> )+(7 bjbjUU (77lRRRRRRRf8.:fRRRRRRRR ?
($] }LRRRRRRLRRRRaR.RRRR R :4 oRR RFT`)f
w0
cc ffRRRROperation of the LPA1 analyzer and its operational statistics
Zero measurements and negative values
XRF analysis, like all other methods of measurements, is influenced by both random and systematic errors. The random errors are those that their magnitude can be reduced but not eliminated such as the effect of the radioactive decay of the source in measurements. The systematic errors are those that can be avoided, or at least corrected for. For example the effect of calibration samples, electronics, substrate, and mathematical algorithms.
The statistical terms such as precision, bias, accuracy, and uncertainty refer to these errors and are mathematical approaches for defining and measuring the contribution of each parameter. The uncertainty of a measurement is the summation of the contribution of precision, accuracy, and bias for that measurement.
The scatter on a single substrate represents random errors. We define this to be the precision. Strictly speaking, precision is the standard deviation of this scatter. The error in the mean value of lead, for a single substrate, represents a systematic error. Some would refer to this as the bias for this particular substrate, i.e., a particular piece of wood. We use the word bias to refer to the average of systematic errors for substrates class not only a particular component in that class.
The scatter in the systematic errors (strictly speaking, the standard deviation in the errors in the mean) we call accuracy. For any single reading obtained by the LPA1, there will be some uncertainty which results from the counts used in this reading (i.e., the precision) and the systematic error in our algorithm (which is quantified by the accuracy). Because these two factors are statistically independent, the total uncertainty is given by the square of the sum of the squares of precision and accuracy.
The contribution of random and systematic errors in an analysis is best represented by a statistical distribution curve. A series of replicate measurements results in a statistical distribution curve represented by Gaussian or Normal distribution. The curve is characterized by number of measurements, range or spread, mean, and scatter or divergence. The standard deviation (sigma) for such a curve is calculated to be the square root of the variance. In practice it can be stated that the probability is 68.3% (1 sigma or 1 standard deviation) that any individual measurement will have a value between the average of all readings plus and minus the standard deviation. For 2sigma or 2 standard deviation the probability is 95.4%.
From the above explanation, one can conclude that a set of repeated measurements for a zero lead sample would result in a Guassian distribution curve with mean value of zero. This curve implies that for a perfect zero sample fifty out of one hundred measurements would be to the negative side of the curve as the other fifty would lay on the positive side. Therefore, depending on the standard deviation and degree of confidence a zero lead sample can have measured values ranging from negative to positive numbers.
Therefore, the existence of negative values should be expected and interpolated as zero lead content due to statistical nature of the XRF measurements. The lack of such negative values suggests that data have been manipulated and should be questioned.
Both the HUD and the EPA recognize the statistical nature of the analytical measurements and the possibility of obtaining negative values where the lead content is around zero. In practice, the interpretation of a negative number has been as a reading that is below the regulatory Action Level threshold and as a result is negative lead.
?e 6CJCJ5CJ?ef%&bcX Y Z[;<BC@A$a$&
00&P/ =!"#$%
i0@0Normal_HmH sH tH <A@<Default Paragraph Font,,Header
!, ,Footer
!&)@&Page Number,>@",Title$a$5CJ?ef%&bcXYZ[;
<
BC@
A
(2:
Sia Afshari/D:\TEMP\AutoRecovery save of NegetiveReads1.asdSia Afshari/D:\TEMP\AutoRecovery save of NegetiveReads1.asdSia Afshari3D:\My Documents\LEADWORK\GENERAL\NegetiveReads1.docSia Afshari/D:\TEMP\AutoRecovery save of NegetiveReads1.asdSia Afshari/D:\TEMP\AutoRecovery save of NegetiveReads1.asdSia Afshari3D:\My Documents\LEADWORK\GENERAL\NegetiveReads1.docSia Afshari3D:\My Documents\LEADWORK\GENERAL\NegetiveReads1.docWayne M. Miller*C:\My Documents\GENERAL\NegetiveReads1.docPaul DelmonicoED:\My Documents\Web Page\Support\Technical Details\NegetiveReads1.docJames L. Williams,F:\brandtinst.com\WWW\RMD\NegetiveReads1.doc^DIA(*@h8^8`56>*CJOJQJo(. l='^DIAXV'`1@hh^h`OJQJo(@EPSON Stylus C80 SeriesLPT1:winspoolEPSON Stylus C80 SeriesEPSON Stylus C80 Seriespv
odhhRL***xhhDLLName32=E_DU04GE.DLLd2EPSON Stylus C80 Series ***EPSON Stylus C80 Seriespv
odhhRL***xhhDLLName32=E_DU04GE.DLLd2EPSON Stylus C80 Series ***'m@UnknownGTimes New Roman5Symbol3&Arial"0hWWb!202>Operation of the LPA1 analyzer and its operational statisticsSheldon AronoffJames L. WilliamsOh+'0$8 T`

?Operation of the LPA1 analyzer and its operational statisticsperSheldon AronoffhelhelNormal.dotnJames L. WilliamsPA2meMicrosoft Word 9.0A@F#@ӻ@Z`)@Z`)՜.+,0@
px
RMD, Inc.
?Operation of the LPA1 analyzer and its operational statisticsTitle
!"#$%&'*Root Entry F`),1TablecWordDocument(SummaryInformation(DocumentSummaryInformation8 CompObjjObjectPool``)``)
FMicrosoft Word Document
MSWordDocWord.Document.89q