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["Solution for Exam 15th of December 2014, problem 3 & 4"]
[]
[]
["Parameter","Value"]
["MTTF",{"$f":"8760*2","v":17520}]
["lambda",1.0000000000000001E-5]
["C_PM",15000]
["C_FT",3000]
["C_CR",30000]
["C_U",20000]
["C_Trip",50000]
["C_H",10000000]
["MDT",8]
["tau_PM",5000.2146388985257]
["tau_FT",{"$f":"8760/2","v":4380},{"$f":"8760/2","v":4380}]
["lambda_E",{"$f":"0.71*tau_PM^2/MTTF^3","v":3.3009073726794751E-6},{"$f":"ShowFormula(B16)","v":"=0.71*tau_PM^2/MTTF^3"}]
["PFD",{"$f":"lambda*tau_FT/2","v":2.1900000000000003E-2},{"$f":"ShowFormula(B17)","v":"=lambda*tau_FT/2"}]
["Cost per hour",{"$f":"C_PM/tau_PM+C_FT/tau_FT+lambda_E*(C_CR+(1-PFD)*(C_Trip+C_U*MDT)+PFD*C_H)","v":5.184738340091271},"=C_PM/tau_PM+C_FT/tau_FT+lambda_E*(C_CR+(1-PFD)*(C_Trip+C_U*MDT)+PFD*C_H)"]
["Cost per year",{"$f":"Cost_per_hour*8760","v":45418.307859199536},"=Cost_per_hour*8760"]
[]
["C_I",{"$f":"1000","v":1000},null,null,null,"t","Q0(t)"]
["f_P",{"$f":"1/(1.5*8760)","v":7.6103500761035014E-5},null,null,null,500,{"$f":"Q0(F22,E_PF,SD_PF,q)","v":2.5553710293024778E-4}]
["E_PF",{"$f":"8760/2","v":4380},null,null,null,{"$f":"F22+500","v":1000},{"$f":"Q0(F23,E_PF,SD_PF,q)","v":6.771991029381752E-3}]
["SD_PF",{"$f":"E_PF/3","v":1460},null,null,null,{"$f":"F23+500","v":1500},{"$f":"Q0(F24,E_PF,SD_PF,q)","v":2.8000665828585625E-2}]
["q",0.2,null,null,null,2000,6.1974614858627319E-2]
["tau_I",1019.7786949277338,null,null,null,2500,0.10271470248699188]
["Cost per hour I",{"$f":"C_I/tau_I+C_FT/tau_FT+f_P*Q0(tau_I,E_PF,SD_PF,q)*(C_CR+(1-PFD)*(C_Trip+C_U*MDT)+PFD*C_H) + f_P*C_PM","v":3.0598698207518069},null,null,null,3000,0.14667235314846039]
[null,null,null,null,null,3500,0.19035673141479492]
[null,null,null,null,null,4000,0.23391373455524445]
[]
["Solution"]
[]
["3a)"]
["C(tau_PM,tau_FT)",{"$f":"ShowFormula(Cost_per_hour)","v":"=C_PM/tau_PM+C_FT/tau_FT+lambda_E*(C_CR+(1-PFD)*(C_Trip+C_U*MDT)+PFD*C_H)"}]
[]
["where","lambda_E",{"$f":"ShowFormula(B16)","v":"=0.71*tau_PM^2/MTTF^3"}]
[null,"PFD",{"$f":"ShowFormula(B17)","v":"=lambda*tau_FT/2"}]
[]
["3b)"]
["tau_pm_optim",{"$f":"MTTF*(C_PM/(2*0.71*(C_CR+(1-PFD)*(C_Trip+C_U*MDT)+PFD*C_H)))^(1/3)","v":5000.2146389447398},{"$f":"ShowFormula(B40)","v":"=MTTF*(C_PM/(2*0.71*(C_CR+(1-PFD)*(C_Trip+C_U*MDT)+PFD*C_H)))^(1/3)"}]
[]
[null,null,{"$f":"Cost_per_hour","v":5.184738340091271}]
[null,3500,5.7055511449151153]
[null,{"$f":"B43+500","v":4000},5.3948078854308852]
[null,{"$f":"B44+500","v":4500},5.2331083818249482]
[null,5000,5.1847383483830187]
[null,5500,5.2269705123778234]
[null,6000,5.3446533586578475]
[null,6500,5.527297376733582]
[]
["tau_ft_optim",{"$f":"SQRT(2*C_FT/(lambda*lambda_E*C_H))","v":4263.4282282624417},{"$f":"ShowFormula(B51)","v":"=SQRT(2*C_FT/(lambda*lambda_E*C_H))"}]
[]
[null,"where we have ignored the term (1-PFD)*(C_Trip+C_U*MDT) in the cost function. With this term the interval is slightly higher"]
[]
["Problem 4a"]
["C(tau_I,tau_FT)",{"$f":"ShowFormula(Cost_per_hour_I)","v":"=C_I/tau_I+C_FT/tau_FT+f_P*Q0(tau_I,E_PF,SD_PF,q)*(C_CR+(1-PFD)*(C_Trip+C_U*MDT)+PFD*C_H) + f_P*C_PM"}]
[]
[null,null,{"$f":"Cost_per_hour_I","v":3.0598698207518069}]
[null,500,3.8353208763400772]
["Minimum",{"$f":"B59+500","v":1000},3.0606696724309055]
[null,{"$f":"B60+500","v":1500},3.4614559020681233]
[null,2000,4.4696595864821242]
[null,2500,5.7785132058441091]
[null,3000,7.2319683366068155]
[null,3500,8.6950209152130871]
[null,4000,10.165573431935893]
[]
[]
["It pays off!"]