. Again, the red point is furthest away from the average track of the others, but is it really so bad compa- red to all the others? Will disabling it really affect what all the other points are try- ing to tell us? Again, you will find that dis- abling this point will

26. ©2005 LUDECA, INC. www.ludeca.com Standard Deviation & Repeatability Note the poor repeatability of these readings, and the high standard deviation of the first set.

27. ©2005 LUDECA, INC. www.ludeca.com Standard Deviation & Repeatability Note that all points taken are active in the first set of readings that has the high Standard Deviation.

28. ©2005 LUDECA, INC. www.ludeca.com Standard Deviation & Repeatability Now look at what happens when we disable the worst points and bring down the Standard Deviation: The repeatability is now excellent!

29. ©2005 LUDECA, INC. www.ludeca.com Standard Deviation & Repeatability This proves that if your Standard Deviation is low, your results will be accurate and you do not have to take another set of readings to establish repeatability. Save time!

30. ©2005 LUDECA, INC. www.ludeca.com Standard Deviation Tolerances normal For normal applications: 0 SD 1.0 mils critical For critical alignments: 0 SD 0.5 mils

31. ©2005 LUDECA, INC. www.ludeca.com Standard Deviation Bell Curve This is the SD bell curve. What this shows is that in a normal distribution of measured values, 68.2% of your data will always fall within one SD of the mean, and 95.4% of your data will fall within 2 SDs, and 99.6% of the data will fall within 3 SDs. The important thing to remember is that the actual value of the SD should be kept low.