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Sunday, July 7, 2013

Evaluating Sample Variation



Many times customers attempt to determine the variation of their product to assist in determining reasonable production tolerances. Below is an evaluation that we assisted a customer with on some deep red paper samples.
 
Technidyne Data – Evaluation of red paper samples
A variety of measurements were made on the red paper samples provided by the customer to better understand the characteristics of the samples.  Similar measurements were made on the 90 range, white calibration standard paper to provide a basis for comparison.

Sample Variability (single direction): One single red sample sheet was measured 30 times in various locations but in the same orientation to look at the sample variability.  All three parameters, L*, a* and b*, had a range (high minus low) of about 0.25 units.  Using the standard deviation, the values in L* had the most variation followed by a* and finally b*. 

TABLE A.1 – Red Sample Variability (single direction)
After taking 30 readings (all with the sample in the same orientation)

L*
a*
b*
Range (High – Low)
0.25
0.25
0.22
Standard Deviation
0.073
0.066
0.053

Similar measurements (12 instead of 30 since the physical size is smaller) were made of the white, non-fluorescent paper calibration standard.  The L*, a* and b* range was less than 0.05, or about 20% the spread seen with the red sample.  The standard deviations were on the order of 3 to 12 times smaller than those of the red sample.

TABLE B.1 – White Paper Sample Variability (single direction)
After taking 12 readings (all with the sample in the same orientation)

L*
a*
b*
Range (High – Low)
0.04
0.02
0.05
Standard Deviation
0.011
0.005
0.017

Sample Variability (directionality; MD vs. CD): The same sample sheet was then measured 15 times in machine direction (MD) and then 15 times in cross-machine direction (CD).  L* and b* showed slightly higher directionality as determined by looking at the range and standard deviation of the measurements.  All of these values were higher than those achieved in the single direction test described above. 

TABLE A.2 – Red Sample Variability (directionality; MD vs. CD)
After taking 30 readings (15 MD and 15 CD)

L*
a*
b*
Range (High – Low)
0.36
0.32
0.23
Standard Deviation
0.080
0.086
0.059

A series of 12 measurements were made of the white, non-fluorescent paper calibration standard.  There is no real directionality when compared to the single direction data above.  However, the results are orders of magnitude better then the red sample which shows some measurable directionality.

TABLE B.2 – White Paper Sample Variability (directionality; MD vs. CD)
After taking 12 readings (6 MD and 6 CD)

L*
a*
b*
Range (High – Low)
0.02
0.02
0.04
Standard Deviation
0.008
0.006
0.015


These kind of evaluations are important to help in determining reasonable variations and production tolerances. This information can also be useful to help communicate with the end user on acceptability tolerances.

Feel free to contact me at toddp@technidyne.com.