@5-23-1995 @9:57 NASA-CR-197811 A VOL SCIENCE ASSESSMENT OF ANALYSIS ADMINISTRATION (Co_ M) CORPORATION _ _o/#noe.Appllc,atlons InmrnlHlonBl Corpormtion An _.Om_e¢ Commny (NASA-CR-197811) PROBABILISTIC RISK ASSESSMENT OF THF SPACE ORIGINAL PACE IS SHUTTLE. PHASF 3: A STUDY OF TNE OF PO_QUALIT_ PCTFNTIAL OF LOSING THE VEHICLE DURING N_INAL CPERATICN. VOLUME 4: SYSTEM MOCELS ANC DATA ANALYSIS (Science Applications International G3/16 N95-26401 Unclas 0049089 https://ntrs.nasa.gov/search.jsp?R=19950019981 2020-06-16T07:12:51+00:00Z t_ c_ i I If 'r, lvlr| - _il! le : o o P ! P o o m - ! - ilitlitilil illlil i !! 'i iii, I m.l1.t i ! . :, ,. I !,,!1_ _IIt 1_ ! 8111tI: .",--EIIIi>. iii-' ]! ....11 _ 1 I iiiii! o Ol Iq RI o Ol l-- m--i N Ni ! II ii! i. 'Jl|il iI il !il 8 II I ! ! Lill i i , li I_I 'i-_I !'Ii i : I C | ! I i ! I I If i t i ! ! 1 ! t l ! ill If t ! i .... i ..... i _! 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Hypothesis-2 Insufficient data to support a statistical analysis was available for the NASA Standard Initiators (NSIs) and NASA Standard Detonators (NSDs) however the components were found to be similar in both design and function as the Conf'med Detonating Fuses (CDFs). However due to additional elements in the NSI and NSD assemblies they were assumed to be 2-3 times more prone to fail than the CDF. Hypothesis-3 The data available for the Pyrotechnic Initiator Controllers (PICs) indicates that they are extremely reliable components however the fact that no actual failures have occurred makes the estimation of their failure rate difficult. As a conservative assumption, their failure rate was assumed to be on the same order of magnitude as the CDFs. Hypothesis-4 The ISRB use pyrogenic igniters for which a limited amount of failure data exists. For this reason the analyst made a conservative assumption based on the data available and conversations with USBI personnel. Hypothesis-5 This estimate concerned the possibility of an explosive device detonating without any external influences; an extremely rare event. A conservative • estimate was made which considered such an event to be 10 times less likely than an explosive device (CDF) failing to detonate on command. Hypothesis-6 The Booster Separation Motors (BSMs) have a limited amount of failure related data however it was agreed (USBI & MSFC) that the failure modes were approximately an order of magnitude (10 times) more likely than an explosive device (CDF) failing to detonate. I.-uJ _z_ q_ az w 0___ i m _u,Io_-_ _6 ww _1 ...I w o w n" r_ ,,,, o_ IJ_l_'l_ -_" _1_1"_ _ I_1 • , ._-_ _tu_ , , m m_ 'I[ _ ..2 w_ .oo _g,,, o6._ u___ _o_ m W CO W W n_ I-- 1-- O3 O_ n- O. UJ C_ om m rn O: m W L.U_ ,d* t.J _ < er W ...1 ,( w r-.D. i'w,i 4[ _3 ,_ n i > W OC: CO W W _C I-- iI J < n7 _c o: O. 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O,,, oO_ _'_ ___8 _ 0 c_ m _J W n- W W I-- I- ._I < U_ rn CC _C O. > W 0 °_ m rn _C o,,a oOOC oco N <( m ._._ 8 >Q,,, ___ I_1x,,--_'- m o ___,- _ t,.- _ [hJ w w'<_ l_->uJ Q nr_ It..)W _ m I_ i _- _-LU lUJ c_ r_LIJ 9-r loaF_" F'_Ot- Io_ m _,_-2 011:_ w i,- _ irr 'T-__ I,- w _g m_ u- 03 0 C_ t3_ n i Wl n'l Wl Wl OCl I-_ I--I I,i rnl OCl (/)1 COl nl Wl •-- i .-_1 OCll rrl COl I | _> o C_ _7 m w OC W W O: I- .-I _0 OC: _C o. > W C_ o_ °_ I CO OC m r_ r_ 0 0 cO H o crj 0 0 03 r..9 I..-I 0 Izl o I--I IM CI 0 o o o o Go cq co _-I o o T-t 00 r-t o _--I r-I _o _o o o0 o 00 cr_ r_ o 0o "_ c,_ o4 o,] o 0 o_ o o t--I ,,.o o [..... ,,.o ,-t o,l cx] 00 _ _ 0 0 -_C_ _ _-_ _._ 0_0 0 -_ _:_ _ 0 _ 0 _ • • _ O- _ _ _ ,,_ H _ r_ r_ r_ 0 _ _ _ _ 0 _ _ 0 o_ I_ _ _ 0 0 _ RSRM Joint Leak Data Joint Component Polysutfide Wiper O-Ring Vent Port Plug Primary O-Ring (nozzleandcasecombined) (47 mo(om counled as 23 lests) Vent Port Plug Second O-Ring (nozzle and case combined) Closure Vent Port Plug (nozzle and case combined) Primary O-Ring Leak Check Port Plug (case/nozzle/igniter combined) Stat-O-Seal Secondary O-Ring NOZZLE-TO-CASE JOINTS Source Flights 1-37r39r41 Static Tests Leak Hot Leak Pot_ll_ RdncJs Checks Factor Failures 78 5 9 1 Flights 1-37r39,41 Static Tests Totals: 87 6 6 78 NUES/TPTArOM6 Totals: Flights 1-37r39r41 Static Tests TPTA 1.3r2.1 r2.2 NUES/JES 3C SPC (701bMotor) Totals: 4 Flights 1-37r39_41 Static Tests 23 34 9 87 234 3O 23 287 312 0.2 0.9 40 TPTA 1.3,2.1,2.2 3 NUES/JES 3C 3 Totals: 6 352 0.9 0 312 40 Flights 1-37r39r41 Static Tests 2 Totals: 4 352 0.6 0 78 TPTA 1.3r2.1 NUES/JES 3C Flights 1-37r39r41 Static Tests 11 TPTA 1.2r2.1 NUES 3A,PVM1 Totals: Flights 1-37r39_41 Static Tests SRM01-51 L (rid) SRM01-51L (noz) Totals: 100 87 780 100 Case 880 9(I)00 5040 0.6 Igniter Nozzle Flights 1-37r39r41 Static Tests 0.6 10 TPTA 1.3 1 NUES 3B 1 Totals: 2 88 0.9 0 100 6776 T_als: 200 20816 0.9 0 78 RSRMJointLeakData Joint Component S&A Primary Gasket S&A Secondary Gasket COMMON CAUSE Leak Check Port Plug (case/nozzle/igniter) OPT Primary O-Ring (3/igniter) OPT Secondary O-Ring (3/igniter) COMMON CAUSE Rotor Primary O-Rings Rotor Secondary O-Rings COMMON CAUSE SII Primary O-Ring SII Secondary O-Ring IGNITER INTERNAL JOINTS Leak Hot Leak Potentiality Source Flrin_ls Checks Factor Failures 12Static Tests SRM, HPM r RSRM Totals: 128 SRM, HPM, RSRM 12 128 140 140 0.6 0 Static Test 12 128 Totals: Flights 1-37r39T41 Static Tests 140 SRM01.51 L (rid) SRM01-51L (noz) Totals: SRM,HPMrRSRM Minuteman 78O 100 0.9 11 880 0.6 0 Static Tests 36 384 3300 Totals: 3720 0 TPTA-2.2 3 0 JES-3C 3 24 TPTA-1.3 3 256 Totals: 9 280 0.9 0 Static Tests 12 12 128SRMrHPMrRSRM Totals: Static Tests SRMrHPMrRSRM Totals: SRMrHPMTRSRM Totals: 128 140 12 128 140 140 Static Tests 24 24 256 256 SRMTHPM_RSRM Totals: 0.6 0.9 280 280 0.9 0 Static Tests 2 24 256 28O 0.9 0 RSRM Joint Leak Data Joint Component INNER J-LEG Special Bolt O-Ring 14/i_lniter) Outer J-Leg Inner Gasket]Inner Seal Inner Gasket/Outer Seal Outer Gasket/Inner Seal Outer Gasket/Outer Seal Stat-O-Seals (36/igniter) Leak Check Port Plug (case/nozzle/igniter) IGNITER-TO-CASE JOINT Leak Hot Leak Potentiality Source Flrln_ls Checks Factor 1FSM-3 RSRM 23_35-37,39r41 Totals: 12 13 Static Test 48 48 SRM,HPM,RSRM 512 512 Totals: 560 560 0.6 0 FSM-3 1 12RSRM 23r35-37r39r41 Totals: blow-holes (RSRM) Static Tests SRM,HPMTRSRM Totals: blow-hole (RSRM) Static Tests SRMrHPMrRSRM Totals: blow-holes (RSRM) Static Tests SRM_HPMrRSRM Totals: Static Tests SRM_HPMrRSRM Totals: Totals: Case Igniter Nozzle Flights 1-37_39,41 Static Tests SRM01-51L (rid) SRM01-51L (noz) Totals: 13 6O 6O 6O 60 60 60 lO0 100 200 12 128 140 12 128 140 12 128 140 12 128 900O 5040 6776 20816 780 100 0.6 0.9 0.6 0.9 0 Fallures 4 7 11 880 0.6 0 RSRM Joint Leak Data CASE FIELD JOINT Joint Component J-Seal Capture Feature O-Ring Vent Port Plug Primary O-Ring (nozzle and case combined) (47 motors counted as 23 tests) Vent Port Plug Second O-Ring (nozzle and case combined) Closure Vent Port Plug (nozzle and case combined) Primary O-Ring Outer Gasket/Outer Seal Leak Check Prot Plug (case/nozzle/igniter combinded) Secondary O-Ring Source Flights 1-37r39r41 Static Tests JES 3A TPTA 1.1_ 2.1 Totals: Flights 1-37r39,41 Static Tests Leak Hot Leak PotenUal|ty Firings Checks Factor Failures 234 15 3 254 234 24 JES 3B 1 0 QM-6 1 2 PVM-1 1 1 Totals: 3 261 0.6 0 Flights 1-37r39r41 Static Tests TPTA 1.3T2.1r2.2 NUES/JES 3C SPC(701b Motor} Totals: 4 23 34 Flights 1-37,39,41 23 287 312 0.9 1 Static Tests 40 TPTA 1.3_2.1,2.2 3 NUES/JES 3C 3 Totals: 6 352 0.9 0 312Flights 1-37,39,41 Static Tests TPTA 1.3_2.1 NUES/JES 3C Totals: Flights 1-37r39,41 Static Tests 40 TPTA 1.3_2.112.2 JES3B/3C 352 234 27 0.5 27 TPTA 2.2 2 JES 3C 1 Totals: 3 261 0.9 0 Flights 1-37r39r41 Static Tests 4 7 11 880 0.5 0 SRM01-51L (rid) SRM01-51L (noz} Totals: Flights 1-37_39_41 static Tests 128 780 100 234 SRM_HPMIRSRM Totals: 2 Totals: 8 261 0.9 . 0 Static Tests 12 RSRMJointLeakData Joint Component RTV Backfill NOZZLE JOINT Hot Primary O-Ring Secondary O-Ring Stat-O-Seals Leak Check Port Plug Leak Leak Potentiality Source Firings Checks F=¢tor Failures Joint 1 g0 Joint 2 18 7 Joint 3 88 10 Joint 4 88 10 Joint 5 88 6 Totals: 372 38 Flight Static Tests Totals: Flight Static Tests Totals: Case Igniter Nozzle 24 Flights 1-37r39,41 Static Tests 14 38 100 39O 50 44O 39O 5O 440 9O0O 5040 0.6 0.9 100 6776 Totals: 200 20816 0.9 0 780 1o0 88O SRM01-51L (rid) SRM01-51L (noz) Totals: 11 0.6 --6_'-A-" A A--A-A--dR IIii • i -I 0 K 0 9.0 DEVELOPMENT OF PROBABILITY DISTRIBUTIONS FOR FAULT TREES The development of probability distributions for the fault trees is done using Bayesian updating methods. Prior probability distributions for failure rates are taken from the 1987 APU/HPU study, NPRD-95, [REP, IEEE Std. 500, WASH 1400, Shuttle experience and expert judgment. System level priors for the entire APU/HYD/WSB system (failure to start and failure to run distri- butions) are developed using component data mostly from the 1987 study. Bayesian updating was done at the system level using data found in the in-flight anomaly list (IFAS), PRACA re- ports, and Post Flight Mission Safety Evaluation Reports. Data obtained shows that there have been four APU shutdowns on ascent due to the water spray boiler failing to provide adequate cooling, and a near hydraulic system failure due to a massive hy- draulic leak during descent. Due to the fact that the APU/HYD/WSB systems have redundancy, i.e., they are a two-out-of- three or better system, common cause failures become a concern. The fault trees are evaluated using the Multiple Greek Letter (MGL) method to determine the common cause and independent failure rates Section 9.1 describes how the MGL method is used to determine the independent failure rates and common cause failure rates from the generic failure rate for each sequence. Section 9.2 describes the prior distributions used in the study. Fault trees are included in this sec- tion to show how prior distributions are calculated for APU/HYD/W'SB failure to start, APU/HYD/WSB failure to run, and APU turbine wheel runaway. 9.1 Models/Equations for Fault Tree Basic Events 9.1.1 List of Basic Events Table 9.1-1 is a complete list of the basic events found in the fault trees, and their two letter iden- tification code used throughout the model. 9.1.2 Assumptions Several assumptions have been made concerning data input probability distributions. The first is that given a common cause leak, all three APU units leak. The second assumption pertains to the detection/confirmtion of the leaks. If all three units leak, and a leak is detected in one unit, then the leaks in all units are assumed to be found. A third assumption concerns the restarts of APU units. All units will have to go through a restart process sometime during the reent_ process Some scenarios have APU hydrazine leaks detected, in which case an APU unit is shutdown dur- ing the entry sequence After an APU unit is shutdown, if another unit fails, then the shutdown unit is restarted. However, in the sequence, only one restart of the shutdown APU is considered. There are several reasons for this simplistic modeling. First, the reentry sequence will not begin until an APU unit is working to perform the flight controls check. Second, leaking APUs are shutdown only when a leak is detected and confirmed, and the probability of a leak being detected is only about one in twenty, so these scenario simplifications will not have a significant impact on the total risk. _._ 9-1 Identification Basic Event CE CF Flight critical equipment damaged given LL or TU Common cause failure to run CL Common cause leak CO No containment given turbine overspeed CS Common cause failure to start or run FIB ID IF IS LA LD _Hub breakup given turbine overspeed I I ilndependent/dependent failure to run (ascent) lindependent failure to run (ascent) plndependent failure to start or run (descent) |Leak detected/confirmed given all three APU units leak Leak detected/confirmed given that one APU unit leaks Own leakage induced failure (ascent)LF LK Leak in one APU unit LL Large exhaust gas or hydrazine leak LO Leakage from another unit induced failure (ascent) LS Leakage from other unit induced failure to start or run (descent) LU Leak undetected given that one APU unit leaks LZ Leak undetected given that all three APU units leak Ol 03 APU unit okay given that one other APU unit leaks unit okay given that all three APU units leak unit okay unit okay given that it leaks OK OL OS SI SR TU UL Own leakage induced failure to start or run (descent) Structural integrity of a/t compartment fails given LL or TU Successful restart of shutdown APU unit Turbine overspeed or hub failure at normal speed Unsuccessful single APU/HYD unit reentry, TAEM and landing Table 9.1-1: List of Basic Events and Descriptions 9.1.3 Derivation of Common Cause Failure Equations As components fail, it is not always entirely clear which failures are truly independent and which are common cause. In order to estimate the frequency of common cause failures from the total estimated frequency, several methods, such as the Multiple Greek Letter (MGL) or beta factor 9-2 methods,areused In thisanalysis,theMGL methodwasused Thelabelingof the APUunits is asfollows: if a singleAPU unit is leakinghydrazine,thenthat unit is labeledasunit 1, or if all three APU units are leaking hydrazine,then the unit that is shutdown (if the leaks are detected/confirmed) is labeled as unit 1. 9.1.3.1 One APU Unit Leaks Hydrazine During Reentrv_ TAEM and Landing (L0 Sequence 4 In this sequence, APU units 1 and 2, or 1 and 3, fail This is basically a 1 out of 3 system, de- noted Q(I/3) There are two wavs in which independent failures of this type can occur: Q_Q: and Q_Q3 For the common cause failures, there are also two ways that those may occur: Q__, and Qw Rewriting those terms in the MGL format using Q_ for independent failures and Q: for com- mon cause failure of two components yields the following equation for system failures: Q(I/3) =2Q2 +2Q_ In this form of the MGL method where we are dealing both with common cause failures for two systems and common cause failures for three systems. The MGL method defines two parameters: and y. Beta is the ratio of two and three unit common cause failures of each unit to all failures for each unit. Gamma is the ratio of three unit common cause failures to two and three unit com- mon cause failures. For each unit, beta is thus: 2Q_23 -- QI+2Q.,+Q3 and gamma is: Q3 Y = 2Q2-,2: Omitting the algebra, the single system and common cause for two system failures can be written as; Q1 = (1 - _)Q Q2 = ½(1 - 7)[30 Since Q represents the failures due to start or run failures, it should be rewritten as: Q =qs+_.t ':_)The LO descent initiating event state is equivalent to the IL0 ascent end state. 9-3 whereqs is the failure to start probability, and _t is the probability of a failure during the run time. ':33 If we substitute into Q( 1/37 for Q, Q: and Q, then the equation for failures becomes: O(1/3) = [( 1 - ¥+)13,q, + ( I - y, )13,.Xtl + 21( t - 13+.)q,-+( I - 13r)Xt] 2 This is the total failure rate+ We now need to relate the above equation to the fault tree basic events. The first term in the above equation is the common cause term, and does not need to be changed. The second term in the above equation needs to represent the independent failures as depicted in the fault tree. For example, if we examine the fault tree for the sequence 4 LOV with the initiating L0 state (one APU unit is leaking), then by analysis at the basic event level, the prob- ability of the component failures in the sequence can be expressed as: P(1,2 or 1,3) =P(I It,')P( 2 IU) + P( I IF)P(3 IF) + P( CCF) + P(1 IF)P(3 LO) + . . . where IF, CCF and LO where defined previously as independent failures, common cause failure, and own leak induced failure. Since we are only concerned about independent and common cause failures, we will ignore the fourth and remaining terms as being inapplicable to the determination of the common cause failure rate and the independent failure rate. If the independent failure rates are the same for all APU units, then the previous two expressions can be combined as: P(CCF) = [(1 - y_.)13,.q, +( I - y,.)13_kt] 2P(IF) 2 = 2[( 1 - 13,,.)c1_+ ( 1 - 13,.)_.tl2 If we reduce the independent failure rate probability, we get: P(IF) = I/I(1 - 13_)q_.+( 1 - 13r)_.tl: which reduces to: P(IF) = [(1 - 13_.)q_+( I - [3,.)_.tl Sequence 6 In this sequence, both APU units 2 and 3 have failed. This is basically a 1 out of 3 system, de- noted Q(1/3). There is one way in which independent failures of this type can occur: Q:Qs. For the common cause failures, there is also only one way that this may occur: Q_,3. Rewriting those terms in the MGL format using Q_ for independent failures and Q2 for common cause failure of two components yields the following equation for system failures: Q(l/3) = Q_ +Q2 As before, the single and common cause (for two systems) factors are defined as: Q I = ( 1 - 13)Q 02 = ½(1 - ¥)13Q ,\ _-'_In this analysis the 13, and [3r are given the same numerical value, and 2, and Z are given the same numerical value. ,3) For ascent sequences, _is the probability of basic event ID (or IF) in Table 9.3.1. For descent sequences q_ + _is the probability of a basic event IS in Table 9.3-1. 9-4 SinceQ representsthe failures due to start or run failures, it should be rewritten as: Q =qs +_,t where q_ is the failure to start probability, and _.t is the probability of a failure during the run time. If we substitute into Q(1/3) tbr Q,, Q_, and Q, then the equation for failures becomes: Q(1/3) = ½[(1 - ¥_)13_q, +( I -7,)[3r_.t] +[(1 - 13_)q, +(1 -- [_r)_l] 2 As before, we can see that the first term represents the common cause failure rate, and the second tern represents the independent failure rate. If we examine the fault tree for the sequence 6 LOV with the initiating LO state, then by analysis at the basic event level, the probability of the compo- nent failures in the sequence can be expressed as: P(2, 3) = P(2 IF)P(3 IF) +f'(("(7:) +P(2 IF)P(3 LO)+... where IF, CCF and LO where defined previously as independent failures, common cause failure, and own leak induced failure. Since we are only concerned about independent and common cause failures, we will ignore the third and remaining terms as being inapplicable to the determination of the common cause failure rate and the independent failure rate. If the independent failure rates are the same for all APU units, then the previous two expressions can be combined as: P(CCF) = ½[(l -y,.)13._q_ +(l -yr)13_.t] P(IF): = [(1 - [3s)q, +(1 - [3r)_.t] 2 If we reduce the independent failure rate probability, we get: P(IF) = _/[(l - 15s)q,. +(l - [_)_.tl: which reduces to_ P(If) = [(1 - [3_)q, + (i - 13_)_.t] This is the same expressions as determined in the Sequence 4 LOV. Sequence 7 In this sequence, since there is no leak detection, no distinction is made between which units fail and which do not. All three units fail, even though 1 out of 3 is needed for survival, so this is de- noted Q(I/3). There is one way in which independent failures of this type can occur: Q_Q,Q, For the common cause failures, there is also only one common cause for all three, QI:3. There are three combinations of pairs of common cause failures for two systems, i.e., Q_: and Q:3 is one pair, and three combinations of an independent failure and a common cause failure for two sys- tems, i.e., Q_ and Q:; and one pair. Rewriting those terms in the MGL format using Q_ for inde- pendent failures, Q: for common cause failures of two components and Qs for common _use failures of three components yields the following equation for system failures: Q(1/3) = Q3 + 3(__)1(._)2+ 3Q_ + (.)_ 9-5 Omittingthealgebra,thefailurescanbewrittenas: Q I = (1 - [3)Q Q2 = ½(1 - y)[sQ Q3 = Y_Q Substituting for Q_, Q, and Q, into Q(1/3) yields: , lit-vaF _"Q(1/3) = "_]Q + _(1 - [5)[3(1 - yjQ2 + 2___i._,..L2( l _ 13)[5(1 -y)Q2] +(1 - [3)3(2 3 If we examine the above expression, we see that there are four terms, which from left to right we'll call one, two, three and four. The third term is negligible because I It-y) R 2 _,., << 1 and is, furthermore, much less than the second term. As before: Q =qs +_.t where qs is the failure to start probability, and _.t is the probability of a failure during the run time. Substitute Q into Q(1/3) with the simplifying assumption yields: 3Q(1/3) = (ys[ssq_. + y,.[5,3.t) + 2{[( 1 - [ss)[3A 1 - y_)q2] + [(1 - [3A[L(1 - YAq,_]+ [(1 - [3,)[3 _( 1 - y,.)q.,._.t] + [( 1 - [3A[3A 1 - y,)_.2: ]} + [( 1 - [5_)q_ + ( 1 - [3,)_.tl 3 As before, we can see that the first term represents the common cause failure rate, and the second tern represents the independent failure rate. If we examine the fault tree for the sequence 7 LOV with the initiating L0 state, then by analysis at the basic event level, the probability of the compo- nent failures in the sequence can be expressed as: P( 1,2, 3) = P( 1 IF)P(2 1F)P( 3 IF) + P( CCF) + P( 1 LO)P( 2 IF)P(3 IF) +... where IF, CCF and LO where defined previously as independent failures, common cause failure, and own leak induced failure. Since we are only concerned about independent and common cause failures, we will ignore the third and remaining terms as being inapplicable to the determination of the common cause failure rate and the independent failure rate. If the independent failure rates are the same for all APU units, then the previous two expressions can be combined as: P(CCF) = y_[5,q,. + yr[5),.t + _{ [(1 - [3_)[5_(1 - y_)q_21 + [( 1 - [3ALL(1 - yAq_.t]+ [(1 - [3,)[3_( 1 - y_)q,_.tl + [(1 - [5,)[5,.( 1 -yA_?t2l } P(IF) = [(1 - [5_)q._+ ( 1 - [3,)_,.t] Sequence 11 ... In this sequence, two APU units fail, and since the event is undetected, no distinction is made as to which two have failed. System failures are thus defined as: ,., 2Q(1/3) = 3Q2 + -,Ql 9-6 Asbefore,thefailuresaredefinedas: Q,= II-_)Q Q_ =½(*-YI_Q Since Q represents the failures due to start and run failures, it should be rewritten as: Q=q_+kt where qs is the failure to start probability, and kt is the probability of a failure during the run time If we substitute into Q(1/3) for Qt, Q: and Q, then the equation for failures becomes: ,,p Q(1/3) = 3[(1 - y_)13,q, + (I - y, )[Lkt] + 3[( 1 - [3_)qs + (! - [3r)kt]" AS before, we can see that the first term represents the common cause failure rate, and the second tern represents the independent failure rate. If we examine the fault tree for the sequence 11 LOV with the initiating L0 state, then by analysis at the basic event level, the probability of the compo- nent failures in the sequence can be expressed as: P(2 fail) = P(1 IF)P(2 It,') + P(1 IF)P(3 IF) +P(2 IF)P(3 IF) + P(CCF) +P(2 IF)P(3 LO) +... where IF, CCF and LO where defined previously as independent failures, common cause failure, and own leak induced failure. Since we are only concerned about independent and common cause failures, we will ignore the fifth and remaining terms as being inapplicable to the determination of the common cause failure rate and the independent failure rate. If the independent failure rates are the same for all APU units, then the previous two expressions can be combined as: P(CCF) = }[(1 - ¥_.)13_.q+ (_- ¥,.)[3,.Z.,1 3P(IF) 2 = 3[(1 - [3_.)q, + (l - [3r)kt] 2 If we reduce the independent failure rate probability, we get: P(IF) = [{1- IL)q_+{1 - 13r)Z.tl Sequence 12 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for IL0 sequence 7 Sequence 16 This sequence occurs when APU/HYD systems l and 2 or l and 3 fail. The equations for inde- pendent system failures and common cause failures are the same as those described for L0 se- quence 4 9-7 Thissequencealsomodelstheremainingtwo APU units developing a common cause leak, given the initial leak in one unit. _ As described for OK sequence 21, the formula for common cause leakage is given by: P(CCF)= yLI3LX . + - 1- yL)X,:t Here, _t is the probability ot'the initial state, LO. So, since the conditional probability of devel- oping the common cause leak is multiplied against the initial state probability, and given that the first term in the equation is by far the dominant factor, the common cause conditional probability should be entered as: P(CCF) = YL[_L Sequence 18 This sequence occurs when APU/HYD systems 2 and 3 fail. The equations for independent sys- tem failures and common cause failures are the same as those described for L0 sequence 6. The equation for a common cause leak is the same as that described for L0 sequence 16. Sequence 19 This sequence occurs when all APU/HYD systems fail. The equations for independent system failures and common cause failures are the same as those described for L0 sequence 7. The equa- tion for a common cause leak is the same as that described for L0 sequence 16. Sequence 23 This sequence occurs when any two out of the three APU/HYD systems fail. The equations for independent system failures and common cause failures are the same as those described for L0 se- quence 11. The equation for a common cause leak is the same as that described for L0 sequence 16. Sequence 24 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for L0 sequence 7. The equation for a common cause leak is the same as that described for L0 sequence 16. 9.1.3.2 All Three APU Units Leak Hydrazine During Reentry_ TAEM and Landing {LT state Sequence 4 This sequence occurs when APU/HYD systems 1 and 2 or 1 and 3 fail. The equations for inde- pendent system failures and common cause failures are the same as those described for L0 se- quence 4. _) _'L is the frequency of event LK in Table 9,3-1. 9-8 Sequence 6 This sequence occurs when APU/HYD systems 2 and 3 fail. The equations for independent sys- tem failures and common cause failures are the same as those described for L0 sequence 6. Sequence 7 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for L0 sequence 7. Sequence 11 This sequence occurs when any two out of the three APU/HYD systems fail. The equations for independent system failures and common cause failures are the same as those described for L0 se- quence 11. Sequence 12 This sequence occurs when any two out of the three APU/HYD systems fail The equations for independent system failures and common cause failures are the same as those described for L0 se- quence 12 9.1.3.3 All Three APU Units are OK During Reentry_ TAEM and Landing (OK State) Sequence 4 This sequence occurs when any two out of the three APU/HYD systems fail The equations for independent system failures and common cause failures are the same as those described for L0 se- quence 11 Sequence 5 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for L0 sequence 7. Sequence 9 This sequence occurs when APU/HYD systems 1 and 2 or 1 and 3 fail. The equations for inde- pendent system failures and common cause failures are the same as those described for L0 se- quence 4. This sequence also involves a common cause treatment of APU leaks. Here, we are modeling any one of the three APUs develops a leak, which is basically a 1 out of 3 system, denoted as Q( I/3) There are three ways in which independent failures of this type can occur: Q_, Q_, or Q_. Rewrit- ing those terms in the MGL format using Q, for the independent failures yields the following equation for system failures: Q(1/3) = 3Q_ As before, the failures are identified as: Q,=11 9-9 Since Q in this case represents leakage failures over the exposure time, Q is replaced bv: Q=kct where _'L is the leakage failure rate and t is the exposure time of the system. If we substitute into Q(1/3) for QI, then the equation for failures becomes: O(1/3) = 3(1 - _3c)_._t Since independent failures are the only contributors in this equation, we get: P(IF) = 3( 1 - [3L)kct Sequence 11 This sequence occurs when APU/HYD systems 2 and 3 fail. The equations for independent sys- tem failures and common cause failures are the same as those described for L0 sequence 6. The equation for independent leaks is the same as that described for OK sequence 9. Sequence 12 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for L0 sequence 7 The equation for independent leaks is the same as that described for OK sequence 9. Sequence 16 This sequence occurs when any two out of the three APU/HYD systems fail. The equations for independent system failures and common cause failures are the same as those described for L0 se- quence 11. The equation for independent leaks is the same as that described for OK sequence 9. Sequence 17 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for L0 sequence 7. The equation for independent leaks is the same as that described for OK sequence 9. Sequence 21 This sequence occurs when APU/HYD systems 1 and 2 or 1 and 3 fail. The equations for inde- pendent system failures and common cause failures are the same as those described for L0 se- quence 4. This sequence also involves a common cause treatment of APU leaks. Here, we are modeling all three APUs develop leaks The equations for independent and common cause failures are similar to those described for L0 sequence 7, but with Q defined differently as in OK sequence 9. Omit- ting the algebra, the new independent and common cause failure rates can be determined by the following equations: P(CCF) = Tr-[3LkLt + _(I - [3L)[3L( I - YL)kL_t: P(IF) = (1 - 13c)kLt 9-10 Sequence 23 This sequence occurs when APU/HYD systems 2 and 3 fail. The equations for independent sys- tem failures and common cause failures are the same as those described for L0 sequence 6 The equations for independent and common cause leaks are the same as those described for OK se- quence 21. Sequence 24 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for L0 sequence 7. The equations for independent and common cause leaks are the same as those described for OK se- quence 21. Sequence 28 This sequence occurs when any two out of the three APU/HYD systems fail. The equations for independent system failures and common cause failures are the same as those described for L0 se- quence 11. The equations for independent and common cause leaks are the same as those de- scribed for OK sequence 2 I. Sequence 29 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for L0 sequence 7. The equations for independent and common cause leaks are the same as those described for OK se- quence 21. 9.1.3.4 All Three APU Units are OK During Ascent (OK State) For the ascent phase, it is assumed that all APU units are already started, otherwise the launch se- quence would not have been completed. Hence, Q is now defined as: Q = _.t Sequence 4 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are similar to those described for L0 sequence 7, but with Q defined differently. Omitting the algebra, the new independent and common cause failure rates can be determined by the following equations: P(]F) = (1 - [_r)_,t P(CCF) = y_lg_.t + }( 1 - _3_)13,.(1 - y,.)_._t 2 9.1.3.5 At Least One APU Unit is Leaking Hydrazine During Ascent {LK State) \ Sequence 6 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for OK sequence 4. The equation for independent leaks is the same as that described for OK sequence 9. 9-11 Sequence 7 This sequence occurs when one APU unit has an undetected leaks. The equation for independent leaks is the same as that described for OK sequence 9. Sequence 12 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for OK sequence 4. The equation for independent leaks is the same as that described for OK sequence 9 Sequence 16 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for OK sequence 4. The equations for independent and common cause leaks are the same as those described for OK se- quence 21. Sequence 17 This sequence occurs when all three APU units have undetected leaks. The equations for inde- pendent and common cause leaks are the same as those described for OK sequence 21. Sequence 20 This sequence occurs when all three APU/HYD systems fail. The equations for independent sys- tem failures and common cause failures are the same as those described for OK sequence 4 The equations for independent and common cause leaks are the same as those described for OK se- quence 21. 9.1.3.6 MGL Parameters The following point estimates are generic over all components and all failure modes. They were developed as part of a recent effort funded by EPRI to completely automate the process of ana- lyzing common cause failures in PRAs. The software is available through Boyer Chu at EPRI. This recent effort was based on previous data development and MGL method development found in EPRI INP 3967 (1985), NUREG/CR-4780 (1988), and NUREG/CR-5801 (1993). For information on methods and procedures for common cause failure you can refer to NUREG/CR-4780 (1988) and NUREG/CR-5801 (1993). APU component failure rates are generally within the variability range of the generic database from which the Beta and Gamma factors are derived. We believe, therefore, that these are an in- dication of future failure rates of the APU, and the generic factors apply to the APUs. We also used the generic data for common cause hydrazine leakage. We have found six leaks (see Section 9.2.2.6). Two of the leaks happened in the same mission (STS-9) for a common cause (carbonization and stress cracking of the injector). The Beta factor could be estimated as 1/3 (3 of 6). However, we know that the manufacturing process has been altered to reduce the likelihood of this cause. There has also been an effort to reduce the exposure of the nozzles to hydrazine between missions We have used, therefore, a generic Beta factor of 0.1 instead of the 9-12 data driven Beta factor of 1/3. \Ve see no justification to apply a Beta factor less than indicated by the generic level. 9.1.4 Equations Graphed in Fault Tree for Illustration As an example of how the independent failure rate and common cause failure rate equations de- veloped in the previous section are applied, see Figure 9. l-1. In tile figure is a simple fault tree that shows the sequence 4 LOV for the ascent phase in which no hydrazine leaks have occurred. l APU/HYD ]Unit 1 Failure Independent Failure LOV All Three APU/HYD Units Have Failures (I APU/HYD APU/HYD Unit 2 Failure Unit 3 Failure I APU/HYD Unit 2 Independent Failure J Common Cause Failure I APU/HYD Unit 3 Independent Failure P(1 IF) P(CCF) P(2 IF) P(CCF) P(3 IF) P(CCF) CommonCause Failure Figure 9.1-1: Fault Tree for LOV Sequence 4 for an OK State During Ascent 9-13 For the LOV to occur, all three APU/HYD systems must fail. System failures can occur inde- pendently, or as common cause failures. These failure rates were determined from the total failure rate using the Multiple Greek Letter method previously described, and are shown under the basic events to which they pertain From before, we defined P(CCF) and P(IF) as: P(IF) = (1 - [L)kt P(CC = + }(1 - 1 -¥,.)x2r: 9.2 Prior Distribution for Model The priors used in the assessment of P(IF) came from a previous study (McDonnell Douglas As- tronautics Company Engineering Services, Space Shuttle Probabilistic Risk Assessment Proof-of- Concept Study Volume III: Auxiliary Power Unit and Hydraulic Power Unit Analysis Report, pa- per WP-VA88004-03, 1987) As described previously, the priors were updated at the system level with observed Shuttle in flight failures. 9.2.1 Inputs Needed to Develop Priors The study performed in 1987 was done at a component level; i.e., the failure rates of the compo- nents in the system were calculated, and no quantification was done on the system level. This study has defined basic events on the system level in order to have such information for future decision-making Two prior distributions, the failure to start on demand and the run failure rate, were estimated using the component level data. The fault tree in Figure 92-1 depicts the component failures that most contribute to a system fail- ure to run. These components failure rates were agglomerated to obtain a prior distribution for APU system failure to run (events, [D, IF and IS). Similarly, Figure 92-2 depicts a fault tree in which any of the component failures may cause a failure to start condition. These component failure rates were agglomerated for the start contribution of event IS. The 1987 study performed a detailed fault tree for turbine overspeed Quantification of that tree showed that four events dominated the failure probability. These are shown in a simplified fault tree in Figure 9.2-3. 9-14 c< >_f i ____2 i"_ :5 .° _ _- m _ = z _=_1F'_ -_ _ I -- ;",_'-" _ _ i I -_ - -=--_ 1 =_-_ I Figure 9.2-1 : Fault Tree for APU/HYD/XVSB Run Failures 9-15 .° _. .,t i w I [._. >'_ _ ' .o w w .A" I -= m =-,-' .-.2 I .=. = m .. Figure 9.2-2: Fault Tree for APU/HYD/WSB Start Failures 9-16 _-3 >_ t _" -_ "=3 =_.--" < Figure 9.2-3: Fault Tree for Turbine Overspeed Failures 9-17 9.2.2 Output Distributions for Priors 9.2.2.1 APU Failure to Run The first prior calculated is that for an APU to fail to run. Table 92-1 lists the component failures frequency distributions that were in the model for APU subsystem run failures, Failure Primary Valve Falls Closed When Pulsing Isol. Valve Plugs (Contamination _When Open Magnetic Pickup Unit Fails l,ox_ Fuel Pump Fails To Run Lube Oil Pump Falls To Run Lube Oil System Loss Or" Flo_ Gas Generator Falls To Run [ Mean-Dist 4.481E-03 (1) 1 086E-06 2.240E..O3 7685E-05 7.685E-O5 2.664E-O3 1.436E-O4 I 5th percentile [ I 3494E-04 1 4681E-08 1.747E4)4 6.04 IE-04 2.791E-06 2.791E-O6 9 334E-O5 9.020E-07 Median ] 95th percentile[ Reti (I_ 2.404E--03 4.343E-07 1202E-O3 2.SgTE-05 2.g87E-05 9.698E4)4 2.467E-O5 1.225E-02 3.875E-06 6.127E-03 2797E-04 2797E4).4 9.681E-03 4 429E4M 1 837E-032,722E-O5 4.332E-04 3.385E-O5 i 2.350E-04Turbine Fails To Run i I Gearbox Fails To Run 2.628E-O5 9.323E-O7 9.672E-O6 9651E-05 1 Fuel Inline Filter Plugs 7.959E-O6 2.799E-07 2.907E-06 2894E-05 1 Fuel Pump Filter Plugs 2.040E-0,-I 2.722E-O6 5.002E-O5 6 507E-04 1 Failure Of Electric F_'r 1'o Secondary Valves 4.926E-O5 9231E-O7 1.357E-O5 1.866E4)4 1 HYD Accumulator Falls To Run 2.664E-O5 I.OE-O6 1.0E-O5 1.OE-04 2 HYD Reservoir Fails To Run 2.664E-O5 1.0E-O6 1.0E-O5 1.0E-O4 2 HYD Lme Filter Plugs 7.840E-06 60E-O6 7.746E-O6 1.0E-05 3 HYD Relief Valve Opens Spuriously 1.212E-05 YOE-O6 9.487E-06 3OE-O5 5 HYD Main Pump Fails Fo Run 4.040E-O5 I.OE-O5 3.162E-O5 1 0E-0.4 25 HYD Circulation Pump Fails To Run 1.127E-O4 7.0E-O6 5.292E-05 4.0E-O4 2,3 HYD Fluid Leak (Catastrophic) 5.0E-O6 5.0E-O5 5.0E-O4 1,3,4 2.236E-05 5,0E-06 2,51.0E-O4 3.059E-O3 6.956E-O3 2.174E-.O2 i 9.150E-O3 [ Shuttle history of O failures is 882 demands in a maximum entropy log normal- 882 = (6 APU Starts/Missions + 4 I_U starts + 4 HPU Hot Fire Tests ) x 63 Water Spray Boiler Fails To Cool Total Fail To Run/Hr I. t 987 APU Stud,,' 40REDA 2. NPRD-95 5 WASH-1400 3. IEEE-STD-500 Table 9.2-1: Component Failures Leading to APU System Run Failure (Failures/hour) In order to calculate the distribution of the sum of these failures, an @Risk Monte Carlo simula- tion (20,000 trials) in a Lotus 1-2-3 spreadsheet was used. A graphical representation of this dis- tribution can be seen in Figure 9.2-4. 9-18 9.2.2.2 APU Failure to Start In Table 9.2-2, various component failures are listed that will lead to a failed-start condition. Once again, to calculate the failed-start distribution based on the sum of the various component failures, an @Risk Monte Carlo simulation (20,000 trials) in a Lotus 1-2-3 spreadsheet was used. Forecast: TOTAL FAIL TO RUN Frequency ChartCell D23 047 .035 ................................................ 690.7 00oiliit tlqlilHt11,,,i,ii,ii i;iiiiiiiiiiii iiiii iiiiil" O 0.000E*0 8.750E-3 1.750E-2 2.625E-2 3.500E-2 19,718 Trials Shown [ 921 Figure 9.2-4: f-WRisk Simulation Results for Failure to Run Frequency 9-19 Failure Bypass Valve Fails To Open (m I)emaxld Mean-Dtst t ! 4.689E-II4 5th percentile Median _ 95th percentile t p 1276E-03 r 1690E4)5 1.730E-O4 Common Cause Heater Tram 13 Failure 6 5E-O5 4.6Eq)06 36E-O5 l 1.5E-O4 I I Common Cause Lube Oil Heater Dam Fatlure 2. IE-O5 5 3E-O7 7 8E-O6 5 7E-O5 I Fuel Pump Falls To Start I 278E-05 9 139E-O8 2.138E-06 4 702E-05 1 I 278E-05Lube Oil Pump Falls To Start 9 139E-O8 Turbine Fails To Start Gearbox Fails To Start 2 138E-06 4 702E-05 Electnc Pwr To Pnmarv Valve Falls i !Electric Power To Secondarx Valve Fails 6.207E-04 1.329E-05 2045E-04 1.879E-03 1 7.409E-O4 3.447E-05 3260E-O4 2.032E413 1 1.278E-O5 9.139E-O8 2.138E4)6 4.702E-O5 1 1.278E4)5 9.139E-O8 2.138E-06 4 702E-05 1 6 2E-04 1.3E-05 2.0E-04 I 9E-O3 1 4 0E-04 4 475E-03 4 475E-03 1 1205E-O2 multiplication MPU Fails Lo_ HYD Main Pump Fails To Start HYD Accumulator Has No Pressure At Start HYD Reservoir Low/No Fhud At Start Total Failures To Start "' Converted hourly failure rate to a start thilure by 4683E-05 168E-O4 1,68E4)4 3.322E-03 1, 1987 APU Study 2. NPRD-95 3. IEEE-STD-500 4. OREDA 2.426E-O-I 1.680E-O3 1.680E4)3 7949E-O3 ! by exposure time ( 168 hours ) 1.257E-O5 6 1.68E-02 2 ''' 1 68E-O2 3 342E-O2 6. Shuttle history of 0 failures is 882 demands m Table 9.2-2: Reference I 2111 5. WASH-1400 a maxmmm entropy log normal: 882 = (6 APU Starts/ Missions + 4 HPU Starts + HPU Hot Fire Tests) x 63 Component Failures Leading to APU System Start Failure (Failures/Demand to Start) The @Risk Monte Carlo simulation (20,000 trials) for the failure to start probability distribution can be seen in Figure 9.2-5. Cell D47 .064 .048 032 r,_ o16 .000 0.000E÷0 Forecast: TOTAL FAILURES TO START Frequency Chart 19,671 Trials Shown 1258 !! ,,,, ! • II I,,, ,,..,..... ........ 0 I. 375E-2 2.750E-2 4.125E-2 5.500E-2 Figure 9.2-5: @Risk Simulation Results for Failure to Start Frequency 9-20 9.2.2.3 Turbine Overspeed and Hub Failure at Normal Speed Figure 9.2-3 depicted the fault tree for a turbine overspeed condition which is an initiating event (TU). Prior distributions were obtained from the 1987 APU study. The following Table 92-3 provides the priors and the in-flight shuttle data used for the likelihood function. The posterior failure rates of these various components are listed in Table 9.2-5. To calculate the turbine over- speed frequency distribution based on fault tree logic, @Risk Monte Carlo simulation (20,000 tri- als) in a Lotus 1-2-3 spreadsheet was used. Event PASVC TASVE TAMIL PAPVE Prior (Log Normal) 5 Percentile 8x10 -5/D Ix i 0 -4/hr 5x10 -5/hr 1x 10 -4/hr Prior (Log Normal) '95 Percentile 7x10 -3/D I x 10 -2/hr 5x10 -3/hr lxl0 -2/hr Shuttle Specific Data 1/378 Demands 0/0 ,z:> 1/796 hrs _3, 1/292 hrs ,4, qll ¢_ 2 Demand/APU x 63 millions x 3 APUs/Missons = 378 Demands <:) Failure of primary valve in mission SB-31 generated a demand on the secondary valve for a few minutes before the launch was scrubbed. The secondary valve did not fail. _3) 1.33 hours/APU x 3 APUs/Missions x 3 FIPUs/APUs x 63 Missions = 796 hours c_) 1.33 hours/APU x 3 APUs/Missions x 63 Missions = 292 Table 9.2-3: Priors and In-Flight Shuttle Data Used for the Likelihood Function Shuttle in-flight failures used in the above table are described below in Table 9.2-4: Car No. AC8511-01 Date 08/06/84 Flight APU Basic No. No. Event 41B 3 PASVC AC0055-01 07/24/81 1 04/24/91 STS-31IFA STS-31-01 2 TAMIL 1 PAPVE Description GGVM Shut offvalve leaking at a rate of 248 scim due to a broken poppet valve seat !MPU #2 was inopr.; MPU resistance measured open Primary pulse control valve chipped (valve sent failure) allowing hydrazine to continue flowing. Secondary valve took over. Launch" scrubbed. Table 9.2-4: APU Turbine Component Failure Descriptions 9-21 The@RiskMonteCarlo simulation(20,000trials) for the failureto start probabilitydistribution canbeseenin Figure9 2-6 Failure PrimaryValveFailsOpenDuringPulsing MagneticPickupUnitFallsLo_ SecondaryValveFailsOpenDuringPulsing i Mean-Dist ! 1477E-03 2.240E-03 9.602E-04 5thpercentile 6852E-05 1.747E-04 5.032E-05 Median 195th percentile ! 6,500E-04 4.0_4E-0__ 1.202E-03 6.127E-03 4.484E-04 2.685E-03 Secondary Valve Fails To Close On Demand 2.631E-03 2.305E-04 1504E-03 Total Probabilit3 For Turbine 2.518E-04 6.733E-06 7.530E-05 Overspeed/Flight"' _1_ All APUs included Table 9.2-5: Posterior Failure Rate Data for Component Failures Leading to Turbine Overspeed 7 500E-03 I 9 403E-04 Forecast: TOTAL TURBINE OVERSPEED FREQUENCY PER FL Cell D5 Frequency Chart 19.591 Trials Shown .033 i i , r 643 ! llliil,,,,, !!!!!N . . . . ,= hi • 0.000E÷0 5.625E-5 1.125E-4 1.688E-4 2.250E-4 Figure 9.2-6: @Risk Simulation Results for Turbine Overspeed Frequency Turbine hub failure at normal speed is not a significant contributor to the probability of this e_ent. APU hub cracking is mapped and it has been shown by analysis (at JSC) that the likelihood of blade cracking propagating to a hub crack is very small. Furthermore, experiments on hub breakup show that even a notched or drilled hub requires a speed significantly above nominal to induce hub failure. NPRD-95 has a value of turbine failure of about 10 -Sdar. for all modes com- bined, not just hub failure. Therefore, hub failure at normal speed is at least an order of magni- tude less in probability then turbine overspeed 9-22 9.2.2.4 Other Prior Distributions The remaining prior distributions were taken directly from the 1987 study, were defined by MGL analysis, or were a result of our assessment. U1 of the prior distributions are in Table 92-8_ The two letter descriptions were discussed previously in Table 9 I-1. Some events, such as an APU OK state, are not in this table since they are not incorporated into the quantification of the scenarios. For some inputs only a mean value was estimated. 9.2.2.5 Large Exhaust Gas or Hydrazine Leak (LL) This prior distribution was generated by breaking the event down into its three major contribu- tors: tank/pipe rupture: hot gas leak; and isolation valve leak/rupture. For both the tank/pipe rup- ture and hot gas leak modes, a failure rate range based on variability was defined from Nonelectronic Parts Reliability Data 1995 (NPRD-95). The median value from this range was multiplied by the 1.5 hour total APU run time for ascent and descent, and times 3 for the number of APUs, to get a point estimate failure probability for the system per flight. A failure rate range was also defined for the isolation valve leak from NPRD-95. In this case, the range was treated as defining the 5th and 95th percentiles of a iognormal distribution which was used as the prior in a Bayesian update. The evidence data consisted of two incidents in which cracks were found in APU and HPU isolation valves which did not propagate to a through crack of the valve casing that separates the flow path from the solenoid cavity. The concern here is that when hydrazine comes in contract with the solenoid it could decompose and rupture the isolation valve causing an unisolatable leak. These were not "hard" failures, but are valid evidence of fail- ure potential. They were treated, therefore, by a near miss methodology as follows. The solution was to treat the data according to the probability that these incidents might propa- gate into "hard" failures on other flights, where the circumstances might be different. This is a matter of judgment on the part of the analyst. In this case, since these incidents were determined to have a low probability of propagating to "hard" failures, the evidence was treated as having a 5% probability of representing l failure in 72000 hours (a lower bounding estimate of the total ex- posure time for APU and HPU isolation valves), and a 95% chance of representing zero failures in 72000 hours. The overall posterior distribution was then generated by taking a weighted average (according to the previously determined weights) of the two possible posterior distributions. The following Table 9.2-6 shows the prior distributions. Tank/Pipe Replace (prior 0nly) 5 Percentile 10 -9/hr. 95 Percentile 10 -7/hr. Exposure Time 63x3x 1.5hrs. Hot Gas Leak (prior only) same same same Isolation Valve (prior) 1 x 10 -7/hr. 10 -7/hr. 72000 hrs. Isolation Valve (updated) 1.2 x 10 -9/hr. 8 x 10 -8/hr. Table 9.2-6: Distributions for Large Hydrazine or Exhaust Gas Leak 9-23 The data used in the isolation valve analysis is anecdotal. We are aware of a crack discovered in an APU isolation valve before STS-I. We are also aware of a recent crack found in an HPU, that when tested post-flight, leaked hydrazine into the solenoid cavity. 9.2.2.6 Leak in One APU Unit (LK) A Bayesian analysis was not performed for hydrazine leaks. Shuttle in-flight experience was used to generate a point estimate of the rate at which hydrazine leaks develop. This rate was based on the data in Table 92-7, showing 6 leaks in 31752 hours of exposure time (63 flights x 3 APUs x assumed average flight duration of 7 days x 24 hours/day). To generate a probability distribution, the point estimate was assumed to be the mean value of a maximum entropy (_ = 1.0) lognormal distribution. This assessment was based on a number of assumptions. We assume that the APUs are leak checked and only launched if found acceptable. Hydrazine leaks may occur at any time during the mission. Exposure to hydrazine may cause leaks even without the system operating. However, the leaks may only be revealed when the system is operating. CAR IFAS i Flight Date APU # Description ** ICR 04/12/81 1 Hyd. leak from fuel pump cover ** I CR 04/12/81 2 Hyd. leak at fuel pump inlet fitting 09F012-01 STS-9 11/28/83 1 Hyd. leak from cracked fuel injector tube * 09F013-01 STS-9 11/28/83 2 Hyd. leak from cracked fuel injector tube * X STS-51F 07/29/.85 1 Hyd. leak into gearbox *** X i STS-45 03/24/92 1 Hyd. leak into gearbox **** APU failed due to the hydrazine leak ** Data from APU subsystem manager database :*** This leak was detected by increased pressure in the gearbox and the start of APU2 was delayed until Vrel = !Ok **** On this same mission APU2 leaked oil / GN2 from the gearbox to the aft compartment X STS-45 03/24/92 2 Lube oil / GN2 leak from gearbox through turbine seal Table 9.2-7: Hydrazine Leakage History on STS 9-24 TheAPUscontainmanypotentialleakagesites. Thedatasimplyindicatesthat somehavealready occurred.Othershaveyet to becomeactive Becauseof this,wedo not necessarilyview correctiveactionsto individualleakagesitesasreducingthepredictedfrequencyof leaks. Rather. we treatpastleaksasindicativeof futurerates. 9.2.2.7 Leak Detected Confirmed (LD and LA) The first four leaks above were not detected during the mission. The last two leaks were detected by increased pressure in the gearbox. We assess the probability of leak detection, and APU de- layed start, as ! in 6 based on this data. Since no action has ever been taken on leaks during as- cent, this indicated zero probability of leak detection on ascent. The use of zero detected and confirmed leaks during ascent avoids the paradox associated with a groundrule of this study The groundrule is that aborts are assumed to be successful. Therefore, a failure that leads to an APU induced abort actually reduces the calculated risk. Flight rules call for an APU shutdown and an MDF abort if a single hydrazine leak is detected and confirmed. Two such leaks lead to a PLS abort. To avoid having to treat leaks as successes, we assume no detection on ascent. 9.2.2.8 Own Leakage/Other Leakage Induced Failures (LF and LO) These prior distributions were defined through a data based assessment utilizing the 1987 study, PRACA records, hazards analyses and an understanding of the phenomenology of the failure _nodes. Specifically, the mean value for own leakage induced failure during descent was defined from the data shown in Table 92-7, indicating 2 APU failures in 6 leaks. The mean values for the other three conditional probabilities were then derived by maintaining the ratios between the val- ues from the 1987 study and scaling them to the 0.3 defined for LF (des). This produced values of 02 for LO (des), 0. ! for LF (asc) and 0.008 for LO (asc). An assessment of the applicable distributions was then made for the four probabilities. In the case of LF (des), an upper 40 bound of 0.5 was defined for the distribution, assuming a normal distri- bution. For LF (asc), an upper 40 bound of 0.2 was defined, again assuming a normal distribu- tion. And for LO (asc), given the small value of the mean (0.008), a lognormal distribution was judged to be more applicable, as greater uncertainty is expected for small defined values. For this distribution, an Error Factor of 5 was assumed. For the normal distributions, values below zero should be truncated when using the defined distributions. In the case of LO (des), data is available for a Bayesian update of the assessed value, so the distri- bution needs to be defined much broader than for the other cases (where the posterior was being defined directly), in order to overlap the likelihood function of the evidence. The prior distribu- tion was defined using 0.2 as the mean value for a maximum entropy (o = 1.0) lognormal distribu- tion. This was updated with evidence of 0 APU failures in 12 APUs exposed to other units leaking. Note the following for each leak: There are 2 opportunities for another APU to fail ow- ing to the leak and 1 opportunity for itself to fail. For 6 leaks, there are 6 x 2 = 12 opportunities for failure of another APU owing to the leak. None has occurred. The mean value of LO (des) drops to 0.07 given this evidence. The result of the Bayesian analysis is shown graphically in Fig- ure 9.2-7. 9-25 9.2.2.8.1 Sensitivity Treatment ofAPU 3 Failures The previous section described the baseline treatment of these conditional probabilities. In the case of APU failure due to another units leakage (LO), it could be argued that APU 3 needs to be treated differently APU 3 is physically located about 6' (on the starboard side) from the other two units, which are only a few inches apart Thus, we believe that there is a lesser chance of APU 3 failing due to leakage in unit 1 than an APU 2 failure. Our fault tree treatment is conservative in that each APU is considered "identical" It does not capture "full credit" for cases in which the actual APU 3 is leaking, which would lead to reduced LO conditional probabilities for both of the other units. One way of capturing this logic would be to drop the LO conditional probability to a lower value for all of the APU 3 terms In order to illustrate the affect this would have on the results, two of the most significant leakage fault trees have been quantified, at the mean value, for these two cases. For the baseline case: OK Initial State on Entry, Seq. 16 4.159E-04 • OK Initial State on Entry,, Seq. 17 1.700E-04 For the sensitivity case, using as an example O.01 as the unit 3 LO (des) probability: • OK Initial State on Entry, Seq. 16 2.479E-04 • OK Initial State on Entry, Seq. 17 6.214E-05 014 -r- Or2 -'_ 4 010 -_- _. 008 -- ,,a 00o _ i I , i: 004 -_¢ ii , / 0 02 _,,/ L' 000 -J_-- 001 0 20 0 40 ; UIx_tm:l Probebdtw i .......... b 0 oO 0 -o 0 oo Frequency Figure 9.2-7: Bayesian Analysis Result for LO (Des) 9-26 9.2.2.9 Unsuccessful Single APU/HYD Unit Reentry_ TAEM and Landing {UL) This prior distribution was generated according to judgment weighted by several factors. First, such landings are regularly simulated successfully in training. To the extent that the simulator is successful in characterizing the vehicle response given a single APU/HYD unit, this gives cre- dence to a very high probability of success However, this is tempered by the fact that a single APU/HYD unit landing is not certified by the program. Unfavorable weather conditions coupled with slower control rates could potentially indicate a much higher probability of a failed landing. The assessment team has translated this into a range of 80% to 100% for a successful landing It was also determined that the lack of a strong conviction for any values within this range war- ranted a uniform distribution for this range. 9-27 ID CE CF CL CO CS FIB ID IF IS LA LD LF OS LK LL LO LS LU LZ SI SR TU UL 136-factor N/A Calculated Calculated N/A Calculated N/A N/A N/A N/A N/A N/A N/A see posterior N/A N/A N/A N/A N/A N/A N/A N/A N/A PRIOR (/hr or/demand) m__ ; Mean + 05 (EL) 0.88 (TU) 'using applicable using applicable using applicable 0.9 9.150E-03/hr 9.150E-03/hr 1.205E-02/start 9.150E-03/hr 0.0 (asc) O. 1667 (des) 0.0 (asc) 0.1667 (des) 1.0E-01 (asc) 1.890E-04/hr 2.8E-05 8OE-03 (asc) 2.0E-1 (des) 1.0 (asc) 0.8333 (des) 1.0 (asc) 0.8333 (des) 1.0 (LL) 0.88 (TU) 0.98795/start 2.5 ! 8E-04 0.1 Median 5th 95th MGL method ,'formulas MGL method MGL method 6.956E-03/hr 6.956E-03/1-u" 7.949E-03/start 6.956E-03/hr 1.0E-01 (asc) 1.152E-04/hr 5.0E-03 (asc) 1.2E -01 0.99205/start 7.530E-05 0.1 formulas formulas 3.059E-03/hr 3.059E-03/hr 3.322E-03/start 3.059E-O3/hr 6.0E-02 (asc) 2.224E-05/hr 9.9E-04 (asc) 2.3E-02 0.99668/start 6.733E-06 0.01 2.174E-02/hr 2.174E-02/hr 3.342E-02/start 2.174E-02/hr 1.4E-01 (asc) 5.971E-04/hr 2.5E-02 (asc) 6.36-01 .96658/start 9.403E-04 0.19 Table 9.2-8: Prior Probability Distributions 9-28 9.3 Posterior Distributions for APU/HYD/WSB Failure to Run and Start (Ascent and Descent Posterior distributions were determined by updating the prior distributions with available data us- ing Bayes' Theorem Data points not only include failures of the APU and HYD systems, but also the Water Spray Boiler (WSB) WSB failures, which lead to an APU shutdown and subsequent hydraulic loss, were not examined in the previous 1987 study, so data was extracted for these fail- ures from all Shuttle flights Other data points pertaining to these failures were taken from post- Challenger flights (1988) to STS-65 (flight 63, 7/8/94). 9.3.1 Water Spray Boiler Failures Used in the Analysis 9.3.1.1 03-23-1982 STS-3 WSB 3 freeze-up during ascent. APU temperature message at lift-off plus 4 minutes 23 seconds reported lube oil temperature climbing. Controller B was then selected, but the temperature con- tinued to rise. APU 3 shutdown at liftoff plus 8 minutes, and the right main engine went into hy- draulic lock-up. After ascent, at lift-off plus one hour, controller A was then selected: both controllers appeared to be working properly. The maximum APU 3 lube oil temperature was 330°F, and the maximum bearing temperature was between 355 and 360°F. FCS checkout tested both controllers, and both were 100% nominal. This situation was also seen on STS-1 and 2. 9.3.1.2 08-02-1991 STS-43 WSB 2 failed to provide cooling to the auxiliary power unit 2 lube oil throughout the mission. APU 2 (serial number 208) has been involved in lube oil over temperatures during seven of its eight flights. The WSB did not cool the lube oil on controller A following ascent. The crew switched to controller B when the lube oil return temperature reached approximately 297°F. The APU was operated an additional 1.5 minutes on the B controller, and still no cooling was ob- served. The APU was shutdown when the lube oil return temperature reached 323°F. The WSB is designed to control the lube oil temperature to 250-a:2°F. An extended flight control system check-out using APU 2 was performed and the WSB was not cooling on either controller. The APU ran for 11 minutes during check-out, then was shutdown and declared lost. During descent, APU 2 was activated at terminal area energy management due to the lack of cooling. The lube oil reached 259°F before shutdown after wheel stop with no evi- dence of cooling. The spray boiler may not have had the chance to function, however, as this temperature is close to the 250°F control limit. 9.3.1.3 09-12-1992 STS-47 During ascent, WSB 3 (serial number 15) exhibited no cooling until just prior to the early shut- down of APU 3. The lube oil temperature reached approximately 292°F when the controller was switched from A to B. The lube oil temperature continued to rise to 31 I°F when the decision was made to shut down APU 3 early. Prior to APU 3 deactivation, the WSB GN2 regulator outlet pressure indicated that spraying had begun. WSB 3 continued to spray until the spray logic was turned off(1 minute 43 seconds). Steady-state cooling was never achieved on either controller since the lube oil temperature was not allowed to drop to 250°F prior to boiler spray logic shutdown. 9-29 APU 3 was selected to perform FCS checkout The checkout time frame was extended to verify WSB 3 cooling performance. The extended run time demonstrated satisfactory, cooling on both controllers (3 minutes 42 seconds for B, then 1 minute 47 seconds for A). WSB lube oil and hy- draulic cooling performance during entry was nominal. Spray bar freeze up remains the most likely cause of the WSB failure, although it could have re- sulted from spray valve or controller failures. 9.3.1.4 01-13-1993 STS-54 During ascent, WSB 3 (serial number 15) exhibited no cooling until just after the early shutdown of APU 3. The lube oil return temperature reached approximately 295°F when the WSB was switched from controller A to B The lube oil return temperature reached 315°F when the deci- sion was made to shut down APU 3 early. After deactivation, the WSB 3 GN2 regulator pressure indicated that spraying had started. WSB 3 continued to spray until the spray logic was turned off (approximately 35 seconds). Steady-state cooling was never achieved on controller A or B. APU 3 was selected to perform the FCS check-out The FCS checkout time frame was extended to verify WSB cooling performance The extended APU 3 run-time demonstrated satisfactory cooling on both controllers, with a minor overcool observed on controller A APU performance using controller B during entry was nominal Spray bar freeze-up remains the most probabl e cause of this cooling problem. However, data analysis also indicated that the local pressure at the vent nozzle of system 3 during ascent was somewhat higher than the other two systems. This high pressure is due to the location of the sys- tem 3 vent nozzle outlet (it is farther forward than the system l and 2 vent nozzle outlets). Sys- tem 3's pressure remains higher than the other systems for the first 80 seconds of ascent, which is believed to be a contributing factor toward the repeated freeze-up anomalies observed in system 3. Spray bar freeze-up conditions occur when the water triple point condition is met inside the heat exchanger. In the worst case freeze-ups, it is postulated the water triple point was reached prior to MECO. By increasing the water preload, the duration of heat exchanger tube bundle/water preload contact can be increased, which will reduce the likelihood/severity of spray bar freeze-up by maintaining pressure above the water triple point past MECO. The ongoing spray bar freeze- up test analysis indicates that the severity of the bar freeze-up at water triple point conditions may inversely correlate to the amount of water in the boiler. Therefore, KSC has been requested to preload WSB 3 to 5 +/-0.1 ibs. of water (normal is 3.75 +/-0.24 lbs.). 9.3.2 Possible Water Spray Boiler Failure It is unknown whether or not this reported problem is an actual failure or not. For this analysis, it has not been considered as an actual data point. 9.3.2.1 04-29-1985 STS-SIB Shortly aiter MECO, the backup flight system indicated an APU 3 lube oil over temperature con- dition. The crew switched from controller A to B at a lube oil temperature of 320°F. The tem- perature continued to rise for an additional 20 seconds and reached a peak of 337°F, The crew was instructed to shutdown APU 3 to avoid reaching the lube oil temperature limit of 355°F The 9-30 APU 3 lube oil temperature had decreased to approximately 320°F at shutdown, indicating that water spray boiler controller 3B was properly controlling iube oil cooling Post flight testing has been unsuccessful in duplicating this problem The A controller was replaced 9.3.3 Possible Hydraulic System Failure 9.3.3.1 02-28-1990 STS-36 Appendix C contains descriptions from PRACA records and hazards analyses of a "near-miss" failure involving a flex hose rupture in the hydraulic system. 9.3.4 Updated Posterior Distribution The four WSB failures in Section 9.3.1 were counted as APU shutdowns. All three of these fail- ures occurred during the ascent phase. One of these failures was permanent and caused a late re- start of the APU during the entry phase, but was not counted as a failure during the reentry phase because it successfully completed its mission. For reentry, the hydraulic system rupture is counted as a possible APU/HYD unit failure in the update. The methodology for this type of up- date is described in section 9.2.2.5, where in this case the weighting uses 50% for 1 failure and 50% for zero failures. In the data column, if no data is available (i.e., no "trials"), an N/A for not applicable is placed in the box. The common cause failure calculations for the MGL formulas used the ID and IS values, assum- ing 20 minutes for ascent and l hour for descent. The MGL calculations also used generic 13and y values of 0.1 and 0.27, respectively. Table 9.3-1 lists the data and corresponding posterior probability distributions for the basic events. The means from these data distributions are used as basic event probability distribution inputs for use in SAIC's CAFTA model. 9-31 ID CE CF CL CO CS lib ID IF IS LA LD LF OS LK LL LO LS LU LZ SI SR TU UL Data N/A POSTERIOR /hr or/demand) P Median 5th 95th' Mean 0.5 (LL) 0.88 (TU) Calculated using applicable MGL method Calculated Jusing applicable MGL method N/A 1 Calculated using applicable MGL method N/A 0.9 4/63 hrs 1.931E-02/hr2078E-02/hr 2.078E-02/hr 5.677E-03/start formulas formulas formulas 1.030E-02/hr 3.622E-02/hr 1.030E-02/hr4/63 hrs 1.931E-02/hr 3.622E-02/hr 0/189 starts 4.448E-03/start 1.433E-03/start 1. 194E-02/start 0 to 1/252 hrs i 6.479E-03/hr 5.614E-03/hr 2.369E-03/hr 1219E-02/hr b N/A I 0.0 (asc) 0.1667 (des) N/A 0.0 (asc) 0.1667 (des) N/A 1.0E-01 (asc) 1.0E-01 (asc) 2/6 Leaks 3.0E-01 (des) 3.0E-01 (des) 6.0E-02 (asc) 1.4E-01 (asc) 2.2E-01 (des) 3.8E-01 (des) N/A 1.890E-04/hr 1.152E-04/hr 2.224E-05/hr 5.971E-04/hr N/A 2.8E-05 N/A 80E-03 (asc) 5.0E-03 (asc) 9.9E-04 (asc) 2.5E-02 (asc) 0/12 Leaks 7.0E-02 (des) 5.3E-02 (des) 1.4E-02 (des) 1.6E-01 (des) N/A 1.0 (asc) 0.8333 (des) N/A 1.0 (asc) 0.8333 (des) N/A 1.0 (EL) 0.88 (TU) N/A 0.99432/start 0.99555/start 0.99857/start 0.98806/start N/A 6.962E-05 5.501E-05 1.974E-05 1.672E-04 N/A 0.1 0.1 0.01 0.19 \ Table 9.3-I: Posterior Probability Distributions 9-32 9.4 APU/HYD/WSB ANALYSIS FOR SSME MODEL The APU failure probability assessment for the SSME model being produced at SAIC is some- what different than that for this APU model. First, the exposure time is at most 520 seconds in- stead of 20 minutes Second, only 1 of the WSB failures is relevant (STS-3) for purposes of calculating engine hydraulic lockup probability. We started with the prior distribution for IF, given in Table 92-6, multiplied against the 520 sec- ond time period to produce a probability of failure (POF). We updated with I failure in 63 mis- sions to produce a posterior This represents the case in which the WSB failure and APU shutdown continues to be representative of how MCC and crew will react to a WSB failure Since STS-3, other WSB failures have not resulted in a call for APU shutdown before MECO. Flight Rules indicate that APU shutdowns should occur post-MECO. We also updated the same prior distribution for IF with 0 failures in 63 missions. This is like say- ing that STS-3 never happened and gives an overly optimistic assessment. An accurate assess- ment lies somewhere in between. We used a weighted average of each posterior where each update was given equal probability of being the correct one. The Bayesian calculation is shown in Figure 9.4.1. The MGL method was used to calculate the probability of loss of hydraulics for a single engine and for two engines as follows: 1 Engine Goes into Hydraulic Lockup via Hydraulic Failure During Ascent Q = 3(1- _)qAP_, = 3 (1-0.1) i.5E-04 = 4E-04 2 Engines Go into Hydraulic Lookup via Hydraulic Failure During Ascent (First 5.6 minutes) Q = 3/2 (1-),)[_(3.36/520)q_t +3(1-13):(336/520) -"c/Z_u = 3/2(1-0.27)0.1 (336/520) 1.5E-04+3(1-0.1)2 (336/520)-" 1.5E-04 = IE-04 9-33 0.05 - 0.04 - 003- 0.02 + i 0.01 *_ I 'l 0]-- 5.00E-05 1 43E-03 BAYESIAN UPDATE-E Template SafeO., Factor Associates, Inc. i -- _or _[ PARAMETERS Pro_abilirv JlOr'a5.1 _;.5 failures - Lpdatod J[ - "189;time/trials Probability 2 80E._)3 4 18E-03 5.55E-03 Frequency 693E-03 f Buttons PRIOR UPDATE Mean 1.330E-O3 Median 1.041E-03 Mode 6.693E-04 5th °o 3321E-04 20th % 5.805E-04 80th % 1.864E-03 95th °o (5 3.250E-O3 9.472E-O4 I 464E-03 1 159E-03 7 381E-04 3 646E-O4 6.452E-04 2.053E-O3 3.449E-03 1.005E-03 Figure 9.4-1: APU Failures on Ascent Causing SSME Hydraulic Lockup (POF) 9-34 I_. 0 I-. 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Shuttle sensors

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Shuttle sensors

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