1. PEER UC Science Building Testbed Meeting 16 Sep 2002 Porter, Beck, & Shaikhutdinov

2. 2 Methodology Overview

3. 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

4. 4 Decision Variables Applies to an operational unit DV O : binary RV for operational state = 1  operational failure DV L : binary RV for life-safety state = 1  life-safety failure C R = repair cost, a scalar RV D R = repair duration, a scalar RV Goal: P[DV O =1 | T, O, D] P[DV L =1 | T, O, D] F CR|T,O,D (c r |t,o,d) – a CDF of repair cost given T,O,D F DR|T,O,D (d r |t,o,d)

5. 5 Damage Measures Applies to a component DM R,i : binary RV for component i requiring repair or replacement –DM R,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 DM O,i : binary RV for operation-critical-component i operational state –DM O,i = 1  operational failure of component –Operational failure means Operation-critical equipment or specimen & DM R,i = 1 Door of refrigerator containing operation-critical specimens opens, or DM L,i : binary RV indicating component i life-safety state –DM L,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

6. 6 DV|DM for Equipment DV O = max i (DM O,i ) DV L = max i (DM L,i ) C R = ΣDM R,i C R,i –C R,i = uncertain repair or replacement cost, equipment component i. The equation is different for construction. D R = Max(DM R,i D R,I ) –D R,i = uncertain repair or replacement time, equipment component i. The equation is different for construction.

7. 7 DV|DM for Construction Cost C R = (1 + C O&P )  j  d N j,d C j,d CR = repair cost C O&P = overhead & profit, ~U(0.15, 0.20) j = index of assembly type d = index of damage state N j,d = number of assemblies of type j in state d C j,d = unit cost to restore assemblies of type j from state d, ~LN(  Cj,d,  Cj,d )

8. 8 DV|DM for Construction Duration T R,m = T 0 +  j  d T j,d N j,d /n j,d +  t N t T t T R,m = time to restore operational unit m T 0 = design, contracting, and mobilization time T j,d = time for one crew to restore one unit of assembly type j from state d, weeks. n j,d = number of crews available N t = number of changes of trade T t = change-of-trade delay, weeks. Slow repair: high T 0, low n j,d, high T t, operational units restored in series (trades move from one unit to next) Fast repair: low T 0, high n j,d, low T t, operational units restored in parallel

9. 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[DM L,i |EDP i ], P[DM O,i |EDP i ] –May depend on P[O/T|EDP], P[URD|EDP] or P[O/T or URD|EDP]

10. 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

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