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[null,null,null,null,"This Excel workbook has been produced The 61508 Association to support the content of the maths documents T6A041, T6A042, T6A043 and T6A044. The 61508 Association makes this document available under a Creative Commons CC BY-SA 4.0 Licence:"]
[null,null,null,null,"https://creativecommons.org/licenses/by-sa/4.0/"]
[]
["Revision",null,"Date","By","Comments"]
[]
[]
[0.1,null,"2020-01-31","R Martin","First draft"]
[0.2,null,"2023-01-04","R Martin","Added new page for simplex staggered coefficients;\nMoved staggered coefficients on existing sheet and changed vba code to suit\nUpdated vba program and standard form formulae so that the common cause element for PFDu is calculated as βu.λdu.T/2N for staggered proof testing and remains as βu.λdu.T/2 for synchronised tesing. This is to reflect the fact that advice is that if a channel has been found to have failed during testing, other channels should be checked for common cause failure."]
[0.3,null,"2023-02-14","R Martin","The term for PFDd has always appeared as λdd.MTTR. Normally this is very small compared to the term for PFDu (λdu.T/2) and thus becomes invisible. If during a test a fault is discovered, it follows that at the point, the fault is 'diagnosed' and the item will be out of service until it is restored - hence there is also a term λdu.MTTR which may be considered as of similar size. Also, there is the unavailability due to change out at mission time. This is not a diagnosed fault but has a similar effect on unavailability. The obvious way to handle this in the maths is to use PFDd = (λdd+λdu).MTTR. Note: where multi-channel and common cause is taen into acount, it becomes  PFDd = [ (1-βd)λdd + (1-βu)λdu + 1/MT ].MTTR. Note: in most practical instances this will have negligible effect but is there to cover outliers. Calc-Sheet and vba (thus N-f) updated to mirror this."]
[0.4,null,"2023-02-22","R Martin","Restore time occurs when a failure is diagnosed, when a fault is found during testing and when an item is changed out at MT. It is unlikely that the same restore time will apply to all three. Therefore MTTRD, MTTRR and MTTRU have been devised. Calc Sheet updated to suit and N-f (vba) corrected to suit. Vba udated to use more recognisable variables rather that cell references. Added 1oo3 and 2oo4 to Calc Sheet."]
[0.5,null,"2024-01-23","R Martin","It was pointed out that if proof testing and replacement (or T1 and T2) are synchronised and synchronised with one another, this leads to the need for a further correction factor. This version includes that correction factor. "]
["1.0",null,"2024-02-01","R Martin","First issue - no change from v0.5"]
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[null,null,null,null,"DISCLAIMER: Whilst every effort has been made to ensure the accuracy of the information contained in this document neither “The 61508 Association” nor its members will assume any liability for any use made thereof."]

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["λd","Dangerous failure rate",0.01]
["C","Dignostic Coverage Factor (λdd/λd)",0.1]
["R","Untested Factor (λdr/λd)",0.1]
["MTTRD","MTTR for diagnosed failures",5.0000000000000001E-3]
["MTTRR","MTTR for planned change out",5.0000000000000001E-3]
["MTTRU","MTTR for failures found in manual proof testing",5.0000000000000001E-3]
["MT","Mission Time (time at which part is replaced or refurbished)",5]
["T","Proof Test Interval",1]
["βD","Beta applicable to λdd",0.05]
["βR","Beta applicable to λdr",0.05]
["βU","Beta applicable to λdu",0.05]
["SYNCU","Synchronised proof testing = 1, staggered = 0",0]
["SYNCR","Synchronised mission time change out = 1, staggered = 0",1]
["SYNCUR","Both synchronised together",0]

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[null,"Number\n(N)","Fault Tolerance\n(f)","Failure Rate (dengerous failure rate of single item)\n(λd)\n[y-1]","Diagnostic Coverage\n(C)\n[no units]","Residual Factor\n(R)\n[no units]","Dangerous detected failure rate\n(λdd)\n[y-1]","Dangerous Residual failure rate\n(λdr)\n[y-1]","Dangerous undetected failure rate\n(λdu)\n[y-1]","Mean Time to Restore (for diagnosed)\n(MTTRd)\n [y]","Mean Time to Restore (found in test)\n(MTTRu)\n [y]","Mean Time to Restore (planned change out)\n(MTTRr)\n [y]","Mission Time  (MT)\n[y]","Test Interval (T)\n[y]","Beta Factor (diagnosed)\n(βD)\n[no units]","Beta Factor (residual)\n(βR)\n[no units]","Beta Factor (undiagnosed)\n(βU)\n[no units]","Synchronous Proof Testing?\n[1/0]","Synchronous Replacement?\n[1/0]","Synchronous Proof Testing and Replacement?\n[1/0]"]
[]
[null,"N","f","λd","C","R","λdd","λdr","λdu","MTTRD","MTTRR","MTTRU","MT","T","βD","βR","βU","SYNCU","SYNCR","SYNCUR"]
["PFD"]
["1oo1",1,0,{"$f":"'Data Entry for Test'!C5","v":0.01},{"$f":"'Data Entry for Test'!C6","v":0.1},{"$f":"'Data Entry for Test'!C7","v":0.1},{"$f":"D5*E5","v":1E-3},{"$f":"D5*F5","v":1E-3},{"$f":"D5-G5-H5","v":8.0000000000000002E-3},{"$f":"'Data Entry for Test'!C8","v":5.0000000000000001E-3},{"$f":"'Data Entry for Test'!C9","v":5.0000000000000001E-3},{"$f":"'Data Entry for Test'!C10","v":5.0000000000000001E-3},{"$f":"'Data Entry for Test'!C11","v":5},{"$f":"'Data Entry for Test'!C12","v":1},{"$f":"'Data Entry for Test'!C13","v":0.05},{"$f":"'Data Entry for Test'!C14","v":0.05},{"$f":"'Data Entry for Test'!C15","v":0.05},{"$f":"'Data Entry for Test'!C16","v":0},{"$f":"'Data Entry for Test'!C17","v":1},{"$f":"'Data Entry for Test'!C18","v":0},{"$f":"G5*O5","v":5.0000000000000002E-5},{"$f":"H5*P5","v":5.0000000000000002E-5},{"$f":"I5*Q5","v":4.0000000000000002E-4},{"$f":"(O5*G5)*J5","v":2.5000000000000004E-7},{"$f":"P5*H5*M5/2","v":1.25E-4},{"$f":"Q5*I5*N5/(2*B5^(1-R5))","v":2.0000000000000001E-4},{"$f":"G5*(1-O5)*J5+I5*(1-Q5)*L5+IF(M5=0,0,K5/M5)","v":1.0427500000000001E-3},{"$f":"H5*M5/2","v":2.5000000000000001E-3},{"$f":"I5*N5/2","v":4.0000000000000001E-3},"1oo1",{"$f":"AA5+AB5+AC5","v":7.54275E-3}]
["1oo2",2,1,{"$f":"D5","v":0.01},{"$f":"E5","v":0.1},0.1,1E-3,1E-3,8.0000000000000002E-3,5.0000000000000001E-3,5.0000000000000001E-3,5.0000000000000001E-3,5,1,0.05,0.05,0.05,0,1,0,{"$f":"G6*O6","v":5.0000000000000002E-5},{"$f":"H6*P6","v":5.0000000000000002E-5},{"$f":"I6*Q6","v":4.0000000000000002E-4},{"$f":"(O6*G6)*J6","v":2.5000000000000004E-7},{"$f":"P6*H6*M6/2","v":1.25E-4},{"$f":"Q6*I6*N6/(2*B6^(1-R6))","v":1E-4},{"$f":"G6*(1-O6)*J6+I6*(1-Q6)*L6+IF(M6=0,0,K6/M6)","v":1.0427500000000001E-3},{"$f":"H6*(1-P6)*M6/2","v":2.3749999999999999E-3},{"$f":"I6*(1-Q6)*N6/2","v":3.8E-3},"1oo2",{"$f":"AA6^2+AB6^2*IF(S6=1,4/3,5/6)+AC6^2*IF(R6=1,4/3,5/6)+2*(AA6*AB6+AA6*AC6+AB6*AC6*IF(T6=1,1+N6/3/M6,1))+X6+Y6+Z6","v":2.7681945672916667E-4}]
["2oo3",3,1,{"$f":"D5","v":0.01},{"$f":"E5","v":0.1},0.1,1E-3,1E-3,8.0000000000000002E-3,5.0000000000000001E-3,5.0000000000000001E-3,5.0000000000000001E-3,5,1,0.05,0.05,{"$f":"Q5","v":0.05},{"$f":"R5","v":0},1,0,5.0000000000000002E-5,5.0000000000000002E-5,4.0000000000000002E-4,2.5000000000000004E-7,1.25E-4,6.666666666666667E-5,{"$f":"G7*(1-O7)*J7+I7*(1-Q7)*L7+IF(M7=0,0,K7/M7)","v":1.0427500000000001E-3},{"$f":"H7*(1-P7)*M7/2","v":2.3749999999999999E-3},{"$f":"I7*(1-Q7)*N7/2","v":3.8E-3},"2oo3",{"$f":"3*(AE6-X6-Y6-Z6)+X7+Y7+Z7","v":3.4662503685416678E-4}]
["1oo3",3,2,{"$f":"D5","v":0.01},{"$f":"E5","v":0.1},{"$f":"F5","v":0.1},{"$f":"G5","v":1E-3},1E-3,8.0000000000000002E-3,5.0000000000000001E-3,5.0000000000000001E-3,5.0000000000000001E-3,5,1,0.05,0.05,0.05,0,1,0,5.0000000000000002E-5,5.0000000000000002E-5,4.0000000000000002E-4,2.5000000000000004E-7,1.25E-4,6.666666666666667E-5,1.0427500000000001E-3,2.3749999999999999E-3,3.8E-3,"1oo3",{"$f":"AA8^3+AC8^3*IF(R8=1,2,2/3)+AB8^3*IF(S8=1,2,2/3)+3*AA8^2*(AC8+AB8)+3*AC8^2*IF(R8=1,4/3,5/6)*(AA8+AB8*IF(T8=1,1+N8/2/M8,1))+3*AB8^2*IF(S8=1,4/3,5/6)*(AA8+AC8*IF(T8=1,1+N8/2/M8,1))+6*AA8*AB8*AC8*IF(T8=1,1+N8/3/M8,1)+X8+Z8+Y8","v":1.9229042775703611E-4}]
["2oo4",4,2,{"$f":"D5","v":0.01},{"$f":"E5","v":0.1},{"$f":"F5","v":0.1},{"$f":"G5","v":1E-3},1E-3,8.0000000000000002E-3,5.0000000000000001E-3,5.0000000000000001E-3,5.0000000000000001E-3,5,1,0.05,0.05,0.05,0,1,0,{"$f":"G9*O9","v":5.0000000000000002E-5},5.0000000000000002E-5,4.0000000000000002E-4,2.5000000000000004E-7,1.25E-4,5.0000000000000002E-5,1.0427500000000001E-3,2.3749999999999999E-3,3.8E-3,"2oo4",{"$f":"4*(AA9^3+AC9^3*IF(R9=1,2,2/3)+AB9^3*IF(S9=1,2,2/3)+3*AA9^2*(AC9+AB9)+3*AC9^2*IF(R9=1,4/3,5/6)*(AA9+AB9*IF(T9=1,1+N9/2/M9,1))+3*AB9^2*IF(S9=1,4/3,5/6)*(AA9+AC9*IF(T9=1,1+N9/2/M9,1))+6*AA9*AB9*AC9*IF(T9=1,1+N9/3/M9,1))+X9+Z9+Y9","v":1.7674504436147778E-4}]
[]
["\nλ"]
["1oo1",1,0,{"$f":"D5","v":0.01},{"$f":"E5","v":0.1},0.1,1E-3,1E-3,8.0000000000000002E-3,5.0000000000000001E-3,5.0000000000000001E-3,5.0000000000000001E-3,5,1,0.05,0.05,0.05,0,1,0,{"$f":"G12*O12","v":5.0000000000000002E-5},{"$f":"H12*P12","v":5.0000000000000002E-5},{"$f":"I12*Q12","v":4.0000000000000002E-4},{"$f":"(O12*G12)*J12","v":2.5000000000000004E-7},{"$f":"P12*H12*M12/2","v":1.25E-4},{"$f":"Q12*I12*N12/(2*B12^(1-R12))","v":2.0000000000000001E-4},{"$f":"AA5","v":1.0427500000000001E-3},{"$f":"AB5","v":2.5000000000000001E-3},{"$f":"AC5","v":4.0000000000000001E-3},"1oo1",{"$f":"D12","v":0.01}]
["1oo2",2,1,{"$f":"D5","v":0.01},{"$f":"E5","v":0.1},0.1,1E-3,1E-3,8.0000000000000002E-3,5.0000000000000001E-3,5.0000000000000001E-3,5.0000000000000001E-3,5,1,0.05,0.05,0.05,0,1,0,5.0000000000000002E-5,5.0000000000000002E-5,4.0000000000000002E-4,{"$f":"(O13*G13)*J13","v":2.5000000000000004E-7},{"$f":"P13*H13*M13/2","v":1.25E-4},{"$f":"Q13*I13*N13/(2*B13^(1-R13))","v":1E-4},{"$f":"AA6","v":1.0427500000000001E-3},2.3749999999999999E-3,3.8E-3,"1oo2",{"$f":"2*D13*(AA13+AB13+AC13)+U13+V13+W13","v":6.443550000000001E-4}]
["2oo3",3,1,{"$f":"D5","v":0.01},{"$f":"E5","v":0.1},0.1,1E-3,1E-3,8.0000000000000002E-3,5.0000000000000001E-3,5.0000000000000001E-3,5.0000000000000001E-3,5,1,0.05,0.05,0.05,0,1,0,5.0000000000000002E-5,5.0000000000000002E-5,4.0000000000000002E-4,2.5000000000000004E-7,1.25E-4,6.666666666666667E-5,{"$f":"AA7","v":1.0427500000000001E-3},2.3749999999999999E-3,3.8E-3,"2oo3",{"$f":"6*D14*(AE5-X5-Y5-Z5)+U14+V14+W14","v":9.3304999999999994E-4}]
["1oo3",3,2,{"$f":"D5","v":0.01},{"$f":"E5","v":0.1},0.1,1E-3,1E-3,8.0000000000000002E-3,5.0000000000000001E-3,5.0000000000000001E-3,5.0000000000000001E-3,5,1,0.05,0.05,0.05,0,1,0,5.0000000000000002E-5,5.0000000000000002E-5,4.0000000000000002E-4,2.5000000000000004E-7,1.25E-4,6.666666666666667E-5,{"$f":"AA8","v":1.0427500000000001E-3},2.3749999999999999E-3,3.8E-3,"1oo3",{"$f":"3*D15*(AE6-X6-Y6-Z6)+U15+V15+W15","v":5.0154708370187505E-4}]
["2oo4",4,2,{"$f":"D5","v":0.01},{"$f":"E5","v":0.1},0.1,1E-3,1E-3,8.0000000000000002E-3,5.0000000000000001E-3,5.0000000000000001E-3,5.0000000000000001E-3,5,1,0.05,0.05,0.05,0,1,0,5.0000000000000002E-5,5.0000000000000002E-5,4.0000000000000002E-4,2.5000000000000004E-7,1.25E-4,5.0000000000000002E-5,{"$f":"AA9","v":1.0427500000000001E-3},2.3749999999999999E-3,3.8E-3,"2oo4",{"$f":"4*D16*(AE7-X7-Y7-Z7)+U16+V16+W16","v":5.0618833480750006E-4}]
[]
[]
[null,"N","f","λd","C","R","λdd","λdr","λdu","MTTRD","MTTRR","MTTRU","MT","T","βD","βR","βU","SYNCU","SYNCR","SYNCUR"]
["PFD"]
["1oo1",1,0,{"$f":"'Data Entry for Test'!C21","v":0},{"$f":"'Data Entry for Test'!C22","v":0},{"$f":"'Data Entry for Test'!C23","v":0},{"$f":"D21*E21","v":0},{"$f":"D21*F21","v":0},{"$f":"D21-G21-H21","v":0},{"$f":"'Data Entry for Test'!C24","v":0},{"$f":"'Data Entry for Test'!C25","v":0},{"$f":"'Data Entry for Test'!C26","v":0},{"$f":"'Data Entry for Test'!C27","v":0},{"$f":"'Data Entry for Test'!C28","v":0},{"$f":"'Data Entry for Test'!C29","v":0},{"$f":"'Data Entry for Test'!C30","v":0},{"$f":"'Data Entry for Test'!C31","v":0},{"$f":"'Data Entry for Test'!C32","v":0},{"$f":"'Data Entry for Test'!C33","v":0},{"$f":"'Data Entry for Test'!C34","v":0},{"$f":"G21*O21","v":0},{"$f":"H21*P21","v":0},{"$f":"I21*Q21","v":0},{"$f":"(O21*G21)*J21","v":0},{"$f":"P21*H21*M21/2","v":0},{"$f":"Q21*I21*N21/(2*B21^(1-R21))","v":0},{"$f":"G21*J21+I21*L21+IF(M21=0,0,K21/M21)","v":0},{"$f":"H21*M21/2","v":0},{"$f":"I21*N21/2","v":0},"1oo1",{"$f":"AA21+AB21+AC21","v":0}]
["1oo2",2,1,{"$f":"D21","v":0},{"$f":"E21","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"Q22*I22*N22/(2*B22^(1-R22))","v":0},{"$f":"G22*(1-O22)*J22+I22*(1-Q22)*L22+IF(M22=0,0,K22/M22)","v":0},{"$f":"H22*(1-P22)*M22/2","v":0},{"$f":"I22*(1-Q22)*N22/2","v":0},"1oo2",{"$f":"AA22^2+AB22^2*IF(S22=1,4/3,5/6)+AC22^2*IF(R22=1,4/3,5/6)+2*(AA22*AB22+AA22*AC22+AB22*AC22*IF(T22=1,1+N22/3/M22,1))+X22+Y22+Z22","v":0}]
["2oo3",3,1,{"$f":"D21","v":0},{"$f":"E21","v":0},0,0,0,0,0,0,0,0,0,0,0,{"$f":"Q21","v":0},{"$f":"R21","v":0},0,0,0,0,0,0,0,0,{"$f":"G23*(1-O23)*J23+I23*(1-Q23)*L23+IF(M23=0,0,K23/M23)","v":0},{"$f":"H23*(1-P23)*M23/2","v":0},{"$f":"I23*(1-Q23)*N23/2","v":0},"2oo3",{"$f":"3*(AE22-X22-Y22-Z22)+X23+Y23+Z23","v":0}]
["1oo3",3,2,{"$f":"D21","v":0},{"$f":"E21","v":0},{"$f":"F21","v":0},{"$f":"G21","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"U21","v":0},{"$f":"V21","v":0},0,0,0,0,0,0,0,"1oo3",{"$f":"AA24^3+AC24^3*IF(R24=1,2,2/3)+AB24^3*IF(S24=1,2,2/3)+3*AA24^2*(AC24+AB24)+3*AC24^2*IF(R24=1,4/3,5/6)*(AA24+AB24*IF(T24=1,1+N24/2/M24,1))+3*AB24^2*IF(S24=1,4/3,5/6)*(AA24+AC24*IF(T24=1,1+N24/2/M24,1))+6*AA24*AB24*AC24*IF(T24=1,1+N24/3/M24,1)+X24+Z24+Y24","v":0}]
["2oo4",4,2,{"$f":"D21","v":0},{"$f":"E21","v":0},{"$f":"F21","v":0},{"$f":"G21","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"U21","v":0},{"$f":"V21","v":0},0,0,0,0,0,0,0,"2oo4",{"$f":"4*(AA25^3+AC25^3*IF(R25=1,2,2/3)+AB25^3*IF(S25=1,2,2/3)+3*AA25^2*(AC25+AB25)+3*AC25^2*IF(R25=1,4/3,5/6)*(AA25+AB25*IF(T25=1,1+N25/2/M25,1))+3*AB25^2*IF(S25=1,4/3,5/6)*(AA25+AC25*IF(T25=1,1+N25/2/M25,1))+6*AA25*AB25*AC25*IF(T25=1,1+N25/3/M25,1))+X25+Z25+Y25","v":0}]
[]
["\nλ"]
["1oo1",1,0,{"$f":"D21","v":0},{"$f":"E21","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"Z21","v":0},{"$f":"AA21","v":0},{"$f":"AB21","v":0},{"$f":"AC21","v":0},"1oo1",{"$f":"D28","v":0}]
["1oo2",2,1,{"$f":"D21","v":0},{"$f":"E21","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"Z22","v":0},0,0,0,"1oo2",{"$f":"2*D29*(AA29+AB29+AC29)+U29+V29+W29","v":0}]
["2oo3",3,1,{"$f":"D21","v":0},{"$f":"E21","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"Z23","v":0},0,0,0,"2oo3",{"$f":"6*D30*(AE21-X21-Y21-Z21)+U30+V30+W30","v":0}]
["1oo3",3,2,{"$f":"D21","v":0},{"$f":"E21","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"U21","v":0},{"$f":"V21","v":0},0,0,0,{"$f":"Z24","v":0},0,0,0,"1oo3",{"$f":"3*D31*(AE22-X22-Y22-Z22)+U31+V31+W31","v":0}]
["2oo4",4,2,{"$f":"D21","v":0},{"$f":"E21","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"U21","v":0},{"$f":"V21","v":0},0,0,0,{"$f":"Z25","v":0},0,0,0,"2oo4",{"$f":"4*D32*(AE23-X23-Y23-Z23)+U32+V32+W32","v":0}]
[]
[]
[null,"N","f","λd","C","R","λdd","λdr","λdu","MTTRD","MTTRR","MTTRU","MT","T","βD","βR","βU","SYNCU","SYNCR","SYNCUR"]
["PFD"]
["1oo1",1,0,{"$f":"'Data Entry for Test'!C37","v":0},{"$f":"'Data Entry for Test'!C38","v":0},{"$f":"'Data Entry for Test'!C39","v":0},{"$f":"D37*E37","v":0},{"$f":"D37*F37","v":0},{"$f":"D37-G37-H37","v":0},{"$f":"'Data Entry for Test'!C40","v":0},{"$f":"'Data Entry for Test'!C41","v":0},{"$f":"'Data Entry for Test'!C42","v":0},{"$f":"'Data Entry for Test'!C43","v":0},{"$f":"'Data Entry for Test'!C44","v":0},{"$f":"'Data Entry for Test'!C45","v":0},{"$f":"'Data Entry for Test'!C46","v":0},{"$f":"'Data Entry for Test'!C47","v":0},{"$f":"'Data Entry for Test'!C48","v":0},{"$f":"'Data Entry for Test'!C49","v":0},{"$f":"'Data Entry for Test'!C50","v":0},{"$f":"G37*O37","v":0},{"$f":"H37*P37","v":0},{"$f":"I37*Q37","v":0},{"$f":"(O37*G37)*J37","v":0},{"$f":"P37*H37*M37/2","v":0},{"$f":"Q37*I37*N37/(2*B37^(1-R37))","v":0},{"$f":"G37*J37+I37*L37+IF(M37=0,0,K37/M37)","v":0},{"$f":"H37*M37/2","v":0},{"$f":"I37*N37/2","v":0},"1oo1",{"$f":"AA37+AB37+AC37","v":0}]
["1oo2",2,1,{"$f":"D37","v":0},{"$f":"E37","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"Q38*I38*N38/(2*B38^(1-R38))","v":0},{"$f":"G38*(1-O38)*J38+I38*(1-Q38)*L38+IF(M38=0,0,K38/M38)","v":0},{"$f":"H38*(1-P38)*M38/2","v":0},{"$f":"I38*(1-Q38)*N38/2","v":0},"1oo2",{"$f":"AA38^2+AB38^2*IF(S38=1,4/3,5/6)+AC38^2*IF(R38=1,4/3,5/6)+2*(AA38*AB38+AA38*AC38+AB38*AC38*IF(T38=1,1+N38/3/M38,1))+X38+Y38+Z38","v":0}]
["2oo3",3,1,{"$f":"D37","v":0},{"$f":"E37","v":0},0,0,0,0,0,0,0,0,0,0,0,{"$f":"Q37","v":0},{"$f":"R37","v":0},0,0,0,0,0,0,0,0,{"$f":"G39*(1-O39)*J39+I39*(1-Q39)*L39+IF(M39=0,0,K39/M39)","v":0},{"$f":"H39*(1-P39)*M39/2","v":0},{"$f":"I39*(1-Q39)*N39/2","v":0},"2oo3",{"$f":"3*(AE38-X38-Y38-Z38)+X39+Y39+Z39","v":0}]
["1oo3",3,2,{"$f":"D37","v":0},{"$f":"E37","v":0},{"$f":"F37","v":0},{"$f":"G37","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"U37","v":0},{"$f":"V37","v":0},0,0,0,0,0,0,0,"1oo3",{"$f":"AA40^3+AC40^3*IF(R40=1,2,2/3)+AB40^3*IF(S40=1,2,2/3)+3*AA40^2*(AC40+AB40)+3*AC40^2*IF(R40=1,4/3,5/6)*(AA40+AB40*IF(T40=1,1+N40/2/M40,1))+3*AB40^2*IF(S40=1,4/3,5/6)*(AA40+AC40*IF(T40=1,1+N40/2/M40,1))+6*AA40*AB40*AC40*IF(T40=1,1+N40/3/M40,1)+X40+Z40+Y40","v":0}]
["2oo4",4,2,{"$f":"D37","v":0},{"$f":"E37","v":0},{"$f":"F37","v":0},{"$f":"G37","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"U37","v":0},{"$f":"V37","v":0},0,0,0,0,0,0,0,"2oo4",{"$f":"4*(AA41^3+AC41^3*IF(R41=1,2,2/3)+AB41^3*IF(S41=1,2,2/3)+3*AA41^2*(AC41+AB41)+3*AC41^2*IF(R41=1,4/3,5/6)*(AA41+AB41*IF(T41=1,1+N41/2/M41,1))+3*AB41^2*IF(S41=1,4/3,5/6)*(AA41+AC41*IF(T41=1,1+N41/2/M41,1))+6*AA41*AB41*AC41*IF(T41=1,1+N41/3/M41,1))+X41+Z41+Y41","v":0}]
[]
["\nλ"]
["1oo1",1,0,{"$f":"D37","v":0},{"$f":"E37","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"Z37","v":0},{"$f":"AA37","v":0},{"$f":"AB37","v":0},{"$f":"AC37","v":0},"1oo1",{"$f":"D44","v":0}]
["1oo2",2,1,{"$f":"D37","v":0},{"$f":"E37","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"Z38","v":0},0,0,0,"1oo2",{"$f":"2*D45*(AA45+AB45+AC45)+U45+V45+W45","v":0}]
["2oo3",3,1,{"$f":"D37","v":0},{"$f":"E37","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"Z39","v":0},0,0,0,"2oo3",{"$f":"6*D46*(AE37-X37-Y37-Z37)+U46+V46+W46","v":0}]
["1oo3",3,2,{"$f":"D37","v":0},{"$f":"E37","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"U37","v":0},{"$f":"V37","v":0},0,0,0,{"$f":"Z40","v":0},0,0,0,"1oo3",{"$f":"3*D47*(AE38-X38-Y38-Z38)+U47+V47+W47","v":0}]
["2oo4",4,2,{"$f":"D37","v":0},{"$f":"E37","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"U37","v":0},{"$f":"V37","v":0},0,0,0,{"$f":"Z41","v":0},0,0,0,"2oo4",{"$f":"4*D48*(AE39-X39-Y39-Z39)+U48+V48+W48","v":0}]
[]
[]
[null,"N","f","λd","C","R","λdd","λdr","λdu","MTTRD","MTTRR","MTTRU","MT","T","βD","βR","βU","SYNCU","SYNCR","SYNCUR"]
["PFD"]
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["1oo2",2,1,{"$f":"D53","v":0},{"$f":"E53","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"Q54*I54*N54/(2*B54^(1-R54))","v":0},{"$f":"G54*(1-O54)*J54+I54*(1-Q54)*L54+IF(M54=0,0,K54/M54)","v":0},{"$f":"H54*(1-P54)*M54/2","v":0},{"$f":"I54*(1-Q54)*N54/2","v":0},"1oo2",{"$f":"AA54^2+AB54^2*IF(S54=1,4/3,5/6)+AC54^2*IF(R54=1,4/3,5/6)+2*(AA54*AB54+AA54*AC54+AB54*AC54*IF(T54=1,1+N54/3/M54,1))+X54+Y54+Z54","v":0}]
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[]
["\nλ"]
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["2oo4",4,2,{"$f":"D53","v":0},{"$f":"E53","v":0},0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,{"$f":"U53","v":0},{"$f":"V53","v":0},0,0,0,{"$f":"Z57","v":0},0,0,0,"2oo4",{"$f":"4*D64*(AE55-X55-Y55-Z55)+U64+V64+W64","v":0}]

{"sheet":"N-f","index":3,"n_rows":100,"n_cols":32,"rows_kept":100,"cut":false,"hidden":false,"merged":[[1,0,1,2]]}
["Ref","Number\n(N)","Fault Tolerance\n(f)","Failure Rate (dengerous failure rate of single item)\n(λd)\n[y-1]","Diagnostic Coverage\n(C)\n[no units]","Residual Factor\n(R)\n[no units]","Dangerous detected failure rate\n(λdd)\n[y-1]","Dangerous Residual failure rate\n(λdr)\n[y-1]","Dangerous undetected failure rate\n(λdu)\n[y-1]","Mean Time to Restore (for diagnosed)\n(MTTRd)\n [y]","Mean Time to Restore (found in test)\n(MTTRu)\n [y]","Mean Time to Restore (planned change out)\n(MTTRr)\n [y]","Mission Time  (MT)\n[y]","Test Interval (T)\n[y]","Beta Factor (diagnosed)\n(βD)\n[no units]","Beta Factor (residual)\n(βR)\n[no units]","Beta Factor (undiagnosed)\n(βU)\n[no units]","Synchronous Proof Testing?\n[1/0]","Synchronous Replacement?\n[1/0]","Synchronous Proof Testing and Replacement?\n[1/0]"]
["Enter reference in column A to enable calculation. Ctrl+Shift+C to Calculate",null,null,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]
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{"sheet":"vba Test","index":4,"n_rows":43,"n_cols":23,"rows_kept":43,"cut":false,"hidden":true,"merged":[]}
[null,"Number\n(N)","Fault Tolerance\n(f)","Failure Rate (dengerous failure rate of single item)\n(λd)\n[y-1]","Diagnostic Coverage\n(C)\n[no units]","Dangerous undetected failure rate\n(λdu)\n[y-1]","Dangerous detected failure rate\n(λdd)\n[y-1]","Test Interval (T)\n[y]","Mean Time to Restore\n(MTTR)\n [y]","Beta Factor (undiagnosed)\n(β)\n[no units]","Beta Factor (diagnosed)\n(βD)\n[no units]","Synchronous Testing?\n[1/0]","Combin f+1 from N","Combin i from f","Synch test factor","Undiag core","Undiag index","Diagnosed core","Diag index","Non common cause part","Undiag common cause part","Diag common cause part","Reliability"]
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[null,"N","f","λd","C","λdu","λdd","T","MDT","β","βD","Sync?"]
[null,{"$f":"B16","v":3},{"$f":"C16","v":1},7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1]
[0,{"$f":"B26","v":3},{"$f":"C26","v":1},7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,{"$f":"IF((A27<C27+1),COMBIN(B27,C27),0)","v":3},{"$f":"IF((A27<C27+1),COMBIN(C27,A27),0)","v":1},{"$f":"IF((A27<C27+1),(2^(C27-A27)/(C27-A27+1))^L27,0)","v":1},{"$f":"IF((A27<C27+1),(1-J27)*F27*H27/2,0)","v":8.1962500000000004E-4},{"$f":"IF((A27<C27+1),C27-A27,0)","v":1},{"$f":"IF((A27<C27+1),(1-K27)*G27*I27,0)","v":1.3474635E-5},{"$f":"IF((A27<C27+1),A27,0)","v":0},{"$f":"IF((A27<C27+1),M27*N27*O27*P27^Q27*R27^S27,0)","v":2.4588750000000001E-3},{"$f":"J27*F27","v":3.3575000000000006E-4},{"$f":"K27*G27","v":1.0072500000000001E-3}]
[1,{"$f":"B27","v":3},1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,{"$f":"IF((A28<C28+1),COMBIN(B28,C28),0)","v":3},{"$f":"IF((A28<C28+1),COMBIN(C28,A28),0)","v":1},{"$f":"IF((A28<C28+1),(2^(C28-A28)/(C28-A28+1))^L28,0)","v":1},{"$f":"IF((A28<C28+1),(1-J28)*F28*H28/2,0)","v":8.1962500000000004E-4},{"$f":"IF((A28<C28+1),C28-A28,0)","v":0},{"$f":"IF((A28<C28+1),(1-K28)*G28*I28,0)","v":1.3474635E-5},{"$f":"IF((A28<C28+1),A28,0)","v":1},{"$f":"IF((A28<C28+1),M28*N28*O28*P28^Q28*R28^S28,0)","v":4.0423905000000005E-5}]
[2,{"$f":"B28","v":3},1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,0,0,0,0,0,0,0,0]
[3,3,1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,0,0,0,0,0,0,0,0]
[4,3,1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,0,0,0,0,0,0,0,0]
[5,3,1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,0,0,0,0,0,0,0,0]
[6,3,1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,0,0,0,0,0,0,0,0]
[7,3,1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,0,0,0,0,0,0,0,0]
[8,3,1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,0,0,0,0,0,0,0,0]
[9,3,1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,0,0,0,0,0,0,0,0]
[10,3,1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,0,0,0,0,0,0,0,0,null,null,"λd"]
[null,3,1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,null,null,null,null,null,null,null,{"$f":"SUM(T27:T37)*(B38-C38)*D38","v":3.9488922699000002E-5},{"$f":"IF((B38>1),SUM(U27:U37),0)","v":3.3575000000000006E-4},{"$f":"IF((B38>1),SUM(V27:V37),0)","v":1.0072500000000001E-3},{"$f":"T38+U38+V38","v":1.3824889226990002E-3}]
[]
[]
["1oo1",1,0,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,null,null,null,null,null,null,null,null,null,null,{"$f":"D41","v":7.9000000000000008E-3}]
["2oo2",2,1,{"$f":"D41","v":7.9000000000000008E-3},0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,null,null,null,{"$f":"(1-J42)*F42*H42/2","v":8.1962500000000004E-4},null,{"$f":"(1-K42)*G42*I42","v":1.3474635E-5},null,{"$f":"2*D42*(P42+R42)","v":1.3162974233000002E-5},{"$f":"J42*F42","v":3.3575000000000006E-4},{"$f":"K42*G42","v":1.0072500000000001E-3},{"$f":"T42+U42+V42","v":1.3561629742330002E-3}]
["2oo3",3,1,7.9000000000000008E-3,0.75,1.9750000000000002E-3,5.9250000000000006E-3,1,2.7399999999999998E-3,0.17,0.17,1,null,null,null,{"$f":"(1-J43)*F43*H43/2","v":8.1962500000000004E-4},null,{"$f":"(1-K43)*G43*I43","v":1.3474635E-5},null,{"$f":"6*D43*(P43+R43)","v":3.9488922699000009E-5},{"$f":"J43*F43","v":3.3575000000000006E-4},{"$f":"K43*G43","v":1.0072500000000001E-3},{"$f":"T43+U43+V43","v":1.3824889226990002E-3}]

{"sheet":"Coeff-stag-simplex","index":5,"n_rows":98,"n_cols":28,"rows_kept":98,"cut":false,"hidden":true,"merged":[]}
[]
["Coefficients needed for generation of PFDAV for staggered testing of N components in parallel"]
["E.g. for 3oo3 to fail:"]
[]
[]
["From deriving the first few rows, we can spot the algebraic progression (pattern) which the coefficients are subject to. The spreadsheet is used to repeat the formula. "]
["In the above example, the coefficients are 1, 3, 2"]
["For 4oo4 to fail, the coefficients turn out to be 1, 6, 11, 6",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"This column shows the ratio for simple redundancy to (PFD1oo1)N"]
["Below is the coefficient number pattern generator:"]
[]
[]
[null,null,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
[]
[1,null,1,{"$f":"D13+($A14-1)*C13","v":0},{"$f":"E13+($A14-1)*D13","v":0},{"$f":"F13+($A14-1)*E13","v":0},{"$f":"G13+($A14-1)*F13","v":0},{"$f":"H13+($A14-1)*G13","v":0},{"$f":"I13+($A14-1)*H13","v":0},{"$f":"J13+($A14-1)*I13","v":0},{"$f":"K13+($A14-1)*J13","v":0},{"$f":"L13+($A14-1)*K13","v":0},{"$f":"M13+($A14-1)*L13","v":0},{"$f":"N13+($A14-1)*M13","v":0},{"$f":"O13+($A14-1)*N13","v":0},{"$f":"P13+($A14-1)*O13","v":0},{"$f":"Q13+($A14-1)*P13","v":0},{"$f":"R13+($A14-1)*Q13","v":0},{"$f":"S13+($A14-1)*R13","v":0},{"$f":"T13+($A14-1)*S13","v":0},{"$f":"U13+($A14-1)*T13","v":0},{"$f":"V13+($A14-1)*U13","v":0},null,1]
[2,null,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0.83333333333333326,null,null,null,"This is the PFD for 1ooN for staggered testing"]
[3,null,1,3,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0.66666666666666663]
[4,null,1,6,11,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0.5229166666666667]
[5,null,1,10,35,50,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0.40533333333333338]
[6,null,1,15,85,225,274,120,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0.31169573453524074]
[7,null,1,21,175,735,1624,1764,720,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0.23831340116221417]
[8,null,1,28,322,1960,6769,13132,13068,5040,0,0,0,0,0,0,0,0,0,0,0,0,null,0.18141292995876734]
[9,null,1,36,546,4536,22449,67284,118124,109584,40320,0,0,0,0,0,0,0,0,0,0,0,null,0.13762430824870492]
[10,null,1,45,870,9450,63273,269325,723680,1172700,1026576,362880,0,0,0,0,0,0,0,0,0,0,null,0.10411540557575757]
[11,null,1,55,{"$f":"E23+($A24-1)*D23","v":1320},{"$f":"F23+($A24-1)*E23","v":18150},{"$f":"G23+($A24-1)*F23","v":157773},{"$f":"H23+($A24-1)*G23","v":902055},{"$f":"I23+($A24-1)*H23","v":3416930},{"$f":"J23+($A24-1)*I23","v":8409500},{"$f":"K23+($A24-1)*J23","v":12753576},{"$f":"L23+($A24-1)*K23","v":10628640},{"$f":"M23+($A24-1)*L23","v":3628800},{"$f":"N23+($A24-1)*M23","v":0},{"$f":"O23+($A24-1)*N23","v":0},{"$f":"P23+($A24-1)*O23","v":0},{"$f":"Q23+($A24-1)*P23","v":0},{"$f":"R23+($A24-1)*Q23","v":0},0,0,0,0,null,7.8584587509692425E-2]
[12,null,1,66,1925,32670,357423,2637558,13339535,45995730,105258076,150917976,120543840,39916800,0,0,0,0,0,0,0,0,null,5.9199877690817776E-2]
[13,null,1,78,2717,55770,749463,6926634,44990231,206070150,657206836,1414014888,1931559552,1486442880,479001600,0,0,0,0,0,0,0,null,4.4523388561769794E-2]
[14,null,1,91,3731,91091,1474473,16669653,135036473,790943153,3336118786,9957703756,20313753096,26596717056,19802759040,6227020800,0,0,0,0,0,0,null,3.3437739589227529E-2]
[15,null,1,105,5005,143325,2749747,37312275,368411615,2681453775,14409322928,56663366760,159721605680,310989260400,392156797824,283465647360,87178291200,0,0,0,0,0,null,2.5081029434705412E-2]
[16,null,1,120,6580,218400,4899622,78558480,928095740,8207628000,54631129553,272803210680,1009672107080,2706813345600,5056995703824,6165817614720,4339163001600,1307674368000,0,0,0,0,null,1.8792204866521139E-2]
[17,null,1,136,8500,323680,8394022,156952432,2185031420,23057159840,185953177553,1146901283528,5374523477960,18861567058880,48366009233424,87077748875904,102992244837120,70734282393600,20922789888000,0,0,0,null,1.4066539517319898E-2]
[18,null,1,153,10812,468180,13896582,299650806,4853222764,60202693980,577924894833,4308105301929,24871845297936,110228466184200,369012649234384,909299905844112,1583313975727488,1821602444624640,1223405590579200,355687428096000,0,0,null,1.0520068996331228E-2]
[19,null,1,171,13566,662796,22323822,549789282,10246937272,147560703732,1661573386473,14710753408923,102417740732658,557921681547048,2353125040549984,7551527592063024,1.7950712280921504E+16,3.0321254007719424E+16,3.401224959382272E+16,2.23769880585216E+16,6402373705728000,0,null,7.8615740085195649E-3]
[20,null,1,190,16815,920550,34916946,973941900,20692933630,342252511900,4465226757381,46280647751910,381922055502195,2503858755467550,1.2953636989943896E+16,5.226090336251272E+16,1.6142973653011898E+17,3.7138478734522803E+17,6.1011607574049178E+17,6.6860973034115328E+17,4.315651468176384E+17,1.21645100408832E+17,null,5.8707334043777652E-3]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[1,2,3,4,5,6,7,8,9,10,11,12,13,14]
[]
[]
["Staggered Proof Test Coefficients for NooM, generated by subroutine 'Coefficients_Stag' which calls 'Fav_for_selection' which calls 'Products_IooJ'"]
[null,null,1,2,3,4,5,6,7,8,9,10]
[1,null,1]
[2,null,1,0.83333333333333326,null,null,null,null,null,null,null,null,null,null,null,"Note: the leading diagonal returns the same coefficients as above (as expected)"]
[3,null,1,0.88888888888888895,0.66666666666666663]
[4,null,1,0.91666666666666652,0.75,0.52291666666666714]
[5,null,1,0.93333333333333335,0.80000000000000038,0.61440000000000039,0.4053333333333316]
[6,null,1,0.94444444444444464,0.83333333333333326,0.67654320987654359,0.49382716049382652,0.31169573453523536]
[7,null,1,0.95238095238095222,0.8571428571428571,0.72147716229348857,0.55976676384839619,0.39167353738663385,0.238313401162212]
[8,null,1,0.95833333333333293,0.875,0.75546875000000036,0.61067708333333293,0.45577566964285665,0.30761718749999989,0.18141292995873926]
[9,null,1,0.96296296296296313,0.88888888888888873,0.78207590306355812,0.6511202560585273,0.50804833327822774,0.36658067405412875,0.23978411735472113,0.1376243082487594]
[10,null,1,0.96666666666666667,0.89999999999999969,0.80346666666666633,0.68399999999999883,0.55137523809523714,0.41696000000000399,0.29200383999998419,0.1857945599998661,0.10411540557569046]

{"sheet":"Coeff-sync","index":6,"n_rows":54,"n_cols":5,"rows_kept":54,"cut":false,"hidden":true,"merged":[]}
[]
["Coefficients needed for generation of PFDAV for synchronised testing of N components in parallel"]
[]
[0,null,1,null,"Note: The row 0 is necessary to allow the program to work properly"]
[1,null,{"$f":"2^A5/(A5+1)","v":1}]
[2,null,{"$f":"2^A6/(A6+1)","v":1.3333333333333333}]
[3,null,2]
[4,null,3.2]
[5,null,5.333333333333333]
[6,null,9.1428571428571423]
[7,null,16]
[8,null,28.444444444444443]
[9,null,51.2]
[10,null,93.090909090909093]
[11,null,170.66666666666666]
[12,null,315.07692307692309]
[13,null,585.14285714285711]
[14,null,1092.2666666666667]
[15,null,2048]
[16,null,3855.0588235294117]
[17,null,7281.7777777777774]
[18,null,13797.052631578947]
[19,null,26214.400000000001]
[20,null,49932.190476190473]
[21,null,95325.090909090912]
[22,null,182361.04347826086]
[23,null,349525.33333333331]
[24,null,671088.64000000001]
[25,null,1290555.076923077]
[26,null,2485513.4814814813]
[27,null,4793490.2857142854]
[28,null,9256395.0344827585]
[29,null,17895697.066666666]
[30,null,34636833.032258064]
[31,null,67108864]
[32,null,130150524.12121212]
[33,null,252645135.05882353]
[34,null,490853405.25714284]
[35,null,954437176.88888884]
[36,null,1857283155.0270271]
[37,null,3616814565.0526314]
[38,null,7048151460.1025639]
[39,null,13743895347.200001]
[40,null,26817356775.024391]
[41,null,52357696560.761902]
[42,null,102280151421.02325]
[43,null,199911205050.18182]
[44,null,390937467653.6889]
[45,null,764877654105.04346]
[46,null,1497207322929.0212]
[47,null,2932031007402.6665]
[48,null,5744387279809.3057]
[49,null,11258999068426.24]
[50,null,22076468761620.078]

{"sheet":"Coeff-stag","index":7,"n_rows":101,"n_cols":52,"rows_kept":101,"cut":false,"hidden":true,"merged":[]}
["Staggered Proof Test Coefficients for NooM, generated by subroutine 'Coefficients_Stag' which calls 'Fav_for_selection' which calls 'Products_IooJ'"]
[null,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50]
[0,1,1,null,null,null,null,null,"Note: The rows and columns 0 are necessary to make the program work"]
[1,1,1,null,null,null,null,null,"The numbers in blue are estimates."]
[2,1,1,0.83333333333333326]
[3,1,1,0.88888888888888895,0.66666666666666663]
[4,1,1,0.91666666666666652,0.75,0.52291666666666714]
[5,1,1,0.93333333333333335,0.80000000000000038,0.61440000000000039,0.4053333333333316]
[6,1,1,0.94444444444444464,0.83333333333333326,0.67654320987654359,0.49382716049382652,0.31169573453523536]
[7,1,1,0.95238095238095222,0.8571428571428571,0.72147716229348857,0.55976676384839619,0.39167353738663385,0.238313401162212]
[8,1,1,0.95833333333333293,0.875,0.75546875000000036,0.61067708333333293,0.45577566964285665,0.30761718749999989,0.18141292995873926]
[9,1,1,0.96296296296296313,0.88888888888888873,0.78207590306355812,0.6511202560585273,0.50804833327822774,0.36658067405412875,0.23978411735472113,0.1376243082487594]
[10,1,1,0.96666666666666667,0.89999999999999969,0.80346666666666633,0.6835,0.55137523809523714,0.41696000000000399,0.29200383999998419,0.1857945599998661,0.10411540557569046]
[11,1,1,0.97,0.90900000000000003,0.82,0.70899999999999996,0.58399999999999996,0.46,0.34,0.23400000000000001,0.15,7.8584587509692425E-2]
[12,1,1,0.97199999999999998,0.91900000000000004,0.83,0.72899999999999998,0.61,0.495,0.378,0.27700000000000002,0.19600000000000001,0.12,5.9199877690817776E-2]
[13,1,1,0.97350000000000003,0.92500000000000004,0.84150000000000003,0.74450000000000005,0.63500000000000001,0.52,0.41,0.315,0.23,0.157,9.2999999999999999E-2,4.4523388561769794E-2]
[14,1,1,0.9748,0.92900000000000005,0.84950000000000003,0.75600000000000001,0.65500000000000003,0.54600000000000004,0.4355,0.34499999999999997,0.26500000000000001,0.19,0.129,7.4999999999999997E-2,3.3437739589227529E-2]
[15,1,1,0.97499999999999998,0.93200000000000005,0.85650000000000004,0.76800000000000002,0.67100000000000004,0.56499999999999995,0.45800000000000002,0.373,0.28999999999999998,0.219,0.159,0.10100000000000001,5.8000000000000003E-2,2.5081029434705412E-2]
[16,1,1,0.97599999999999998,0.93400000000000005,0.86499999999999999,0.77800000000000002,0.68700000000000006,0.57999999999999996,0.47499999999999998,0.39500000000000002,0.3145,0.24199999999999999,0.185,0.124,7.9000000000000001E-2,4.65E-2,1.8792204866521139E-2]
[17,1,1,0.97650000000000003,0.9355,0.87,0.78800000000000003,0.70099999999999996,0.59599999999999997,0.49,0.41299999999999998,0.33300000000000002,0.26300000000000001,0.20549999999999999,0.14499999999999999,9.9000000000000005E-2,6.6000000000000003E-2,3.5999999999999997E-2,1.4066539517319898E-2]
[18,1,1,0.9768,0.93659999999999999,0.878,0.79700000000000004,0.71499999999999997,0.60699999999999998,0.504,0.42899999999999999,0.35,0.28000000000000003,0.2228,0.16300000000000001,0.11749999999999999,8.3000000000000004E-2,5.1499999999999997E-2,2.8000000000000001E-2,1.0520068996331228E-2]
[19,1,1,0.97699999999999998,0.93720000000000003,0.88300000000000001,0.80500000000000005,0.72199999999999998,0.62,0.51849999999999996,0.442,0.36699999999999999,0.29499999999999998,0.23849999999999999,0.18,0.13400000000000001,9.8500000000000004E-2,6.5000000000000002E-2,3.9699999999999999E-2,2.3599999999999999E-2,7.8615740085195649E-3]
[20,1,1,0.97719999999999996,0.9375,0.89,0.81,0.73,0.63,0.53300000000000003,0.45500000000000002,0.38,0.31,0.253,0.19500000000000001,0.15,0.11,7.6999999999999999E-2,0.05,3.3000000000000002E-2,1.4999999999999999E-2,5.8707334043777652E-3]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[]
["This is just a copy",null,1]
[null,null,1,0.83333333333333326]
[null,null,1,0.88888888888888895,0.66666666666666663]
[null,null,1,0.91666666666666652,0.75,0.52291666666666714]
[null,null,1,0.93333333333333335,0.80000000000000038,0.61440000000000039,0.4053333333333316]
[null,null,1,0.94444444444444464,0.83333333333333326,0.67654320987654359,0.49382716049382652,0.31169573453523536]
[null,null,1,0.95238095238095222,0.8571428571428571,0.72147716229348857,0.55976676384839619,0.39167353738663385,0.238313401162212]
[null,null,1,0.95833333333333293,0.875,0.75546875000000036,0.61067708333333293,0.45577566964285665,0.30761718749999989,0.18141292995873926]
[null,null,1,0.96296296296296313,0.88888888888888873,0.78207590306355812,0.6511202560585273,0.50804833327822774,0.36658067405412875,0.23978411735472113,0.1376243082487594]
[null,null,1,0.96666666666666667,0.89999999999999969,0.80346666666666633,0.68399999999999883,0.55137523809523714,0.41696000000000399,0.29200383999998419,0.1857945599998661,0.10411540557569046]
[]
["This is the series of numbers printed out during a test to demonstrate that the constituents of the integer vector S() are what you would expect for combinations of 4 integers in the range 1 to 7."]
[null,null,null,null,null,null,null,1,2,3,4]
[null,null,null,null,null,null,null,1,2,3,5]
[null,null,null,null,null,null,null,1,2,3,6]
[null,null,null,null,null,null,null,1,2,3,7]
[null,null,null,null,null,null,null,1,2,4,5]
[null,null,null,null,null,null,null,1,2,4,6]
[null,null,null,null,null,null,null,1,2,4,7]
[null,null,null,null,null,null,null,1,2,5,6]
[null,null,null,null,null,null,null,1,2,5,7]
[null,null,null,null,null,null,null,1,2,6,7]
[null,null,null,null,null,null,null,1,3,4,5]
[null,null,null,null,null,null,null,1,3,4,6]
[null,null,null,null,null,null,null,1,3,4,7]
[null,null,null,null,null,null,null,1,3,5,6]
[null,null,null,null,null,null,null,1,3,5,7]
[null,null,null,null,null,null,null,1,3,6,7]
[null,null,null,null,null,null,null,1,4,5,6]
[null,null,null,null,null,null,null,1,4,5,7]
[null,null,null,null,null,null,null,1,4,6,7]
[null,null,null,null,null,null,null,1,5,6,7]
[null,null,null,null,null,null,null,2,3,4,5]
[null,null,null,null,null,null,null,2,3,4,6]
[null,null,null,null,null,null,null,2,3,4,7]
[null,null,null,null,null,null,null,2,3,5,6]
[null,null,null,null,null,null,null,2,3,5,7]
[null,null,null,null,null,null,null,2,3,6,7]
[null,null,null,null,null,null,null,2,4,5,6]
[null,null,null,null,null,null,null,2,4,5,7]
[null,null,null,null,null,null,null,2,4,6,7]
[null,null,null,null,null,null,null,2,5,6,7]
[null,null,null,null,null,null,null,3,4,5,6]
[null,null,null,null,null,null,null,3,4,5,7]
[null,null,null,null,null,null,null,3,4,6,7]
[null,null,null,null,null,null,null,3,5,6,7]
[null,null,null,null,null,null,null,4,5,6,7]

{"sheet":"Combin","index":8,"n_rows":54,"n_cols":53,"rows_kept":54,"cut":false,"hidden":true,"merged":[]}
[]
["Combinations"]
[null,null,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50]
[0,null,{"$f":"COMBIN($A4,C$3)","v":1}]
[1,null,1,1]
[2,null,1,2,1]
[3,null,1,3,3,1]
[4,null,1,4,6,4,1]
[5,null,1,5,10,10,5,1]
[6,null,1,6,15,20,15,6,1]
[7,null,1,7,21,35,35,21,7,1]
[8,null,1,8,28,56,70,56,28,8,1]
[9,null,1,9,36,83.999999999999986,126,126,83.999999999999986,36,9,1]
[10,null,1,10,45,120,209.99999999999997,252,209.99999999999997,120,45,10,1]
[11,null,1,11,55,165,330,461.99999999999994,461.99999999999994,330,165,55,11,1]
[12,null,1,12,66,220,495,792,923.99999999999977,792,495,220,66,12,1]
[13,null,1,13,78,286,715,1287,1716,1716,1287,715,286,78,13,1]
[14,null,1,14,91,364,1001,2002,3002.9999999999995,3432,3002.9999999999995,2002,1001,364,91,14,1]
[15,null,1,15,105,455.00000000000006,1365,3003,5005,6434.9999999999991,6434.9999999999991,5005,3003,1365,455.00000000000006,105,15,{"$f":"COMBIN($A19,R$3)","v":1}]
[16,null,{"$f":"COMBIN($A20,C$3)","v":1},16,120,560,1820.0000000000002,4368,8008,11440,12869.999999999998,11440,8008,4368,1820.0000000000002,560,120,16,{"$f":"COMBIN($A20,S$3)","v":1}]
[17,null,1,17,136,680,2380,6188.0000000000009,12376,19448,24310,24310,19448,12376,6188.0000000000009,2380,680,136,17,1]
[18,null,1,18,153,816,3060,8568,18564.000000000004,31823.999999999996,43758,48619.999999999993,43758,31823.999999999996,18564.000000000004,8568,3060,816,153,18,1]
[19,null,1,19,171,969,3876,11628,27132,50388.000000000007,75581.999999999985,92378,92378,75581.999999999985,50388.000000000007,27132,11628,3876,969,171,19,1]
[20,null,1,20,190,1140,4845,15503.999999999998,38760,77520,125970.00000000001,167960,184756,167960,125970.00000000001,77520,38760,15503.999999999998,4845,1140,190,20,1]
[21,null,1,21,210,1330,5985,20349,54264,116280,203490,293930.00000000006,352716,352716,293930.00000000006,203490,116280,54264,20349,5985,1330,210,21,1]
[22,null,1,22,231,1540,7315,26334,74613,170544,319770,497420,646646.00000000012,705432,646646.00000000012,497420,319770,170544,74613,26334,7315,1540,231,22,1]
[23,null,1,23,253,1771,8855,33649.000000000007,100947,245157,490314,817190,1144066.0000000002,1352078.0000000002,1352078.0000000002,1144066.0000000002,817190,490314,245157,100947,33649.000000000007,8855,1771,253,23,1]
[24,null,1,24,276,2024.0000000000002,10626,42503.999999999993,134596.00000000003,346104,735471,1307504,1961256,2496144.0000000005,2704156.0000000009,2496144.0000000005,1961256,1307504,{"$f":"COMBIN($A28,S$3)","v":735471},346104,134596.00000000003,42503.999999999993,10626,2024.0000000000002,276,24,1]
[25,null,1,25,300,2300,12650.000000000002,53129.999999999993,177099.99999999997,480700.00000000012,1081575,2042975,3268759.9999999995,4457400,5200300.0000000009,5200300.0000000009,4457400,3268759.9999999995,2042975,1081575,480700.00000000012,177099.99999999997,53129.999999999993,12650.000000000002,2300,300,25,1]
[26,null,1,26,325,2600,14950,65780.000000000015,230230,657799.99999999988,1562275.0000000005,3124550,5311735,7726160,9657700,10400600.000000002,9657700,7726160,5311735,3124550,1562275.0000000005,657799.99999999988,230230,65780.000000000015,14950,2600,325,26,1]
[27,null,1,27,351,2925,17550,80730,296010,888030,2220074.9999999995,4686825.0000000009,8436285,13037895,17383860,20058300,20058300,17383860,13037895,8436285,4686825.0000000009,2220074.9999999995,888030,296010,80730,17550,2925,351,27,1]
[28,null,1,28,378,3276,20475,98280.000000000015,376740,1184040.0000000002,3108105,6906899.9999999981,13123110.000000004,21474180,30421755,37442160,40116600,37442160,30421755,21474180,13123110.000000004,6906899.9999999981,3108105,1184040.0000000002,376740,98280.000000000015,20475,3276,378,28,1]
[29,null,1,29,406,3654.0000000000005,23751,118754.99999999999,475020.00000000012,1560780,4292145.0000000009,10015005,20030009.999999993,34597290.000000007,51895935,67863915,77558760,77558760,67863915,51895935,34597290.000000007,20030009.999999993,10015005,4292145.0000000009,1560780,475020.00000000012,118754.99999999999,23751,3654.0000000000005,406,29,1]
[30,null,1,30,435,4059.9999999999995,27405.000000000004,142506,593774.99999999988,2035800.0000000005,5852925,14307150.000000004,30045015,54627299.999999978,86493225.000000015,119759850,145422675,155117520,145422675,119759850,86493225.000000015,54627299.999999978,30045015,14307150.000000004,5852925,2035800.0000000005,593774.99999999988,142506,27405.000000000004,4059.9999999999995,435,30,1]
[31,null,1,31,465,4495,31464.999999999996,169911.00000000003,736281,2629574.9999999995,7888725.0000000019,20160075,44352165.000000015,84672315,141120524.99999994,206253075.00000003,265182525,{"$f":"COMBIN($A35,R$3)","v":300540195},300540195,265182525,206253075.00000003,141120524.99999994,84672315,44352165.000000015,20160075,7888725.0000000019,2629574.9999999995,736281,169911.00000000003,31464.999999999996,4495,465,31,1]
[32,null,{"$f":"COMBIN($A36,C$3)","v":1},32,496,4960,35960,201375.99999999997,906192.00000000023,3365856,10518299.999999998,28048800.000000007,64512240,129024480.00000004,225792840,347373599.99999988,471435600.00000012,565722720,601080390,565722720,471435600.00000012,347373599.99999988,225792840,129024480.00000004,64512240,28048800.000000007,10518299.999999998,3365856,906192.00000000023,201375.99999999997,35960,4960,496,32,{"$f":"COMBIN($A36,AI$3)","v":1}]
[33,null,1,33,528,5455.9999999999991,40920,237336,1107567.9999999998,4272048.0000000009,13884156,38567099.999999993,92561040.00000003,193536720,354817320.00000012,573166440,818809199.99999964,1037158320.0000002,1166803110,1166803110,1037158320.0000002,818809199.99999964,573166440,354817320.00000012,193536720,92561040.00000003,38567099.999999993,13884156,4272048.0000000009,1107567.9999999998,237336,40920,5455.9999999999991,528,33,1]
[34,null,1,34,561,5984,46375.999999999993,278256,1344904,5379615.9999999991,18156204.000000004,52451256,131128139.99999997,286097760.00000012,548354040,927983760.00000024,1391975640,1855967519.9999993,2203961430.0000005,2333606220,2203961430.0000005,1855967519.9999993,1391975640,927983760.00000024,548354040,286097760.00000012,131128139.99999997,52451256,18156204.000000004,5379615.9999999991,1344904,278256,46375.999999999993,5984,561,34,1]
[35,null,1,35,595,6545,52360,324631.99999999994,1623160,6724519.9999999991,23535819.999999996,70607460.000000015,183579396,417225899.99999988,834451800.00000036,1476337800,2319959400.0000005,3247943160,4059928949.9999986,4537567650.000001,4537567650.000001,4059928949.9999986,3247943160,2319959400.0000005,1476337800,834451800.00000036,417225899.99999988,183579396,70607460.000000015,23535819.999999996,6724519.9999999991,1623160,324631.99999999994,52360,6545,595,35,1]
[36,null,1,36,630,7139.9999999999991,58905,376992,1947791.9999999995,8347680,30260339.999999996,94143279.999999985,254186856.00000006,600805295.99999988,1251677699.9999995,2310789600.0000014,3796297200,5567902560.000001,7307872110,8597496599.9999962,9075135300.0000019,8597496599.9999962,7307872110,5567902560.000001,3796297200,2310789600.0000014,1251677699.9999995,600805295.99999988,254186856.00000006,94143279.999999985,30260339.999999996,8347680,1947791.9999999995,376992,58905,7139.9999999999991,630,36,1]
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