©2005 LUDECA, INC. Understanding Standard Deviation.
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©2005 LUDECA, INC. Understanding Understanding Standard Standard Deviation Deviation
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Transcript of ©2005 LUDECA, INC. Understanding Standard Deviation.
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UnderstandingUnderstanding
Standard DeviationStandard DeviationUnderstandingUnderstanding
Standard DeviationStandard Deviation
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Unbiased Standard DeviationUnbiased Standard DeviationUnbiased Standard DeviationUnbiased Standard Deviation
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SD
Are you intimidatedintimidated yet?
The whole point of this presentation is to unintimidate you regarding this excellent feature of the Rotalign® Ultra.
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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.
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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.
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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.
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Understanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard DeviationUnderstanding 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.
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Understanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard Deviation
On a very critical alignment, or where you have a lot of vibration, or couldn’t 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 surereally sure the data is good??
With Standard Deviation display, the need for a repeatability check disappears, which can save you time under difficult conditions.
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Understanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard Deviation
The alignment results you get are the averageaverage 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 you’re planning a party for a group of kids. All you are told is: the average age of the group is 10.
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Understanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard Deviation
Obviously, your party will be a bomb. Let’s look at the distribu-tion of ages again: [Please click]
If you had been told thestandard deviation of thegroup, you’d know you werein trouble. [Please click]
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Understanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard Deviation
Now suppose you had this group instead:
All the kids are much closerin age to the average, so yourparty will be a hit! Look at theStandard Deviation: [Please click]
Much better! As you can see,if all you’re told is the averageof the data, it doesn’t tell you anything about the quality of the data.
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Understanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard Deviation
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 averageaverage trajectory of all the dots. Eventually, over a full rota-tion of the shafts, this averaged beam track describes an ellipse.
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Understanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard Deviation
However, just looking at this average is not good enough, because, like the ages of the kids, it doesn’t 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.
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Understanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard Deviation
If we take theellipse, cut it,and lay it outflat, we get thedeviation dia-gram shown here.This is called‘Broken Ellipse’view in the Ultra.
Notice that onepoint seems tobe way out ofthe ‘pattern’ oraverage trackof the others.
Clearly, this particular point represents an aberration of some sort.
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Understanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard DeviationUnderstanding Standard Deviation
Taking theaberrant pointinto considera-tion will affectthe calculatedresults harm-fully. It wouldskew the aver-age. It shouldbe deleted fromconsideration.
How would youever know thisis happening?A high Standard Deviation value would immediately alert you.
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This is the result of a set ofMultipoint readings taken ona large gas turbine. While ta-king the readings, the resultvalues were stable and lookedgreat, but all of a sudden thenumbers changed and the SDvalue jumped up. Since rotatingthe shafts was very difficult,it was not convenient to startover again. Since the numbershad 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 DeviationUsing Standard DeviationUsing Standard DeviationUsing Standard Deviation
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Using Standard DeviationUsing Standard DeviationUsing Standard DeviationUsing Standard Deviation
... selected Edit points. [Please click]
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Using Standard DeviationUsing Standard DeviationUsing Standard DeviationUsing 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...
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Using Standard DeviationUsing Standard DeviationUsing Standard DeviationUsing 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]
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Simply press the key to disable the point. Next, you’ll see what happened when the worst point was disabled.
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Using Standard DeviationUsing Standard DeviationUsing Standard DeviationUsing 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.
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One important thing tolook at in deciding whe-ther or not to disable apoint is how far awayfrom the trajectory oraverage it lies. Look atthe Delta value. If thisnumber is fairly high,chances are greatyou’ll improve the SD.Also make sure that youdon’t disable too manypoints. It is importantthat the number ofremaining active pointsbe sufficient to stillrender 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 DeviationUsing Standard DeviationUsing Standard DeviationUsing Standard Deviation
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Here we see the laser and receiver at about the 12 o’clock 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 o’clock. This can be seen in the Edit Points screen that we saw earlier.[Please click]
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So... When should I disable a So... When should I disable a point??point??So... When should I disable a So... When should I disable a point??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.
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The red point has thelargest absolute de-viation, but, ask your-self, is it really fur-thest away from the“ average track” ofthe others? Would astraight line averagetrack really representwhat these points arecollectively trying totell us? No! Here the
So... When should I disable a So... When should I disable a point??point??So... When should I disable a So... When should I disable a point??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.
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So... When should I disable a So... When should I disable a point??point??So... When should I disable a So... When should I disable a point??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 pointis furthest away fromthe average track ofthe others, but is itreally “so bad” compa-red to all the others?Will disabling it reallyaffect what all theother points are try-ing to tell us? Again,you will find that dis-abling this point will
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Standard Deviation & RepeatabilityStandard Deviation & RepeatabilityStandard Deviation & RepeatabilityStandard Deviation & Repeatability
Note the poor repeatability of these readings, and the high standard deviation of the first set.
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Standard Deviation & RepeatabilityStandard Deviation & RepeatabilityStandard Deviation & RepeatabilityStandard Deviation & Repeatability
Note that all points taken are active in the first set of readings that has the high Standard Deviation.
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Standard Deviation & RepeatabilityStandard Deviation & RepeatabilityStandard Deviation & RepeatabilityStandard Deviation & Repeatability
Now look at what happens when we disable the worst points and bring down the Standard Deviation: The repeatability is now excellent!
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Standard Deviation & RepeatabilityStandard Deviation & RepeatabilityStandard Deviation & RepeatabilityStandard 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!
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Standard Deviation TolerancesStandard Deviation TolerancesStandard Deviation TolerancesStandard Deviation Tolerances
For normalnormal applications:0 SD 1.0 mils
For criticalcritical alignments:0 SD 0.5 mils
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Standard Deviation Bell CurveStandard Deviation Bell CurveStandard Deviation Bell CurveStandard 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 SD’s, and 99.6% of the data will fall within 3 SD’s. The important thing to remember is that the actual value of the SD should be kept low.
