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[]
[]
[]
[]
["Created on Thu Oct 04 2012"]
[]
["author: Janwillem van Dijk"]
["email: jwe.van.dijk@xs4all.nl"]
[null,null,null,null,null,null,null,null,1,"Public Sub QuickSort(vArray As Variant, inLow As Integer, inHigh As Integer)"]
["Calculate uncertainty in dose measurement using statistical sampling,",null,null,null,null,null,null,null,{"$f":"1+I9","v":2}]
["the Monte Carlo method (JCGM 101:2008)",null,null,null,null,null,null,null,{"$f":"1+I10","v":3},"  Dim vPivot As Variant"]
[null,null,null,null,null,null,null,null,4,"  Dim vSwap As Variant"]
["The dose measurement is implemented as a two stage measurement, see e.g.",null,null,null,null,null,null,null,5,"  Dim lLow As Integer"]
["Introduction to the GUM JCGM 101:2009, section 6.8:",null,null,null,null,null,null,null,6,"  Dim lHigh As Integer"]
["    a) The detector in the dosemeter is the primary measurement device",null,null,null,null,null,null,null,7]
["    that will generate a signal x_det wen read",null,null,null,null,null,null,null,8,"  lLow = inLow"]
["    b) The reader that will generate counts dependant on x_det, f_Rd and",null,null,null,null,null,null,null,9,"  lHigh = inHigh"]
["    the blank signal z.",null,null,null,null,null,null,null,10]
["Steps:",null,null,null,null,null,null,null,11,"  vPivot = vArray((inLow + inHigh) / 2)"]
["    1) Define input quatities and uncertainties therein.",null,null,null,null,null,null,null,12]
["    2) Calculate M random samples of the signal a detector would generate",null,null,null,null,null,null,null,13,"  Do While lLow <= lHigh"]
["        given a set op input quantities and the uncertainties therein.",null,null,null,null,null,null,null,14]
["    3) Calculate the dose using the signal samples and expectation values",null,null,null,null,null,null,null,15,"     Do While vArray(lLow) < vPivot And lLow < inHigh"]
["        for the other input quantities.",null,null,null,null,null,null,null,16,"        lLow = lLow + 1"]
["    4) Perform statistical analysis.",null,null,null,null,null,null,null,17,"     Loop"]
[null,null,null,null,null,null,null,null,18]
["The sheet needs the macro subroutine SortArray to sort the measurand",null,null,null,null,null,null,null,19,"     Do While (vPivot < vArray(lHigh)) And (lHigh > inLow)"]
["Apart from sorting this macro also calculates the statistics for improved performance",null,null,null,null,null,null,null,20,"        lHigh = lHigh - 1"]
[null,null,null,null,null,null,null,null,21,"     Loop"]
[null,null,null,null,null,null,null,null,22]
[null,null,null,null,null,null,null,null,23,"     If (lLow <= lHigh) Then"]
[null,null,null,null,null,null,null,null,24,"        vSwap = vArray(lLow)"]
[null,null,null,null,null,null,null,null,25,"        vArray(lLow) = vArray(lHigh)"]
[null,null,null,null,null,null,null,null,26,"        vArray(lHigh) = vSwap"]
[null,null,null,null,null,null,null,null,27,"        lLow = lLow + 1"]
[null,null,null,null,null,null,null,null,28,"        lHigh = lHigh - 1"]
[null,null,null,null,null,null,null,null,29,"     End If"]
[null,null,null,null,null,null,null,null,30]
[null,null,null,null,null,null,null,null,31,"  Loop"]
[null,null,null,null,null,null,null,null,32]
[null,null,null,null,null,null,null,null,33,"  If (inLow < lHigh) Then QuickSort vArray, inLow, lHigh"]
[null,null,null,null,null,null,null,null,34,"  If (lLow < inHigh) Then QuickSort vArray, lLow, inHigh"]
[null,null,null,null,null,null,null,null,35]
[null,null,null,null,null,null,null,null,36,"End Sub"]
[null,null,null,null,null,null,null,null,37]
[null,null,null,null,null,null,null,null,38,"Function SortArray(a As Variant) As Variant"]
[null,null,null,null,null,null,null,null,39,"Dim n0 As Integer, n As Integer"]
[null,null,null,null,null,null,null,null,40,"Dim i As Integer"]
[null,null,null,null,null,null,null,null,41,"Dim ai As Double"]
[null,null,null,null,null,null,null,null,42,"Dim k As Integer, m As Integer"]
[null,null,null,null,null,null,null,null,43,"Dim sum As Double, ssum As Double"]
[null,null,null,null,null,null,null,null,44,"Dim sumB As Double, ssumB As Double"]
[null,null,null,null,null,null,null,null,45,"Dim avg As Double, stdev As Double"]
[null,null,null,null,null,null,null,null,46,"Dim avgB As Double, stdevB As Double"]
[null,null,null,null,null,null,null,null,47]
[null,null,null,null,null,null,null,null,48,"If TypeName(a) = \"Range\" Then a = a.Value2"]
[null,null,null,null,null,null,null,null,49,"n0 = LBound(a)"]
[null,null,null,null,null,null,null,null,50,"n = UBound(a)"]
[null,null,null,null,null,null,null,null,51,"Dim b() As Variant"]
[null,null,null,null,null,null,null,null,52,"ReDim b(n0 To n + 8)"]
[null,null,null,null,null,null,null,null,53]
[null,null,null,null,null,null,null,null,54,"'8 elements space for statistics at the bottom"]
[null,null,null,null,null,null,null,null,55,"For i = n + 1 To n + 8"]
[null,null,null,null,null,null,null,null,56,"    b(i) = 1000000000#"]
[null,null,null,null,null,null,null,null,57,"Next i"]
[null,null,null,null,null,null,null,null,58,"    "]
[null,null,null,null,null,null,null,null,59,"k = 0"]
[null,null,null,null,null,null,null,null,60,"For i = n0 To n"]
[null,null,null,null,null,null,null,null,61,"    ai = a(i, 1)"]
[null,null,null,null,null,null,null,null,62,"    b(i) = ai"]
[null,null,null,null,null,null,null,null,63,"    If ai >= 0 Then"]
[null,null,null,null,null,null,null,null,64,"        sumB = sumB + ai"]
[null,null,null,null,null,null,null,null,65,"        ssumB = ssumB + ai * ai"]
[null,null,null,null,null,null,null,null,66,"        k = k + 1"]
[null,null,null,null,null,null,null,null,{"$f":"1+I74","v":67},"    Else"]
[null,null,null,null,null,null,null,null,68,"        sum = sum + ai"]
[null,null,null,null,null,null,null,null,69,"        ssum = ssum + ai * ai"]
[null,null,null,null,null,null,null,null,70,"    End If"]
[null,null,null,null,null,null,null,null,71,"Next i"]
[null,null,null,null,null,null,null,null,72,"sum = sum + sumB"]
[null,null,null,null,null,null,null,null,73,"ssum = ssum + ssumB"]
[null,null,null,null,null,null,null,null,74]
[null,null,null,null,null,null,null,null,75,"m = n - n0 + 1"]
[null,null,null,null,null,null,null,null,76,"avg = sum / m"]
[null,null,null,null,null,null,null,null,77,"avgB = sumB / k"]
[null,null,null,null,null,null,null,null,78,"stdev = Sqr((ssum - sum * sum / m) / (m - 1))"]
[null,null,null,null,null,null,null,null,79,"stdevB = Sqr((ssumB - sumB * sumB / k) / (k - 1))"]
[null,null,null,null,null,null,null,null,80]
[null,null,null,null,null,null,null,null,81,"Call QuickSort(b, n0, n)"]
[null,null,null,null,null,null,null,null,82]
[null,null,null,null,null,null,null,null,83,"'store statistics in 8 extra array elements"]
[null,null,null,null,null,null,null,null,84,"i = n0"]
[null,null,null,null,null,null,null,null,85,"Do While (b(i) < 0) And (i < n)"]
[null,null,null,null,null,null,null,null,86,"    i = i + 1"]
[null,null,null,null,null,null,null,null,87,"Loop"]
[null,null,null,null,null,null,null,null,88,"m = n - i + 1"]
[null,null,null,null,null,null,null,null,89,"b(n + 1) = avg"]
[null,null,null,null,null,null,null,null,90,"b(n + 2) = stdev"]
[null,null,null,null,null,null,null,null,91,"b(n + 3) = avgB"]
[null,null,null,null,null,null,null,null,92,"b(n + 4) = stdevB"]
[null,null,null,null,null,null,null,null,93,"'JCGM 101 7.7"]
[null,null,null,null,null,null,null,null,94,"b(n + 5) = b(Int(n * 0.025 + 0.5))"]
[null,null,null,null,null,null,null,null,95,"b(n + 6) = b(Int(n * 0.975 + 0.5))"]
[null,null,null,null,null,null,null,null,96,"b(n + 7) = b(i + Int(m * 0.025 + 0.5))"]
[null,null,null,null,null,null,null,null,97,"b(n + 8) = b(i + Int(m * 0.975 + 0.5))"]
[null,null,null,null,null,null,null,null,98]
[null,null,null,null,null,null,null,null,99,"SortArray = b"]
[null,null,null,null,null,null,null,null,100]
[null,null,null,null,null,null,null,null,101,"End Function"]

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["Monte Carlo uncertainty evaluation of TNO C-detector, LiF:Mg,Ti + 1mm Al"]
[null,null,null,null,null,null,null,null,"Bayesian"]
["Htrue",1000,"μSv",null,null,"Hmcm",{"$f":"K15","v":1001.8632888706891},"μSv",{"$f":"L15","v":1001.8632888706891},"μSv"]
["Hnat",100,"μSv",null,null,"stdev",{"$f":"K16","v":164.94103233088782},{"$f":"IF(B3>1,G4/G3,\"-\")","v":0.16463427112576517},{"$f":"L16","v":164.94103233088751},{"$f":"I4/I3","v":0.16463427112576487},null,null,null,null,null,{"$f":"\"u=\" & FIXED(I4,0)&\" uSv\"","v":"u=165 uSv"}]
[]
[null,null,null,null,null,null,"Low 95%",{"$f":"N15","v":689.52048646115247},{"$f":"O15","v":690.69935489807017},"μSv"]
["N",{"$f":"COUNT(A20:A32010)","v":10000},null,null,null,null,"High 95%",{"$f":"N16","v":1335.7718529968467},{"$f":"O16","v":1336.2755284813829},"μSv"]
[]
["fE,a","min",null,0.39274999999999999]
[null,"max",null,1.2569999999999999]
["uBg,rel",0.1,null,null,null,null,null,null,null,null,null,"Count",10000]
[null,null,null,null,null,null,null,null,null,null,null,"First >0",{"$f":"IF(L20<0,MATCH(0,L20:L10019),0)","v":0}]
[null,null,"Detector",null,null,null,"Reader",null,null,"Dose (μSv)"]
[null,"Hnat","fBg","fE,a","fDet","xblank","freader","x","ux,rel",null,"Hocc",null,null,"95% coverage"]
["mean",{"$f":"B4","v":100},1,1,1,200,50,"μSv",1,null,{"$f":"AVERAGE(K20:K10019)","v":1001.8632888706891},{"$f":"L10022","v":1001.8632888706891},"Low",{"$f":"L10024","v":689.52048646115247},{"$f":"L10026","v":690.69935489807017}]
["stdev",{"$f":"MAX(B11*B15,0.1)","v":10},0.05,{"$f":"(D10-D9)/6","v":0.14404166666666665},0.05,10,2.5,"μSv",0.02,null,{"$f":"STDEV(K20:K10019)","v":164.94103233088782},{"$f":"L10023","v":164.94103233088751},"High",{"$f":"L10025","v":1335.7718529968467},{"$f":"L10027","v":1336.2755284813829}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Bayesian"]
[null,"Natural","Bg resp,","Response","Detector","Blank","Sensitivity","Signal","Signal","Hgross","Hocc","Sorted",null,"Frequency","Frequency"]
[{"$f":"0","v":0},{"$f":"NORMINV(RAND(),B$15, B$16)","v":86.185167736831275},{"$f":"NORMINV(RAND(),C$15, C$16)","v":1.0313427475260533},1.2051314500538086,1.0600707460794461,{"$f":"NORMINV(RAND(),F$15, F$16)","v":202.39863124746324},44.615880883529002,{"$f":"$B$3*D20*E20*G20 + B20*C20*G20+F20","v":61166.030966888342},{"$f":"H20*NORMINV(RAND(),I$15, I$16)","v":58820.314408082631},{"$f":"(I20-$F$15)/($D$15*$E$15*$G$15)","v":1172.4062881616526},{"$f":"J20-$D$15*$B$15/$C$15","v":1072.4062881616526},{"$f":"TRANSPOSE(SORTARRAY(K20:K10019))","v":430.16147609230109},{"$f":"$K$15-4*$K$16","v":342.09915954713779},{"$f":"FREQUENCY(K20:K10019,M20:M39)","v":0},{"$f":"FREQUENCY(OFFSET(L20,M12,0,M11-M12,1),M20:M39)","v":0},{"$f":"_xlfn.NORM.DIST(M20,$B$3,$G$4,FALSE)*$B$7*($M$21-$M$20)","v":0.56002944703225266}]
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[5,72.619038953112465,1.1266553167762248,0.8785074063014584,1.0534961269545566,187.31955337735261,52.816480148261221,53390.45734172831,53534.557041403626,1066.6911408280725,966.69114082807255,504.31755677266517,671.98122420891355,130,130,220.88466628533018]
[6,88.704985939850815,0.99306098442255197,0.98163321714447926,1.0436575705829632,188.27700119366597,49.493383940545542,55253.5468801799,54855.863273581745,1093.1172654716349,993.11726547163494,505.85909263163546,737.95763714126872,328,328,451.74687615828958]
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[20,91.434598713704233,1.0135897762230404,0.99757367994301671,{"$f":"NORMINV(RAND(),E$15, E$16)","v":1.0680786684696786},206.20400149053705,47.467625375885135,55181.515121849887,56777.041515535304,1131.540830310706,1031.540830310706,567.07628860454804,null,3,3]
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