UC Science Building Testbed Meeting 16 Sep 2002

1. UC Science Building TestbedMeeting 16 Sep 2002 Porter, Beck, & Shaikhutdinov

2. Methodology Overview 2

3. Decision Basis • Applies to an operational unit for a given planning period T, location O, and design D • Probability of operational failure • Operational failure occurs if any component that is critical for operations fails • Probability of life-safety failure • Life-safety failure occurs if any component that is critical for operations fails • Probability distribution of repair cost • Probability distribution of repair duration 3

4. Decision Variables • Applies to an operational unit • DVO:binary RV for operational state = 1  operational failure • DVL: binary RV for life-safety state = 1  life-safety failure • CR = repair cost, a scalar RV • DR = repair duration, a scalar RV • Goal: P[DVO=1 | T, O, D] P[DVL=1 | T, O, D] FCR|T,O,D(cr|t,o,d) – a CDF of repair cost given T,O,D FDR|T,O,D(dr|t,o,d) 4

5. Damage Measures • Applies to a component • DMR,i: binary RV for component i requiring repair or replacement • DMR,i = 1  component requires repair or replacement • Assume repair or replacement required if: • Overturns (including sliding off bench or shelf) • Impact sufficient to damage items • Stored in equipment that overturns • DMO,i: binary RV for operation-critical-component i operational state • DMO,i = 1  operational failure of component • Operational failure means • Operation-critical equipment or specimen & DMR,i = 1 • Door of refrigerator containing operation-critical specimens opens, or • DML,i: binary RV indicating component i life-safety state • DML,i = 1  life-safety failure of component • Life-safety failure means • Life-safety hazard = “D” & overturns (O/T) or • Chemical hazard ≠ “N” & overturns or • Unrestrained weighty object & achieves momentum sufficient to cause trauma • Unrestrained weighty object & displacement is great enough to block egress 5

6. DV|DM for Equipment • DVO = maxi(DMO,i) • DVL = maxi(DML,i) • CR = ΣDMR,iCR,i • CR,i = uncertain repair or replacement cost, equipment component i. The equation is different for construction. • DR = Max(DMR,iDR,I) • DR,i = uncertain repair or replacement time, equipment component i. The equation is different for construction. 6

7. DV|DM for Construction Cost • CR = (1 + CO&P)SjSdNj,dCj,d CR = repair cost CO&P = overhead & profit, ~U(0.15, 0.20) j = index of assembly type d = index of damage state Nj,d = number of assemblies of type j in state d Cj,d = unit cost to restore assemblies of type j from state d, ~LN(mCj,d, bCj,d) 7

8. DV|DM for Construction Duration • TR,m = T0 + SjSdTj,dNj,d/nj,d + StNtTt TR,m = time to restore operational unit m T0 = design, contracting, and mobilization time Tj,d = time for one crew to restore one unit of assembly type j from state d, weeks. nj,d = number of crews available Nt = number of changes of trade Tt = change-of-trade delay, weeks. • Slow repair: high T0, low nj,d, high Tt, operational units restored in series (trades move from one unit to next) • Fast repair: low T0, high nj,d, low Tt, operational units restored in parallel 8

9. Assembly DM|EDP Fragility Functions • Fragility function gives the probability that an undesirable event (“failure”) occurs given input excitation (engineering demand parameter) • Possible equipment EDP • Peak diaphragm acceleration (PDA) or • Peak diaphragm velocity (PDV) or • Both • Need P[DML,i|EDPi], P[DMO,i|EDPi] • May depend on P[O/T|EDP], P[URD|EDP] or P[O/T or URD|EDP] 9

10. Sample Lab Makris will provide fragilities from top of list through fume hoods by 1 Dec. Hutchison will provide others. Draft fragilities to be delivered by early to mid-December 10

11. From Overturning and Unrestrained Displacement to Life-Safety and Operational Failure 11