From: Arthur W. Brooks
Sent: Thursday, February 15, 2007 12:51 PM
To: Wayne T. Reiersen; Steve Raftopoulos; James H. Chrzanowski; Phil
Heitzenroeder; Robert A. Ellis; Thomas G. Brown; Hutch Neilson; Michael
C. Zarnstorff; Lawrence E. Dudek
Subject: Reproducibility of Romer Arm Data

Attachments: Analysis of Overlap Regions.ppt

Folks,

I've tried to go back and do some data mining in an attempt to quantify the reproducibility 
of the Romer Arm measurements. There are two areas in particular where we have multiple
measurements of the same points: 

1) Analyze the repeated measurements of the Conical Seats during the alignment of the arm
 prior to each set of measurements at the various stages of coil winding.

2) Analyze the overlap regions of the casting measurements.

The Conical seats were found to be more repeatable as the Romer Arm as they provide a 
defined point to go back to and are also part of the best fitting process associated 
with each alignment. The overlap regions are less repeatable as there is some uncertainty 
associated with getting back to the same point and the measurements include the alignment 
error.

The attached tables and plots provide a summary of the data. For the conical seats, 
several estimates of the deviation were made with different treatment of the reference 
coordinates of the seats. In the first column of slide 1, the deviations are measured 
with respect to the reference coordinates and show the highest magnitudes. In the second 
column, the deviations are with respect to the average of all measurements with the 
reference coordinates taken as just another set of data. In the last column, the reference 
points are excluded. This represents the best we can expect from the Romer Arm and suggest 
the Romer Arm contribution to the total error (2 sigma) is ~.0055" based on C4, C5 and B1. 
A3 is a bit higher (~.0074") party because it includes some questionable measurements that 
may or may not have been included in the alignment (points that differ significantly are 
normal deleted from the coil alignment but may be included in the inspection reports). 

An interesting point is that the reference coordinates differ from the average of the 
repeated measurements. This implies there is some error in our knowledge of the reference 
points as well. It may be worth doing repeated measurements of the seats to remove some 
of this error prior to coil winding.

The second slide summaries the deviations found in the overlap regions for the castings. 
The initial investigations looked at C4 and C5 showed repeatability of the measurements 
to be ~ 0.010" at the 2 sigma level. B1, B2 and A1 were not significantly different. 
However, A2 and A3 should differences more than twice that. In retrospect, I suspect 
these should have been flagged and remeasured. It seems we (I) need to spend more time 
reviewing data and perhaps adopt a more stringent and comprehensive criteria (ie set a 
limit on average deviation of .010" to .012")

The remaining slides just contain histograms of all the overlap data for each coil. 
Most (B1, B2, A1, C4 and C5) show fairly normal distributions that could be associated 
with multiple measurements. Others seem to suggest a slight shift in the alignment of 
the setups.

To summarize, it would appear the Romer Arm does have the potential to take repeatable 
data with acceptable limits but we are not always achieving it in practice.

Art