{"text_format":"1","workbook":"xlsx","n_sheets":11,"sheets":["RunSimul","MCS","SSP","PERT","HelpFunc","CellNames","Info","3.3 syntax","eMax","3.7 Plot","PDFPlot"],"not_rendered":{"charts":2,"images":4,"macros":1,"external_links":1,"defined_names":29,"comments":1,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"RunSimul","index":0,"n_rows":10,"n_cols":2,"rows_kept":10,"cut":false,"hidden":false,"merged":[]}
["pRisk"]
[]
["Parameter","Value"]
["Number of simulations",3000]
["Cell to analyse",{"$f":"endOfProject","v":11.713394071148777}]
["Plot","cdf"]
["Result: Mean",10.793230151494344]
["Result: SD",0.6334265785801646]
["Result: Min",8.7961349487304688]
["Result: Max",12.966360092163086]

{"sheet":"MCS","index":1,"n_rows":69,"n_cols":11,"rows_kept":69,"cut":false,"hidden":false,"merged":[]}
["Activity","L","M","H","Start","Duration","End",null,"Formulas, Start","Formulas, Duration","Formulas, End"]
["Preparation",1,2,3,0,{"$f":"rndPERT(RAND(),B2,C2,D2)","v":2.2706393863558927},{"$f":"E2+F2","v":2.2706393863558927},null,{"$f":"showformula(E2)","v":"0"},{"$f":"showformula(F2)","v":"=rndPERT(RAND(),B2,C2,D2)"},{"$f":"showformula(G2)","v":"=E2+F2"}]
["Module 1",4,5,7,{"$f":"G2","v":2.2706393863558927},{"$f":"rndPERT(RAND(),B3,C3,D3)","v":5.8214220927474747},{"$f":"E3+F3","v":8.0920614791033678},null,{"$f":"showformula(E3)","v":"=G2"},{"$f":"showformula(F3)","v":"=rndPERT(RAND(),B3,C3,D3)"},"=E3+F3"]
["Module 2",3,5,6,{"$f":"G2","v":2.2706393863558927},5.3165073623848702,7.5871467487407624,null,"=G2","=rndPERT(RAND(),B4,C4,D4)","=E4+F4"]
["Assembling",1.8,2,2.5,{"$f":"MAX(G3,G4)","v":8.0920614791033678},2.0912590235112796,10.183320502614647,null,"=MAX(G3,G4)","=rndPERT(RAND(),B5,C5,D5)","=E5+F5"]
["Shipping offshore",0.1,0.2,0.3,{"$f":"G5","v":10.183320502614647},0.23540074322280949,10.418721245837457,null,"=G5","=rndPERT(RAND(),B6,C6,D6)","=E6+F6"]
["Installation offshore",1,1.2,1.5,{"$f":"G6","v":10.418721245837457},1.2946728253113196,11.713394071148777,null,"=G6","=rndPERT(RAND(),B7,C7,D7)","=E7+F7"]
[null,null,null,null,null,null,null,null,{"$f":"showformula(E8)","v":""}]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,""]
[null,null,null,null,null,null,null,null,{"$f":"showformula(E67)","v":""}]
[null,null,null,null,null,null,null,null,{"$f":"showformula(E68)","v":""}]
[null,null,null,null,null,null,null,null,{"$f":"showformula(E69)","v":""}]

{"sheet":"SSP","index":2,"n_rows":23,"n_cols":13,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
["Activity","L","M","H","mi","si2","EiF","ViF",null,"Formula EiF",null,null,"Formula ViF"]
["Preparation",1,2,3,{"$f":"(B2+4*C2+D2)/6","v":2},{"$f":"((E2-B2)*(D2-E2)/7)","v":0.14285714285714285},{"$f":"0+E2","v":2},{"$f":"0+F2","v":0.14285714285714285},null,{"$f":"showformula(G2)","v":"=0+E2"},null,null,{"$f":"showformula(H2)","v":"=0+F2"}]
["Module 1",4,5,7,5.166666666666667,0.30555555555555564,{"$f":"G2+E3","v":7.166666666666667},{"$f":"H2+F3","v":0.44841269841269848},null,{"$f":"showformula(G3)","v":"=G2+E3"},null,null,{"$f":"showformula(H3)","v":"=H2+F3"}]
["Module 2",3,5,6,4.833333333333333,0.30555555555555564,{"$f":"G2+E4","v":6.833333333333333},{"$f":"H2+F4","v":0.44841269841269848},null,"=G2+E4",null,null,{"$f":"showformula(H4)","v":"=H2+F4"}]
["V",null,null,null,null,null,{"$f":"eMax(G3,H3-H2,G4,H4-H2)","v":7.3397946357727051},{"$f":"varMax(G3,H3-H2,G4,H4-H2)+H2","v":0.36072608189923427},null,"=eMax(G3,H3-H2,G4,H4-H2)",null,null,{"$f":"showformula(H5)","v":"=varMax(G3,H3-H2,G4,H4-H2)+H2"}]
["Assembling",1.8,2,2.5,2.0500000000000003,1.6071428571428577E-2,{"$f":"G5+E6","v":9.3897946357727058},{"$f":"H5+F6","v":0.37679751047066284},null,"=G5+E6",null,null,{"$f":"showformula(H6)","v":"=H5+F6"}]
["Shipping offshore",0.1,0.2,0.3,0.19999999999999998,1.4285714285714284E-3,{"$f":"G6+E7","v":9.5897946357727051},0.37822608189923429,null,"=G6+E7",null,null,{"$f":"showformula(H7)","v":"=H6+F7"}]
["Installation offshore",1,1.2,1.5,1.2166666666666666,8.7698412698412696E-3,10.806461302439372,0.38699592316907555,null,"=G7+E8",null,null,{"$f":"showformula(H8)","v":"=H7+F8"}]
[]
[null,null,null,null,null,null,"Quantity","Value",null,"Formula"]
[null,null,null,null,null,null,"E(Final)",{"$f":"G8","v":10.806461302439372},null,{"$f":"showformula(H11)","v":"=G8"}]
[null,null,null,null,null,null,"SD(Final)",{"$f":"SQRT(H8)","v":0.62208996388711779},null,"=SQRT(H8)"]
[null,null,null,null,null,null,"Pr(T>11)",{"$f":"1-cdfNormal(11,E_SSP,SD_SSP)","v":0.37785845994949341},null,"=1-cdfNormal(11,E_SSP,SD_SSP)"]
[null,null,null,null,null,null,"E(# months delayed)",{"$f":"numInt(\"(x-11)*pdfnormal(x,E_SSP,SD_SSP)\",11,E_SSP+5*SD_SSP)","v":0.16332292556762695},null,"=numInt(\"(x-11)*pdfnormal(x,E_SSP,SD_SSP)\",11,E_SSP+5*SD_SSP)"]
[null,null,null,null,null,null,"Backorder function, B(r)",{"$f":"b(11,E_SSP,SD_SSP)","v":0.16332325296846795},null,"=b(11,E_SSP,SD_SSP)"]
[]
[]
[]
[]
[null,null,null,null,"Note: "]
[null,null,null,null,"Branching point is given in row 2, and we need H2 for accumulated variance at the branching point"]
[null,null,null,null,"End of upper branch is given in row 3, and we need G3 for accumulated expected values, and H3 for accumulated variance"]
[null,null,null,null,"End of lower branch is given in row 4, and we need G4 for accumulated expected values, and H4 for accumulated variance"]

{"sheet":"PERT","index":3,"n_rows":14,"n_cols":10,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
["Activity","L","M","H","mi","si2","In crit. Path","E","V"]
[null,null,null,null,{"$f":"(B2+4*C2+D2)/6","v":0},{"$f":"((E2-B2)*(D2-E2)/7)","v":0},null,{"$f":"E2*G2","v":0},{"$f":"F2*G2","v":0}]
[null,null,null,null,{"$f":"(B3+4*C3+D3)/6","v":0},{"$f":"((E3-B3)*(D3-E3)/7)","v":0},null,0,{"$f":"F3*G3","v":0}]
[null,null,null,null,0,0,null,0,0]
[null,null,null,null,0,0,null,0,0]
[null,null,null,null,0,0,null,0,0]
[null,null,null,null,0,0,null,0,0]
[null,null,null,null,0,0,null,0,0]
[null,null,null,null,0,0,null,0,0]
[null,null,null,null,0,0,null,0,0]
[]
[]
[]
[null,null,null,null,null,null,"Sum",{"$f":"SUM(H2:H13)","v":0},{"$f":"SUM(I2:I13)","v":0},{"$f":"SQRT(I14)","v":0}]

{"sheet":"HelpFunc","index":4,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"CellNames","index":5,"n_rows":19,"n_cols":4,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
["Parameter","Value"]
["mu",10]
["sigma",2]
["L",6]
["M",9.3000000000000007]
["H",17]
["DD",12]
[]
[]
["Examples of use"]
["Parameter","Value","Formula","Comment"]
["ePert",{"$f":"ePERT(L,M,H)","v":10.033333778381348},{"$f":"showformula(B12)","v":"=ePERT(L,M,H)"}]
["ePert",{"$f":"ePERT(B4,B5,B6)","v":10.033333778381348},{"$f":"showformula(B13)","v":"=ePERT(B4,B5,B6)"},"We may still refer to the origianal cell names, i.e., B4, B5 and B6"]
["varPert",{"$f":"varPERT(L,M,H)","v":4.014127254486084},{"$f":"showformula(B14)","v":"=varPERT(L,M,H)"}]
["Pr(T>DD)",{"$f":"1-cdfNormal(DD,mu,sigma)","v":0.15865528583526611},{"$f":"showformula(B15)","v":"=1-cdfNormal(DD,mu,sigma)"},"Note, the result depends on the distribution, i.e., Normal and PERT give different results"]
["Pr(T>DD)",{"$f":"1-_xlfn.NORM.DIST(DD,mu,sigma,TRUE)","v":0.15865525393145696},{"$f":"showformula(B16)","v":"=1-NORM.DIST(DD,mu,sigma,TRUE)"},"Note, that Excel has it's own buildt in function for the normal distribution, different arguments!"]
["Pr(T>DD)",{"$f":"1-cdfPERT(DD,L,M,H)","v":0.1789758085088764},{"$f":"showformula(B17)","v":"=1-cdfPERT(DD,L,M,H)"}]
["E(#days>DD)",{"$f":"numInt(\"(x-DD)*pdfNormal(x,mu,sigma)\",DD,mu+5*sigma)","v":0.16662852466106415},{"$f":"showformula(B18)","v":"=numInt(\"(x-DD)*pdfNormal(x,mu,sigma)\",DD,mu+5*sigma)"},"The syntax for the \"integrand\" is always given in \"English\". List seperator is following settings on your PC/Mac"]
["E(#days>DD)",{"$f":"b(DD,mu,sigma)","v":0.1666309411753728},{"$f":"showformula(B19)","v":"=b(DD,mu,sigma)"},"Backorder function is easier…."]

{"sheet":"Info","index":6,"n_rows":8,"n_cols":3,"rows_kept":8,"cut":false,"hidden":false,"merged":[]}
["Link to this file",null,"https://folk.ntnu.no/jvatn/eLearning/commonFiles/pRiskDemo.xlsm"]
["Link to eLearning",null,"https://folk.ntnu.no/jvatn/eLearning/vba/"]
["Link to pRisk",null,"https://folk.ntnu.no/jvatn/eLearning/commonFiles/pRiskEmpty.xlsm"]
[]
[]
["Note 1: Case-sensitive links!"]
["Note 2: You need to download pRisk in order to use the pRisk functions shown in the examples"]
["Note 3: You need to enable macros to use the pRisk functions"]

{"sheet":"3.3 syntax","index":7,"n_rows":16,"n_cols":6,"rows_kept":16,"cut":false,"hidden":false,"merged":[[6,0,13,2]]}
["Quantity","Value","Formula","Comment"]
["PDF-test",{"$f":"numInt(\"PDFtriangular(x,200,240,350)\",200,350)","v":0.99999183416366577},{"$f":"showformula(B2)","v":"=numInt(\"PDFtriangular(x,200,240,350)\",200,350)"},"Should be 1"]
["Expectation",{"$f":"numInt(\"x*PDFtriangular(x,200,240,350)\",200,350)","v":263.33126831054688},{"$f":"showformula(B3)","v":"=numInt(\"x*PDFtriangular(x,200,240,350)\",200,350)"},"Should be:",{"$f":"(200+240+350)/3","v":263.33333333333331},{"$f":"showformula(E3)","v":"=(200+240+350)/3"}]
["Expected penalty",{"$f":"numInt(\"100*(x-220)*PDFtriangular(x,200,240,350)\",220,350)","v":4438.3837890625},{"$f":"showformula(B4)","v":"=numInt(\"100*(x-220)*PDFtriangular(x,200,240,350)\",220,350)"}]
[]
[]
["Note the use of \"comma\", \"period\" and \"semicolon\":\nIn English a period is used for separating the integer and decimal part of a number, e.g.; p = 3.14. In Norwegian, German and other languages a comma is used, i.e., p = 3,14. \nIn English the comma is used (as default) to separate arguments in functions, for example MAX(4,5) = 5. In Norway and other countries the default is to use a semicolon to separate arguments, for example STØRST(4;5) = 5. It is possible to configure the PC (or Mac?) to use the English convention. \nNote that the integrand is a text-string sent to the VBA programming language, which only accepts standard English notation."]
[]
[]
[]
[]
[]
[]
[]
[]
["Example",{"$f":"numInt(\"min(x,0.5)\",0,1.5)","v":0.625},{"$f":"showformula(B16)","v":"=numInt(\"min(x,0.5)\",0,1.5)"},"Enligsh sytax in the integrand, i.e. the \"string\" "]

{"sheet":"eMax","index":8,"n_rows":17,"n_cols":3,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
["Parameter","Value"]
["mu1",10]
["sigma1",2]
["mu2",11]
["sigma2",2]
[]
[]
[]
["Parameter","Value","Formula"]
["eMax",{"$f":"eMax(mu_1,sigma_1^2,mu_2,sigma_2^2)","v":11.69817066192627},{"$f":"showformula(B10)","v":"=eMax(mu_1,sigma_1^2,mu_2,sigma_2^2)"}]
["varMax",{"$f":"varMax(mu_1,sigma_1^2,mu_2,sigma_2^2)","v":2.8143420219421391},{"$f":"showformula(B11)","v":"=varMax(mu_1,sigma_1^2,mu_2,sigma_2^2)"}]
[]
[]
[]
["Note, the \"numInt\" function cannot \"resolve\" too many cell-names, but original cellnames are OK"]
["Parameter","Value","Formula"]
["eMax",{"$f":"numInt(\"x*(pdfNormal(x,B2,B3)*cdfNormal(x,B4,B5)+cdfNormal(x,B2,B3)*pdfNormal(x,B4,B5))\",0,20)","v":11.698101043701172},{"$f":"showformula(B17)","v":"=numInt(\"x*(pdfNormal(x,B2,B3)*cdfNormal(x,B4,B5)+cdfNormal(x,B2,B3)*pdfNormal(x,B4,B5))\",0,20)"}]

{"sheet":"3.7 Plot","index":9,"n_rows":22,"n_cols":2,"rows_kept":22,"cut":false,"hidden":false,"merged":[[21,0,28,6]]}
["x","PDF"]
[0.5,{"$f":"0.353*PDFPert(A2,2,2.5,3.5)+(1-0.353)*PDFPert(A2,0.5,1,2.5)","v":0}]
[{"$f":"A2+0.2","v":0.7},{"$f":"0.353*PDFPert(A3,2,2.5,3.5)+(1-0.353)*PDFPert(A3,0.5,1,2.5)","v":0.47166286771104304}]
[{"$f":"A3+0.2","v":0.89999999999999991},0.66252795872622283]
[1.0999999999999999,0.66576304644182926]
[1.2999999999999998,0.55900813754745982]
[1.4999999999999998,0.40437511448751651]
[1.6999999999999997,0.2484480598051752]
[1.8999999999999997,0.12228307181842028]
[2.0999999999999996,0.17435461953297846]
[2.2999999999999998,0.38716515015902475]
[2.5,0.46340784516826372]
[2.7,0.40028948896854882]
[2.9000000000000004,0.2598544969297692]
[3.1000000000000005,0.11517395922253791]
[3.3000000000000007,2.2664290631736372E-2]
[3.5000000000000009,0]
[]
[]
[]
["From Problem 3.6"]
["In the unconditional distribution we find E(T) = 1.6667. Using eq. 3.18 we find that when we introduce the event B we have E(T)  = Pr(B)*2.5833+(1-Pr(B))*1.1667. Now, solwing E(T) = 1.6667 with respect to Pr(B) gives Pr(B) = 0.353."]

{"sheet":"PDFPlot","index":10,"n_rows":104,"n_cols":2,"rows_kept":104,"cut":false,"hidden":true,"merged":[]}
["x","Cumulative distribution function"]
[8.3563833236694336,0]
[8.3563833236694336,0]
[8.3988685607910156,0]
[8.4413537979125977,0]
[8.4838390350341797,0]
[8.5263242721557617,0]
[8.5688104629516602,0]
[8.6112957000732422,0]
[8.6537809371948242,0]
[8.6962661743164063,0]
[8.7387514114379883,0]
[8.7812366485595703,3.3333332976326346E-4]
[8.8237218856811523,3.3333332976326346E-4]
[8.8662071228027344,3.3333332976326346E-4]
[8.9086933135986328,3.3333332976326346E-4]
[8.9511785507202148,9.9999993108212948E-4]
[8.9936637878417969,1.3333333190530539E-3]
[9.0361490249633789,1.3333333190530539E-3]
[9.0786342620849609,2.3333332501351833E-3]
[9.121119499206543,2.3333332501351833E-3]
[9.163604736328125,2.6666666381061077E-3]
[9.206089973449707,3.3333334140479565E-3]
[9.2485752105712891,5.3333332762122154E-3]
[9.2910614013671875,6.3333334401249886E-3]
[9.3335466384887695,7.3333336040377617E-3]
[9.3760318756103516,8.6666671559214592E-3]
[9.4185171127319336,1.0333334095776081E-2]
[9.4610023498535156,1.4000001363456249E-2]
[9.5034875869750977,1.5666667371988297E-2]
[9.5459728240966797,2.1333334967494011E-2]
[9.5884580612182617,2.9000002890825272E-2]
[9.6309432983398438,3.4666668623685837E-2]
[9.6734294891357422,4.1666667908430099E-2]
[9.7159147262573242,5.000000074505806E-2]
[9.7583999633789063,6.1000000685453415E-2]
[9.8008852005004883,6.8999998271465302E-2]
[9.8433704376220703,7.9333335161209106E-2]
[9.8858556747436523,8.5666671395301819E-2]
[9.9283409118652344,9.3333341181278229E-2]
[9.9708261489868164,0.1066666767001152]
[10.013312339782715,0.11800000816583633]
[10.055797576904297,0.13433334231376648]
[10.098282814025879,0.14766667783260345]
[10.140768051147461,0.164000004529953]
[10.183253288269043,0.18133333325386047]
[10.225738525390625,0.20000000298023224]
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