reliability-based life-cycle economic analysis

Reliability-Based Life-Cycle Economic Analysis

Dr Bill Wessels, PE CREPrincipal Research Scientist

UAH Research InstituteReliability & Failure Analysis Lab

Dr Bill Wessels PE CRE 2

Part Alternatives

Five Vendors offer part that meets or exceeds reliability requirements

Acquisition Costs A - $6,064 B - $3,803 C - $5,398 D - $6,919 E - $4,376


Part Failure –

MaintenanceCycle

g

f 3P(t)

g

g

f 3P(t)

f 3P(t)

f preRepLog(t)

f postRepLog(t)

Part FailsSystem Down

Total Down Time

Part Completes pre-RepairLogistics Downtime

Part Completes Repair

Part Completes post-RepairLogistics Downtime

System Returns to Service


Labor Allocation & Costs/hr – Part Alpha

Labor Category rate/ hr pre-Repair Repair post-Repair pre-Repair Repair post-Repair

Supervisor $91.81 0.33 0.6 0.25 $30 $55 $23

Master Tech 1 $97.55 0.33 1.5 0.25 $32 $146 $24

Master Tech 2 $86.07 0 0.5 0 $0 $43 $0

J ourneyman 1 $74.59 0.25 1 0 $19 $75 $0

J ourneyman 2 $57.38 0 0.75 0 $0 $43 $0

Helper $45.90 2 3 1 $92 $138 $46

Maintenance planner $78.05 0.25 0.33 0.5 $20 $26 $39

Supply clerk $39.03 0.33 0.5 0.25 $13 $20 $10

$205 $545 $142

Part A Labor Allocation/ hrO & M Cost Estimation - Yr 1 Part A Labor Cost/ hr


Labor Allocation & Costs/hr – Parts Beta & Charlie


Supervisor $94.84 0.5 0.75 0.25 $46 $69 $23

Master Tech 1 $100.77 0.5 1.25 0.25 $49 $122 $24

Master Tech 2 $88.91 0 0.75 0 $0 $65 $0

J ourneyman 1 $77.06 0.33 1 0 $25 $75 $0

J ourneyman 2 $59.27 0 2 0 $0 $115 $0

Helper $47.42 2 3 1 $92 $138 $46


Supply clerk $40.31 0.33 0.5 0.25 $13 $20 $10

$243 $628 $142


Supervisor $97.97 0.33 0.5 0.25 $30 $46 $23

Master Tech 1 $104.09 0.33 2.25 0.25 $32 $219 $24

Master Tech 2 $91.85 0 0.75 0 $0 $65 $0

J ourneyman 1 $79.60 0.25 0.25 0 $19 $19 $0

J ourneyman 2 $61.23 0 1.5 0 $0 $86 $0

Helper $48.98 2 3.33 1 $92 $153 $46


Supply clerk $41.64 0.33 0.5 0.25 $13 $20 $10

$205 $633 $142

Part B Labor Allocation/ hr

Part C Labor Allocation/ hr

O & M Cost Estimation - Yr 2


Part B Labor Cost/ hr

Part C Labor Cost/ hr


Labor Allocation & Costs/hr – Parts Delta & Echo


Supervisor $101.20 0.25 0.33 0.25 $23 $30 $23

Master Tech 1 $107.53 0 0 0 $0 $0 $0

Master Tech 2 $94.88 0.25 0.75 0.25 $22 $65 $22

J ourneyman 1 $82.23 0 0 0 $0 $0 $0

J ourneyman 2 $63.25 0.33 0.75 0 $19 $43 $0

Helper $50.60 2 1 1 $92 $46 $46


Supply clerk $43.02 0.33 0.5 0.25 $13 $20 $10

$188 $229 $139


Supervisor $104.54 0.33 0.5 0.25 $30 $46 $23

Master Tech 1 $111.07 0.33 1 0.25 $32 $98 $24

Master Tech 2 $98.01 0 0.5 0 $0 $43 $0

J ourneyman 1 $84.94 0.25 1 0 $19 $75 $0

J ourneyman 2 $65.34 0 0.67 0 $0 $38 $0

Helper $52.27 2 3 1 $92 $138 $46


Supply clerk $44.44 0.33 0.5 0.25 $13 $20 $10

$205 $483 $142

Part E Labor Cost/ hr

Part D Labor Allocation/ hr

Part E Labor Allocation/ hr



Part D Labor Cost/ hr


Overhead Costs

Retrieval Vehicle -$51.40

Overhead Crane -$13.32

Facility -$268.19 -/ bay-hr

Lost Opportunity Cost/ hr Estimation

-$6,355

Capital Cost/ hr Estimation


Deterministic Part Alternatives

Deterministic Part Summary I nf ormation

Part h b g q h b g m preRep postRep L

Alpha 35.2 6.67 390 423 0.56 2.25 3.15 3.65 5.53 1.51 7.04

Beta 16.8 2.97 295 310 0.91 2.46 3.65 4.46 5.53 1.51 7.04

Charley 25.3 6.67 450 474 0.55 2.25 6.25 6.74 5.53 1.51 7.04

Delta 48.9 7.93 642 688 0.67 3.05 4.33 4.93 5.53 1.51 7.04

Echo 18.5 2.15 401 417 1.55 2.57 3.67 5.05 5.53 1.51 7.04

Failure Math Model Repair Math Model System LDT


Part A Baseline Simulation

Results f rom 59 runs of sim time 21000-hrs

Final_Results_Report f or Aw.rbd

Min Mean Max St.Dev SEM

Availability 0.97436 0.97560 0.97685 0.00052 0.00007

MTBDE 426.28 426.82 427.37 0.23 0.030

MDT 10.13 10.68 11.22 0.23 0.030

MMT 3.58 3.65 3.72 0.04 0.005

LDT 7.03

System_Failures 48 48 48 0 0.000

Green_Percent 97.44 97.56 97.68 0.052 0.007

Red_Percent 2.32 2.44 2.56 0.052 0.007


Part B Baseline Simulation


Final_Results_Report f or Bw.rbd


Availability 0.96304 0.96452 0.96591 0.00067 0.00009

MTBDE 311.14 311.61 312.06 0.22 0.028

MDT 11.01 11.46 11.94 0.22 0.028

MMT 4.37 4.46 4.55 0.040 0.005

LDT 7.01

System_Failures 65 65 65 0 0.000

Green_Percent 96.30 96.45 96.59 0.067 0.009

Red_Percent 3.41 3.55 3.70 0.067 0.009


Part C Baseline Simulation


Final_Results_Report f or Cw.rbd


Availability 0.97074 0.97190 0.97327 0.00048 0.00006

MTBDE 474.08 475.03 486.08 2.09 0.27

MDT 13.05 13.74 14.29 0.24 0.031

MMT 6.67 6.74 6.82 0.034 0.004

LDT 6.99

System_Failures 42 42.97 43 0.18 0.024

Green_Percent 97.07 97.19 97.33 0.048 0.006

Red_Percent 2.67 2.81 2.93 0.05 0.006


Part D Baseline Simulation


Final_Results_Report f or Dw.rbd


Availability 0.98226 0.98321 0.98417 0.00040 0.00005

MTBDE 687.58 699.11 712.64 12.00 1.56

MDT 11.08 11.94 12.71 0.30 0.039

MMT 4.85 4.93 5.02 0.041 0.005

LDT 7.01

System_Failures 29 29.54 30 0.502478 0.065

Green_Percent 98.23 98.32 98.42 0.040 0.005

Red_Percent 1.58 1.68 1.77 0.040 0.005


Part E Baseline Simulation


Final_Results_Report f or Ew.rbd


Availability 0.97103 0.97223 0.97367 0.00061 0.00008

MTBDE 416.28 422.85 425.98 4.06 0.53

MDT 11.46 12.08 12.68 0.25 0.032

MMT 4.85 5.06 5.21 0.080 0.010

LDT 7.02

System_Failures 48 48.29 49 0.456782 0.059

Green_Percent 97.10 97.22 97.37 0.061 0.008

Red_Percent 2.63 2.78 2.90 0.061 0.008


Tests of Hypotheses for Means

D A = Ai - Aj Dq = q i - q j

Part Alpha Beta Charley Delta Part Alpha Beta Charley Delta

Beta 0.00563 Beta 115.21

Charley 0.00548 -0.00015 Charley -48.21 -163.42

Delta -0.00144 -0.00706 -0.00691 Delta -272.28 -387.49 -224.08

Echo 0.00340 -0.00223 -0.00208 0.00483 Echo 3.98 -111.23 52.18 276.26

ttest = D A/ sqrt(sem2i + sem2

j) ttest = Dq / sqrt(sem2i + sem2

j)

Beta 51.00 Beta 2815.79

Charley 59.15 -1.39 Charley -176.03 -597.14

Delta -16.74 -69.78 -84.80 Delta -174.23 -247.96 -141.28

Echo 32.59 -19.01 -20.64 51.11 Echo 7.51 -210.02 87.73 167.47

p-Value = T.DI ST.2T(ttest,n ) | n = ni + nj - 2 p-Value = T.DI ST.2T(ttest,n ) | n = ni + nj - 2

Beta 0.000 Beta 0.000

Charley 0.000 0.168 Charley 0.000 0.000

Delta 0.000 0.000 0.000 Delta 0.000 0.000 0.000

Echo 0.000 0.000 0.000 0.000 Echo 0.000 0.000 0.000 0.000

Test of Hypotheses f or Mean Availability Test of Hypotheses f or MTBF


Costs Table – Part Alpha


Final_Results_Report f or Alpha Lost Op

Min Mean Max pre-Repair Repair post-Repair Spare Ret Veh OH Crane Fac

q 426.28 426.82 427.37 -$6,064

m 3.58 3.65 3.72 -$545.06 -$48.62 -$978.91

MDT 10.13 10.68 11.22 -$67,841L 6.41 7.03 7.63

L preRep 5.03 5.52 6.00 -$205.34 -$283.67L postRep 1.37 1.51 1.64 -$142.03

Part A Labor Cost/ hr Materials & Overhead


Costs Table – Part Beta

Final_Results_Report f or Baker Lost Op

Min Mean Max pre-Repair Repair post-Repair Spare Ret Veh OH Crane Facq 311.14 311.61 312.06 -$3,803m 4.37 4.46 4.55 -$627.68 -$59.38 -$1,195.51

MDT 11.01 11.46 11.94 -$72,844L 6.47 7.01 7.57L preRep 5.08 5.50 5.95 -$243.50 -$282.85L postRep 1.39 1.50 1.62 -$142.03

Part B Labor Cost/ hr Materials & Overhead

Costs Table – Part CharlieFinal_Results_Report f or Charlie Lost Op



Part C Labor Cost/ hr Materials & Overhead


Costs Table – Part Delta

Final_Results_Report f or Delta Lost Op



Part D Labor Cost/ hr Materials & Overhead

Costs Table – Part EchoFinal_Results_Report f or Echo Lost Op



Part E Labor Cost/ hr Materials & Overhead


Engineering Economic Analysis

rd = APRn = qm = CP/yr i = rd/mA = uniform cost per hrPV[A] = PV(i, n, A)F = S [Costs at n]PV[F]= PV(i, n,_, F)NPV = PV[A] + PV[F]AEquiv = PMT(i, n, NPV)


Part A Life-Cycle Economic AnalysisPart A Notes:

nTTF 426.82 = q

AI CC -$2.35 = I CC/ hr

FpreRep -$1,133 =L preRep-hrs*Part pre-Repair LDT Labor Cost/ hr

FTTR -$1,990 =m -hrs*Part Repair Labor Cost/ hr

FPostRep -$214 =L postRep-hrs*Part post-Repair LDT Labor Cost/ hr

FSpare -$6,064 = Burdened Part Cost (Unit Spare Strategy)

FRV $284 =L preRep-hrs*Retrieval Vehicle Cost/ hr

FOC -$49 =m -hrs*Overhead Crane Cost/ hr

FFac -$979 =m -hrs*Facility Cost/ Bay-hrS Fi -$10,144 =Sum(Fi)

PV(AI CC) -$996 =PV of I CC Unif orm Cost/ hr f or q -hrs

PV(S Fi) -$10,001 =PV of Sum(Fi)

PV(TTFA) -$10,997 =PV of Part Expenses @ q -hrs

AEquv(TTFA) -$25.95 =Unif orm Equivent Cost/ hr f or PV of Part Expenses

FLostOp(PartA) -$142,571 =Total Downtime-hrs*Lost opportunity Cost/ hr

PVA(FLostOp) -$140,557 =PV of FLostOp Cost f or q -hrs

AEquv(FLostOp-A) -$331.66 =Unif orm Equivent Cost/ hr f or PV of Lost Opportunity Costs f or q -hrs

F(Part A) -$153,718 =Sum FV of Part Expenses and FV of Lost Opporrtunity Costs

PV(Part A) -$151,554 =Sum PV of Part Expenses and FV of Lost Opporrtunity Costs

AEquv(Part A) -$357.61 =Sum Unif orm Equivalent of Part Expenses and FV of Lost Opporrtunity Costs

Part A Economic Analysis


Part Alternatives Life-Cycle Economic AnalysesPart A Part B Part C Part D Part E

nTTF 426.82 311.61 475.03 699.11 422.85

AI CC -$2.35 -$2.35 -$2.35 -$2.35 -$2.35

FpreRep -$1,133 -$1,340 -$1,128 -$1,033 -$1,132

FTTR -$1,990 -$2,798 -$4,268 -$1,130 -$2,443

FPostRep -$214 -$213 -$213 -$209 -$214

FSpare -$6,064 -$3,803 -$5,398 -$6,919 -$4,376

FRV $284 $283 $282 $283 $283

FOC -$49 -$59 -$90 -$66 -$67

FFac -$979 -$1,196 -$1,809 -$1,323 -$1,358

S Fi -$10,144 -$9,126 -$12,622 -$10,397 -$9,306

PV(AI CC) -$996 -$728 -$1,108 -$1,624 -$987

PV(S Fi) -$10,001 -$9,032 -$12,424 -$10,157 -$9,175

PV(TTFA) -$10,997 -$9,760 -$13,531 -$11,781 -$10,162

AEquv(TTFA) -$25.95 -$31.49 -$28.71 -$17.05 -$24.20

FLostOp(PartA) -$142,571 -$153,085 -$183,437 -$183,437 -$161,313

PVA(FLostOp) -$140,557 -$151,504 -$180,555 -$179,212 -$159,055

AEquv(FLostOp-A) -$331.66 -$488.73 -$383.12 -$259.35 -$378.81

F(Part A) -$153,718 -$162,944 -$197,175 -$195,476 -$171,612

PV(Part A) -$151,554 -$161,264 -$194,087 -$190,993 -$169,217

AEquv(Part A) -$357.61 -$520.21 -$411.83 -$276.40 -$403.02

Lif e-Cycle Economic Analysis


Part Alternatives Economic Ranking

1 - Lowest

5 - highest

Legend

reliability-based life-cycle economic analysis

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