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{"sheet":"Sheet1","index":0,"n_rows":27,"n_cols":9,"rows_kept":27,"cut":false,"hidden":false,"merged":[]}
["Parameter","Value","Comment/Formula"]
["Prior",null,null,null,null,null,"lambda","pdf_prior","pdf_posterior"]
["lambda_low",100,null,null,null,null,0,{"$f":"_xlfn.GAMMA.DIST(G3,U_2_prior,1/U_1_prior,FALSE)","v":0},{"$f":"_xlfn.GAMMA.DIST(G3,U_2_posterior,1/U_1_posterior,FALSE)","v":0}]
["lambda_high",1000,null,null,null,null,{"$f":"G3+lambda_high*0.07","v":70},{"$f":"_xlfn.GAMMA.DIST(G4,U_2_prior,1/U_1_prior,FALSE)","v":7.2829431859454603E-4},{"$f":"_xlfn.GAMMA.DIST(G4,U_2_posterior,1/U_1_posterior,FALSE)","v":8.1884941924627211E-6}]
["conf_level",0.9,"Conf. level for given interval",null,null,null,{"$f":"G4+lambda_high*0.07","v":140},{"$f":"_xlfn.GAMMA.DIST(G5,U_2_prior,1/U_1_prior,FALSE)","v":1.3479007904577906E-3},{"$f":"_xlfn.GAMMA.DIST(G5,U_2_posterior,1/U_1_posterior,FALSE)","v":1.5205624999578636E-4}]
["lambda_mean",{"$f":"SQRT(lambda_low*lambda_high)","v":316.22776601683796},"First approx",null,null,null,{"$f":"G5+lambda_high*0.07","v":210},{"$f":"_xlfn.GAMMA.DIST(G6,U_2_prior,1/U_1_prior,FALSE)","v":1.6498186892503377E-3},{"$f":"_xlfn.GAMMA.DIST(G6,U_2_posterior,1/U_1_posterior,FALSE)","v":5.9084946244783464E-4}]
["lambda_SD",{"$f":"(lambda_high-lambda_low)/4","v":225},"First approx",null,null,null,{"$f":"G6+lambda_high*0.07","v":280},{"$f":"_xlfn.GAMMA.DIST(G7,U_2_prior,1/U_1_prior,FALSE)","v":1.7048795376464771E-3},{"$f":"_xlfn.GAMMA.DIST(G7,U_2_posterior,1/U_1_posterior,FALSE)","v":1.2100923411649692E-3}]
["U_1",{"$f":"lambda_mean/lambda_SD^2","v":6.2464743904560582E-3},"First approx",null,null,null,{"$f":"G7+lambda_high*0.07","v":350},{"$f":"_xlfn.GAMMA.DIST(G8,U_2_prior,1/U_1_prior,FALSE)","v":1.6057054503231976E-3},{"$f":"_xlfn.GAMMA.DIST(G8,U_2_posterior,1/U_1_posterior,FALSE)","v":1.7448575993961625E-3}]
["U_2",{"$f":"U_1*lambda_mean","v":1.975308641975309},"First approx",null,null,null,{"$f":"G8+lambda_high*0.07","v":420},{"$f":"_xlfn.GAMMA.DIST(G9,U_2_prior,1/U_1_prior,FALSE)","v":1.4261222433103978E-3},{"$f":"_xlfn.GAMMA.DIST(G9,U_2_posterior,1/U_1_posterior,FALSE)","v":2.0151393672905686E-3}]
["U_1_adjusted",5.4378913895222689E-3,"Obtain by solver",null,null,null,{"$f":"G9+lambda_high*0.07","v":490},{"$f":"_xlfn.GAMMA.DIST(G10,U_2_prior,1/U_1_prior,FALSE)","v":1.2163630280965811E-3},{"$f":"_xlfn.GAMMA.DIST(G10,U_2_posterior,1/U_1_posterior,FALSE)","v":1.9967695495447298E-3}]
["U_2_adjusted",2.4372861437055833,"Obtain by solver",null,null,null,{"$f":"G10+lambda_high*0.07","v":560},{"$f":"_xlfn.GAMMA.DIST(G11,U_2_prior,1/U_1_prior,FALSE)","v":1.0071612247408326E-3},{"$f":"_xlfn.GAMMA.DIST(G11,U_2_posterior,1/U_1_posterior,FALSE)","v":1.7687268188685018E-3}]
["CDF_low",{"$f":"_xlfn.GAMMA.DIST(lambda_low,U_2_prior,1/U_1_prior,TRUE)","v":4.9999238918431319E-2},{"$f":"_xlfn.FORMULATEXT(B12)","v":"=GAMMA.DIST(lambda_low,U_2_prior,1/U_1_prior,TRUE)"},null,null,null,{"$f":"G11+lambda_high*0.07","v":630},{"$f":"_xlfn.GAMMA.DIST(G12,U_2_prior,1/U_1_prior,FALSE)","v":8.1527584146424005E-4},{"$f":"_xlfn.GAMMA.DIST(G12,U_2_posterior,1/U_1_posterior,FALSE)","v":1.4381549109823979E-3}]
["CDF_high",{"$f":"_xlfn.GAMMA.DIST(lambda_high,U_2_prior,1/U_1_prior,TRUE)","v":0.9499999439918676},{"$f":"_xlfn.FORMULATEXT(B13)","v":"=GAMMA.DIST(lambda_high,U_2_prior,1/U_1_prior,TRUE)"},null,null,null,{"$f":"G12+lambda_high*0.07","v":700},{"$f":"_xlfn.GAMMA.DIST(G13,U_2_prior,1/U_1_prior,FALSE)","v":6.4827003079709594E-4},{"$f":"_xlfn.GAMMA.DIST(G13,U_2_posterior,1/U_1_posterior,FALSE)","v":1.092990140026564E-3}]
["low_0",{"$f":"CDF_low-(1-conf_level)/2","v":-7.6108156867038534E-7},"=CDF_low-(1-conf_level)/2",null,null,null,{"$f":"G13+lambda_high*0.07","v":770},{"$f":"_xlfn.GAMMA.DIST(G14,U_2_prior,1/U_1_prior,FALSE)","v":5.0808203830400914E-4},{"$f":"_xlfn.GAMMA.DIST(G14,U_2_posterior,1/U_1_posterior,FALSE)","v":7.8649166368665777E-4}]
["high_1",{"$f":"CDF_high+(1-conf_level)/2","v":0.99999994399186765},"=CDF_high+(1-conf_level)/2",null,null,null,{"$f":"G14+lambda_high*0.07","v":840},{"$f":"_xlfn.GAMMA.DIST(G15,U_2_prior,1/U_1_prior,FALSE)","v":3.9348808052733312E-4},{"$f":"_xlfn.GAMMA.DIST(G15,U_2_posterior,1/U_1_posterior,FALSE)","v":5.4097269904750014E-4}]
["prior_mean",{"$f":"U_2_prior/U_1_prior","v":448.20427057475757},"=U_2_prior/U_1_prior",null,null,null,{"$f":"G15+lambda_high*0.07","v":910},{"$f":"_xlfn.GAMMA.DIST(G16,U_2_prior,1/U_1_prior,FALSE)","v":3.0170286848733515E-4},{"$f":"_xlfn.GAMMA.DIST(G16,U_2_posterior,1/U_1_posterior,FALSE)","v":3.5826210489944252E-4}]
["prior_SD",{"$f":"SQRT(U_2_prior)/U_1_prior","v":287.09308396231967},"=SQRT(U_2_prior)/U_1_prior",null,null,null,{"$f":"G16+lambda_high*0.07","v":980},{"$f":"_xlfn.GAMMA.DIST(G17,U_2_prior,1/U_1_prior,FALSE)","v":2.2936270567037873E-4},{"$f":"_xlfn.GAMMA.DIST(G17,U_2_posterior,1/U_1_posterior,FALSE)","v":2.2972709048850673E-4}]
["lambda_prior_70",{"$f":"U_2_prior/U_1_prior+0.3*SQRT(U_2_prior)/U_1_prior","v":534.33219576345346},"=U_2_prior/U_1_prior+0.3*SQRT(U_2_prior)/U_1_prior",null,null,null,{"$f":"G17+lambda_high*0.07","v":1050},{"$f":"_xlfn.GAMMA.DIST(G18,U_2_prior,1/U_1_prior,FALSE)","v":1.730905242234055E-4},{"$f":"_xlfn.GAMMA.DIST(G18,U_2_posterior,1/U_1_posterior,FALSE)","v":1.4326656150658371E-4}]
["Data/vendor",null,null,null,null,null,{"$f":"G18+lambda_high*0.07","v":1120},{"$f":"_xlfn.GAMMA.DIST(G19,U_2_prior,1/U_1_prior,FALSE)","v":1.2979063392852303E-4},{"$f":"_xlfn.GAMMA.DIST(G19,U_2_posterior,1/U_1_posterior,FALSE)","v":8.7208543698306397E-5}]
["lambda_new",600,"Failure rate estimate from data or vendor",null,null,null,{"$f":"G19+lambda_high*0.07","v":1190},{"$f":"_xlfn.GAMMA.DIST(G20,U_2_prior,1/U_1_prior,FALSE)","v":9.6776594780446503E-5},{"$f":"_xlfn.GAMMA.DIST(G20,U_2_posterior,1/U_1_posterior,FALSE)","v":5.1967402995275197E-5}]
["n_proxy",4,"Number of \"failures\" behind the estimate",null,null,null,{"$f":"G20+lambda_high*0.07","v":1260},{"$f":"_xlfn.GAMMA.DIST(G21,U_2_prior,1/U_1_prior,FALSE)","v":7.1801529246873566E-5},{"$f":"_xlfn.GAMMA.DIST(G21,U_2_posterior,1/U_1_posterior,FALSE)","v":3.0389107679123586E-5}]
["Posterior"]
["U_1_posterior",{"$f":"U_1_prior+(n_proxy/lambda_new)","v":1.2104558056188937E-2},{"$f":"_xlfn.FORMULATEXT(B23)","v":"=U_1_prior+(n_proxy/lambda_new)"}]
["U_2_posterior",{"$f":"U_2_prior+n_proxy","v":6.4372861437055828},"=U_2_prior+n_proxy"]
["posterior_mean",{"$f":"U_2_posterior/U_1_posterior","v":531.80678830436636},"=U_2_posterior/U_1_posterior"]
["lambda_posterior_70",{"$f":"U_2_posterior/U_1_posterior+0.3*SQRT(U_2_posterior)/U_1_posterior","v":594.68840865031939},"=U_2_posterior/U_1_posterior+0.3*SQRT(U_2_posterior)/U_1_posterior"]
["Pr(lambda<lambda70)",{"$f":"_xlfn.GAMMA.DIST(lambda_70,U_2_posterior,1/U_1_posterior,TRUE)","v":0.66258773077936683},"=GAMMA.DIST(lambda_70,U_2_posterior,1/U_1_posterior,TRUE)"]