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["Parameter","Value"]
["MTTFA",8760]
["MTTFB",17520]
["a",3]
["CPM",3000]
["CPT",1000]
["CCM",10000]
["MDT",4]
["CU",15000]
["CTrip",100000]
["tA",2190]
["tB",8760]
[null,null,{"$f":"ShowFormula(B13)","v":""}]
["a) "]
[]
["PFDB",{"$f":"tauB/(2*MTTFB)","v":0.25},{"$f":"_xlfn.FORMULATEXT(B16)","v":"=tauB/(2*MTTFB)"}]
["CEP",{"$f":"PFDB*(CU*MDT+CTrip)","v":40000},{"$f":"ShowFormula(B17)","v":"=PFDB*(CU*MDT+CTrip)"}]
["tA*",{"$f":"MTTFA/0.893*(CPM/((alpha-1)*(CCM+CEP)))^(1/alpha)","v":3048.0802633993057},{"$f":"ShowFormula(B18)","v":"=MTTFA/0.893*(CPM/((alpha-1)*(CCM+CEP)))^(1/alpha)"},"General formula:"]
[null,null,{"$f":"ShowFormula(B19)","v":""}]
["b) "]
["l(tA*)",{"$f":"(0.893/MTTFA)^alpha*tauAStar^(alpha-1)","v":9.8422605074523645E-6}]
["ii) Use numerical methods for minimizing the cost, e.g., the SOLVER in Excel"]
["iii) Differentiation, and equating to 0, which gives:",null,null,"General formula:"]
["tB*",{"$f":"SQRT(2*CPT*MTTFB/(lambda_E_Astar*(CU*MDT+CTrip)-0*CCM/MTTFB))","v":4717.0950724799832},{"$f":"ShowFormula(B24)","v":"=SQRT(2*CPT*MTTFB/(lambda_E_Astar*(CU*MDT+CTrip)-0*CCM/MTTFB))"}]
["tB*",{"$f":"SQRT(2*CPT*MTTFB/(lambda_E_Astar*(CU*MDT+CTrip)-CCM/MTTFB))","v":5907.6987942517071},{"$f":"ShowFormula(B25)","v":"=SQRT(2*CPT*MTTFB/(lambda_E_Astar*(CU*MDT+CTrip)-CCM/MTTFB))"}]
["c) Optimizaiton machine #2",null,""]
["l(tA)",{"$f":"(0.893/MTTFA)^alpha*tauA^(alpha-1)","v":5.0807788027968036E-6},"=(0.893/MTTFA)^alpha*tauA^(alpha-1)"]
["C(initial)",{"$f":"CPM/tauA+CPT/tauB+lambda_E*(CCM+tauB/(2*MTTFB)*(CU*MDT+CTrip))+CCM/(MTTFB+tauB/2)","v":2.1946782095462325},"=CPM/tauA+CPT/tauB+lambda_E*(CCM+tauB/(2*MTTFB)*(CU*MDT+CTrip))+CCM/(MTTFB+tauB/2)","Unavailability of machine #1"]
["c(a)",{"$f":"CPM/tauAStar+CPT/tauB+lambda_E_Astar*(CCM+tauB/(2*MTTFB)*(CU*MDT+CTrip))+CCM/(MTTFB+tauB/2)","v":2.0471153318256174},"=CPM/tauAStar+CPT/tauB+lambda_E_Astar*(CCM+tauB/(2*MTTFB)*(CU*MDT+CTrip))+CCM/(MTTFB+tauB/2)"]
["c(b)",{"$f":"CPM/tauAStar+CPT/tauBstar1+lambda_E_Astar*(CCM+tauBstar1/(2*MTTFB)*(CU*MDT+CTrip))+CCM/(MTTFB+tauBstar1/2)","v":2.0096932768156743},"=CPM/tauAStar+CPT/tauBstar1+lambda_E_Astar*(CCM+tauBstar1/(2*MTTFB)*(CU*MDT+CTrip))+CCM/(MTTFB+tauBstar1/2)","Simple formula"]
["c(b)",{"$f":"CPM/tauAStar+CPT/tauBstar2+lambda_E_Astar*(CCM+tauBstar2/(2*MTTFB)*(CU*MDT+CTrip))+CCM/(MTTFB+tauBstar2/2)","v":2.0058500269692785},"=CPM/tauAStar+CPT/tauBstar2+lambda_E_Astar*(CCM+tauBstar2/(2*MTTFB)*(CU*MDT+CTrip))+CCM/(MTTFB+tauBstar2/2)","Advance formula"]