M". MORANDUM REPORT BRL-MR-3814

AD-A219 373B ri L__ill j__

COD, PARISONS OF FIELD TESTS WITH SIMULATIONS:ABRAMS PROGRAM LESSONS LEARNED

PAUL H. DEITZJILL H. SMITH

JOHN H. SUCKLING OTICELECTE

MARCH 1990 MAR 16 19901

APPROVED POR PUBLI.C RELEASE: DISThIBtnION UNLMwflE.

U.S. ARMY LABORATORY COMMAND

BALLISTIC RESEARCH LABORATORYAPERDEEN PROVING GROUND, MARYLAND

9i 03 15 03a

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IMairch 1990 I-Final Jul 87 - Oct 894. TitE AND SUBTMTE S. PUNOING NUMBWERS(Comparisons or Field Tests with Simulations: Abrams Program Lessons Learned

6. AUTHOR(S)lPaul 11. lDcvtz, Jill I[. Smith. John 11. Stickling

7. PERFORMING ORGANIZATION NAME(S) AND AIDDRESS(ES) I. PERFORMING ORGANIZATIONREPORT NUMBER

9j. SPONSORING/ MONITORING AGENCY NAME(S) AND ADORES4ES) 16. SPOONSORIMMOMOIN

US Army Ballistic Research Laboratory A3K IP UU

A1TN: SL-CBR-DD-TAberdeen Proving Ground, MID 21005-5006 BRL-MR-3814

111. SUPPLEMENTARY NOTES

Presented as a paper at thc 28th US Army Operations Research Symposium (AORS XXVII) held 11-12 October 1989,Ft. Lee, VA

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Approved for Public Release-, Distribution Unlimited.

13. ABSTRACT (Maxtmum 200 wor&)

'rhe onset or funl-sc, live-lire te-sting (LF"1') has provided vulnerability workers with unprecedented

npport ii itiem to 'xaninre fieild result s ini the light, of model predict ions-. Pre Abrain:s experience with IiIT$lioweCd however, that the extant vulnerability models lacked 11 the capability to predict. componenut (]--mage

states anid 21 the ability to reflect at least, thc prinucipal forms of randomnuess which are intrinsic to thevilhierabilify process.

To remeidy this shortcon'iing, the MLRl/ Vi,!) dIeveloped a niew stochastic point-burst vuulnernhilicy code, calledSlQuASI I, SqWll imhs lwin ised to predict .18 s4hots inl the Abrams IX~ program. Both subjective and

statisitical tests have been wriformed iii ani effort. to romlpare lieldl observations with computer predict ions. Inthis paper, thle -. tnerabi Iy~ fra nework i, deescrild, the k indes or resit yit-lded by the SQtiASI I predict ions.arnd the Ic.aso'is learnedl irom forts toi "cal i huatv& tho lode ilOlnv ed on the statistical tests prrormied .,,, ,

14. SUBJECT TERMS IS. NUMBER OF PAWIS

Svulnerability analysis. stochastic vulnerability modeling; live-fire testing,' -"i(.L 53armor perforation.- vehicle loss or function; component kill assessment/- Is.) - OUm coot

17. SECURITY CLASSIFICATION 1E SCURITY CLASSIFICATION 19i. SICURITY CLASWE(WETUO ft. UMITAION OF AS CTOP REPORT OF THIS PAGE OF ABS"hAC?

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TABLE OF CONTENTS

LIST OF ILLUSTRATIONS ............... ..... ...............

LIST OF TABLES ........................

I. INTRODUCTION .................................... ......

2. COMPONENT DYSFUNCTION.........................................

* 3. S INGLE- SYS TEM FAULT TREE.........................3

4. CRITICALITY ANALYSIS FOR AN AYXr......................3

5. \TLNERABILII\ MODEL ING k- LIVE-FIRE TES7)TING ............................................... 5

5.1 Observations re: STEP 1...............................

5.2 Observations re: STEP 2 ................................................................................... 5

6. EXAIMPLES OF SQuASH OUTPUT .......................................................................... 6

7. COMPARISONS7 ABRAM \S TESTS/SQuASH PREDICTIONS .... ..... ............................... 6

7.2 Catastrophic Kill ............................................................ ............................ 6

7.3 Component Kill Assessment................................................................................ 8

7.3.1 Initial Individual Component Assessment.......................................................... 8

7.3.2 Initial Ranking of Component Discrepancies.......................................... . .......... 9

7.3.3 Revised Individual Crew Data......................................................................9

7.3.4 Component Damnage States .......................................................................... 10

7.3.5 Revised Crew Component Damage States .................................................. 10

7.3.6 Analysis of Loss-of-Function................................................ ...... ............. II1

7.3.7 Secondary Kill Mechianisms.......................................... ............................. .11

8. SUTM MA-RY ...................................................................................... .......... .12

3.1 Similitude of Abrams LF 'Modeling k Field Assessment................................................ 12

8.2 Statistical Comparisons - Field, ,i-ationlData........................ ........................... 12

8.2.1 Perforations and Catastrophic ,I. ............................ . ..................................... 12

8.2.2 Individual C om ponents. ................................................ .12

8.2.3 Secondairy Efferts on CrewN M emibers.............. ... .... ................. 1

8.2.4 Com ponent Damiiage State ......... it............ ............ .. .. J

8 2.5 ........... .i .i.n.............

8.3 C urrent Status k Follow-on Effort .... . . ..... ... ... .. .... ... ......... .....1

DISTRIBUTION .....W...I'... 21

INTE~nONALLY LEFT BLANK.

iv

LI S T O F I L LUST 0TNS

Figure Page

1 . C losed and open swItch es ..... ..... ....... .. .. ... ... . .... ...... .. . .... .... .. .... 3

3. V iew o f M IA I ... ..... .............................. .. ......... ....... 7

A- I Histogram of frequency of occurrence N-3 residual penetration .......................... ..14

A-2 Histograms of ,-zrious kill oitegories..................................................................... ... 19

Accessi~on For

N'TI;? GRA&DTIC TA

Unannonced E

INTEmnroNALLY LE~i' BLANK.

vi

LIST OF TAkBLES

Table Page

I. Components Evaluated and Grouped by System........................................................ 8

11. Components Showing Three or More Mismatched Shots of th'

Twenty-Six Components Investigated .............................................. . .................. 9

III. Improvement in Predicting Crew Based on Binary Field Data ........................................ 10

IN". Improvement in Predicting Crew Component Damage State ............................. 1.............1

A-I1. Listing of all Components Killed in at least 1000 Replicationsof the Vulnerability Modol ................... ........................................................... 15

A-11. Damage States from the SQUASH Simulation for the Subset Crew................................... 16

A-Ill. Component Damage States from the SQUASH Simulation for theSubset ARMAMENT.......................................................................... ............ 17

Vii

ImmNTEoNALLY uHn BLANKC.

viii

1. INTRODUCTION

The National Defense Authorization Act for FY 1987' requires that all major weapon systemsundergo live-fire testing (LFT) prior to entering full-scale production. The intent is to establish thebaseline for either system response to expected threats (vulnerability) or the effectiveness of an offensiveweapon against a particular class of targets (lethality). Planning for the Abrams Live-Fire programbegan late in 1985 and culminated in a series of 48 firings in the period between July 1987 and July1988.

The Abrams LFT Program was preceded by testing of a number of other systems including theM113 Personnel Carrier and the Bradley Fighting Vehicle (M2/3). As such, considerable experiencehad been gained both in testing procedures and pre- and post-shot modeling practice. It had becomeclear to vulnerability workers at the BRL that the extant vulnerability tools were inadequate todescribe vehicle damage in a manner consistent with the field-assessment process. To remedy thisshortcoming, the BRL/VLD developed a new stochastic point-burst vulnerability code called SQuASH(Stochastic Quantitative Analysis of System Hierarchies), 2' 3 in which the following parameters arevaried in a Monte Carlo replication of warhead/target encounters: 11 slight variability in hit location,2] warhead depth-of-penetration, 3] deflection of residual penetrator, 41 spall generation, and 5]individual component-kill assessment.

SQuASH was used to predict 48 shots in the Abrams LF program. Both subjective and statisticaltests have been performed in an effort to compare field observations with computer predictions. Thesecomparisons have been made both for component damage as well as Mobility-, Firepower- andCatastrophic-Kill criteria and will be summarized below.

Just as with prior point-burst models and LFT assessments, substantial subjectivity exists in fourareas: a] the identification of system-critical components, b] the binning of partially functioning (post-shot) components into kill/no-kill categories, cl the characterization of component interconnectivity viathe fault tree synthesis and di the Damage Assessment List (DAL) mapping process (by which M- andF-Kill values are inferred). In order for comparability to exist between field tests and computersimulations, LFT observations must be assessed within the same analytical paradigms of a] through d].

In Reference 3 much of the background of LFT was described and many of the algorithmic detailsof the SQuASH model were presented. Familiarity with that work may aid in the understanding ofthese results. In the present paper extensive elucidations of the operational aspects of SQuASHincluding the means of predicting damage are eschewed; rather, a detailed bottom-up description isgiven of the vulnerability assessment process. This process begins with the characterization ofindividual component damage, moves through a system of detailed fault-tree analyses, and finally tothe Mobility and Firepower Loss-of-Function (LoF) calculations.

As each step in the process is described, the necessary similitude between model representation andactual field assessment will be emphasized. SQuASH outputs include a series of statistical estimates ofwarhead penetration performance, individual component probability-of-kill (PK) and componentdamage-state vectors. Various statistical tests have been applied to the field data vis-a-vis che modelstatistics. We will describe the tests and state our current conclusions concerning them.

1. Live Fire Testing, National Defense Authorization Act for FY 1987. contained in Chapter 139, Section 2366 of Title 10,United States Code.

2. A. Ozolins, Stochastic ligh-Resolution Vulnerability 5imulation for Live-Fire Programs, The Proceedings or the TenthAnnual Symposium on Survivability and Vulnerability of the American Defense Preparedness Association, heldat the Naval Ocean Systems Center, San Diego, CA, May 10-12, 1988.

3. Paul H. Deitz and Aivars Ozolins, Computer Simulationp of the Abrams Live-Fire Field Testing. Proceedings or the XXVI]Annual Meeting of the Army Operations Research Symposium, 12-13 October, 1988, Ft. Lce, VA also BallisticResearch Laboratory Memorandum Report BRL-MR-3755, May 1989.

2. COMPONENT DYSFUNCTION

Consider an Armored Fighting Vehicle (AFV) component characterized by a Loss-of-Function (LoF

on the interval (0.0,1.0) where:0.0 < LoF < 1.0

Zero (0.0) LoF means a component is operating at normal design (pIe-shot) specifications. Complete

(1.0) LoF means there is no component capability. The notion of a (one-diminsional) LoF is quite

natural for describing a component with a single functional characterization such as a pump or electric

generator: here the ability to pump fluid or induce current flow can be described on a (single)

normalized interval. After being struck by one or more fragments, some classes of components might

be operational in a partially functioning state: in the case of a pump. maybe it can supply fluid at half

the normal rate so that its LoF would take the value 0.5. For this class of components, the LoF mayreflect any value in the interval.

Most classes of components exhibit LoFs which are Bernoulli in nature; that is. they either operatefully or not at all. An exampie of such a component might be a portion of a fire-control system with

optical elements. Such a component might be able to absorb fragments up to certain mass velocitycombination and suffer no damage until a certain threshold is reached. Then an optical element breaks

and the component utterly fails. Such a component would then have only two possible states: 0.0 and1.0.

We also note that in the case of complex components which must perform multiple functions, the

use of a one-dimensional LoF characterization can represent an unrealistic simplification. Such asituation occurs in the description of personnel vulnerability to striking fragments. For people, theterm LoF is exchanged for Level of Incapacitation (LoI), 4 but the notion is similar. And in such a ca-se,various combinations of limb, torso and head trauma might possibly map to the same Lol and yvet

reflect entirely different operational capability (e.g. ability to view a battlefield and passively direct fire

over a radio vice maneuver a vehicle slowly through the use of hand-controls only). Thus the first stepin the critical problem of characterizing the potential loss of components is to relate various threatconditions (fragments masses velocities, blast levels, etc.) to (normalized) LoFs.

However for vulnerability analyses such as SQuASH. component characterization must be Bernoulliin nature, i.e. functional/non-functional. Thus in a conceptual sense, a minimum performancethreshold for each component must be applied against a LoF following interaction with a threat. If the

LoF is sufficiently small that, this threshold is at most equaled. the component is considered fullyfunctioning (or alive). If not, it is considered killed.

Thib process thus yields a crisp binary decision process for each component and can be characterizedby a single-pole, single-throw (SPST) electrical switch (either closed alivel or open nonfunctional') as

in Fig. 1. This concept of the behavior of individual components becomes the basis upon N hich theanalyses of the functionality of systems and sub-systems of the vehicle are based and ultimately the

notions of Firepower and \tobility Kills.

To summarize, component dysfunction can be characterized by the following steps:

1, Let a defined threat (fragment, bla.st way, etc.) interact with a given compone.nt

2. Characterize any reduction in compcnent ca)ability on a normalized interval as a Loss-of-Function.

3. Bin the (po.ssibly continuous) Lol into crisp IKill No-l\'ill hittar\ state-

All point-hurst codes acconiphsh such charactcrization ihrough the notion of '-otmpontent cotnditional

4 \\iI .am }okJI:khi in I Jo'-jIh 5p-rrazza. (ritt'ira for Iw,'apaiati i.q S.oldi r." u'with b-ir , h', id l ,h tt.. I4 i B:Ill-teResearch Laboratory Report #12t0. January 195i5

• • u | N • 2

if--'--I .... _/e

Closed Switch -- Live Component Open Switch - Killed Component

Figure 1. All components of an Armored Fighting Vehicle (AFV) start in a working stateindicated here as a closed single-pole, single throw (SPST) switch. After interaction with athreat, if the functionality of the component is insufficient to support a minimalcapability, the component is considered killed and the switch is opened.

kill probability or component Probability of Kill, given a Hit (P1.. ). Whether such a process usesfragment mass 'velocity, shape-factor/orientation or the notion o 'ethality ' , the component PK/Hanalysis effectively concatenates all three steps into one.

- CA VEA TS RE: COMPONENT D YSFUNCTION -

" Components with complex or multimodal capability may not be well described by a one-dimensional !,oss-of-Function.

" The LoF interval may be continuous or discrete.

" The threshold for minimal component operation (to be considered non-killed) is likely to be afunction of a specific mission requirement. Thus a component with a fractional LoF might be"alive" in one scenario while "killed" for another.

3. SINGLE-SYSTEM FAULT TREE

The analytical determination of whether a particular system (or sub-system) is functional startswith connecting all of its components together in the form of a series/parallel circuit. These circuitsare normally called faidt trees and an example is given in Fig. 2. Before a shot occurs, all switchs areclosed (fully operational). After a live-fire shot, some components may have lost enough capability tobe defined as killed (switch open). Three components are killed in this example. The bold line showsthe (single) functional path through this system, so this system is considered fully functional.

- C(A VEATS RE: FAULT- TREE DEVELOPMENT -Note well, this process gives rise to a number possible sources of subjectivity both in the analysis and inthe field assessment: for example:

" What constitutes a switch (i.e. component)?

The subjectivity here has two parts; how is the component defined, and is the component critical tosystem effectiveness? Only the criticai components define the circuit.

" What constitutes a proper subsystem definition?

Clearly considerable subjectivity enters into this decision process as well.

4. CRITICALITY ANALYSIS FOR AN AFV

A complete rriticality analysis of an AFV consists of the determination of 1. which components. iflost. miyht result in a reduction of system mobility or firepower capability and 2' the structming of

s- e. lerenee V1 S,t on VI . or a isoussiorn of the PMs used in the SQuASH model

Figure 2. An example of a fault tree used in vulnerability analysis. Parallel componentsexhibit redundancy; series components do not. An overall system is either fully functional- at least one unbroken path exists from top to bottom, or is killed - no unbroken pathexists.

those "critical" components into fault trees as described above. In the case of the Abrams tank, thecriticality analysis5 resulted in the generation of 76 individual fault trees built from approximately 750critical components.

- CA VEA TS RE: CRITICALITY A4NAL YSIS -The issues here are:

" What sub-set of AFV components should be classified as critical?

" What n fault trees constitute a proper representation of the AFV?

In addition to the unavoidable subjectivities connected with this process it is further critical that boththe live-fire field-assessment process and the live-fire modeling process use the identical fault-treeframework. Otherwise there is no comparability between the two processes and thus no basis forcomparing field and predicted results.

5. J. J. Ploskonka. T. N1. Mu.hl. C. J. Div-]y. Criticalay Analyeii of the tIAI Tanik. Ballistic Re'earch LaboratoryMemorandum Report BRL-MR-3071. Juno 1988.

5. VULNERABILITY MODELING & LIVE-FIRE TESTING

The analytical estimation of vehicle - ulnerability and the assessment of a live-fire test are bothcharacterized by a two-step process:

* STEP 1: Fire a warhead against the target and observe which switches are thrown open by theevent.

At this stagc, we first predict (or observe) whether the munition breached the armor (perforation) andwith what residual energy: then examine the effect- of that residual energy on individual components:compile the resultant state of all of the critical components: and decide whether the vehic!e sufferedtotal irreparable damage (catastrophic failure or K-kill).

* STEP 2: Take the switch states together with the fault-tree logic and process this information in aprecisely consistent (but possibly subjective) fashion :o infer one or more Measures-of-Effectiveness(\IoEs).

For armored fighting vehicles, the \oE' are characteri'ed in terms of loss of the vehicle primaryfunctions: Mobility (N% Lof'), Firepower (F LoF), and the greater of the two, Mobility Firepower (\I 'FLoF).

-CA 1 EAT: MODEL IS. FIELD DATA -

e If both the field and modeling processes differ in the precise processing phases of STEPS I & 2.then comparability is lost.

5.1 Observations re: STEP 1:

If there are n switches (critical components) represented in the criticality process, then there exist 2n

possible unique switch (damage) states. However. LF damage is typically constrained to localizedregions of an AFV. Thus. for a single shot, only a subset of all critical components are candidates fordamage. This reduces significantly the potential number, but from the results of the current model,our simulations typically reveal z 10 distinct component damage states for a given shot.

If the criticality analysis and/or component (binary) kill assessments are inconsistent between themodeling process and live-fire field assessments, then there is no basis for comparability between thetest results and model predictions.

5.2 Observations re: STEP 2:

The process of Step 2 currently involves the Damage Assessment List (DAL). 3 The DAL contains alisting of some 150 major components/AFV systems. If a single major component or system isnonfunctional following a shot. then the M- and F-LoF values are given directly by the DAL. If two ormore maj r components/'systems are nonfunctional. LoF values for each are extracted via the DAL andsurvived T to get single 'I- and F-LoF values. Typically the 'I- and F-LoF values resulting fromSTEP 2-processing are binned into twenty intervals. Since the damage state dimensionality resultingfrom STEP 1 is 10 6 . agreement between predicted and field-derived LoFs. even if processed by thesame methods, does not imply validation or even support calibration.

STEP I and STEP 2 ,'an be related idpntically' to the nmapiing praesss shown in Fig. 2. Ref .3. STEP I her, is thenapping process from Ss,a, 1' to S[,ace 2K. STEP 2 here is th mapping pro,'ess from Spae 2' to Srace 4,.

i The Surrivor Rule states that the overall LoF of an AFV consisting of n independent systems eact with its own LOF. is givenby

Lo = 1- i-1,oF×'l - IoF..x-.- I -loF

• • m l I I n]

6. EXAMPLES OF SQuASH OUTPUT

Figure 3 gives a view of the computer model3 of the MIAI looking at the front-left of tile vehicle.For this display the armor and main armament have been removed to reveal some of the interiordetails of the computer description. This modeling effort has produced one of tile largest target-de-cription files ever assembled, consisting of over 5000 objects. In addition to this high level ofgeometric modeling required for the Abrams Live-Fire Program, the -tochastic nature of thecalculations leads to a complex set of outputs which can best, be displayed in the fornm of summarizingtables and histograms. The samples of these outputs, given in the APPENDIX.' exemplify thiscomplexity. Briefly, they show:

" A histogram of' residual armor penetration for 1000 computer replications of a warhead armorencounter.

" The SQUASH prediction for all critical components killed on at least one of the 1000 replications.

" Listings of component-damage states for several important classes of critical components. They areranked according to expected frequency of occurrence.

" Distributions of Mobility. Firepower. and Mobility/Firepower LoF, plus probability of CatastrophicKill (K-Kill).

7. COMPARISONS: ABRAMS TESTS/SQuASH PREDICTIONS

In the following sections we discuss comparisons between these predictions and the results of theAbrams Live-Fire Tests.6 In order to keep these discussions unclassified, various detail will necessarilybe omitted.

7.1 Perforation

Does the attacking munition succeed in perforating the armor of the vehicle? The answer to thisquestion becomes a first-level input to an estimate of the vulnerability of a tank. Of the 48 shots fired.in 25 tests (52%c) the perforation results were predicted exactly by SQuASH; that is for each encountereither all 1000 re;,lications predicted penetration and penetration was observed in the test or none ofthe 1000 simulations predicted penetration and the field test did not result in penetration. In 43 (90'0)of the shots fired, the field outcome occurred in consonance with the larger percentage of computerpredictions. Three of tile shots were predicted by SQuASH. however, not as the most likely outcomehaving probabilities of occurrence of 0.36. 0.34, and 0.23. Only two (4%) of the shots were notpredicted by SQuASH. One shot gave a result not predicted because the round happened to passthrough a component that, was not modeled in the computer target description. SQuASH failed topredict the perforation outcome of the other shot, due to incomplete information about theperformance of that munition.

When input, data is adequate, the model seems to predict warhead/armor penetration well.

7.2 Catastrophic Kill

To produce a Catastrophic Kill (K IKill), the munition must cause damage that is irreparable on thebattlefield and renders the vehicle completely incapable of carrying out its mission. In every caseSQuASH predicted as the most likely outcome the K-Kill result observed in the field. SQuASIH alsoreminded us that for certain shots the complementary outcome might hare occurred if the field samplesize had been larger.

4 These figures and tal1s wpre taken from Rpr. 3.6 C..I Dively S. L. HenrY. . 1. u,'king, .1. It. Smith. W. E. Baker, D. W. Webb and P. 11 P07. Abranm Lir-Firf T,'t

Pro.gram: Compal-i.on. lhfo,n SQu.I4SI! Prtditiv)., and Fild Out,'ourt. 11'J. Ballistic lh-'u;irch 1,nuoratorv SpeciilPublication. BRL-SP-81. Septemler 1980, SECRET.

6

Figure 3. View of the MLA1 produced by the computer description. The armor and maingun have been removed to reveal the level of interior detail. This description containssome 5000 objects of which approximately 750 are critical components.

7.3 Component Kill Assessment

As discussed in the Component Dysfunctioni Sect ion. all component out come, are characterized asBernoulli trials, i.e. functional 'nonfunct ionali. For each field shot (vach \'et or element ). a1 froha bil itvof killing the given component is comnput ed equal to the meanl of 1000 S'n AS! MoNllu t e-( *a H~Oreplications. Using these -18 probabilities. andf assuling st at istical ind(ependeince of t lie field re'~ufts. atnempirical distribution of the vector is obt a ined by coin1)1!ug al I foi )e on t omnes Thle Ordering ofProbabilities (OP) Test' is used to determnine thle f)-valute withlin tihat Iist ri bit ou. The p-va liie reflect,the probability of real iz jug the observed liv c-tire v-ector or nn ' y veotor les l i kciy than t he one observed.A p-value of less, than 0 05 iiicateCs that hel( tield outcome r''-itlited in a r~are vector anid cause-rejection of the hypot hes that the miodel out put is consistenct with thle field dat a.

7.3.1 Initial Individual Component Assessment: Due to the( time constraints' for anly.zing theLive-Fire data, only twenty-six of the components have been analyzed to date for consistency with themodel predictions. These components were chosen based upon their relative importance to vePhicleLoss-of-Function. Table I gives a listing by system of thle components examined.

Table 1. Components Evaluated and Grouped by System

Components Evaluated

Group 1 - Other Group 4 - Armamentreceiver- trans mit ter comnmander's control panelintercom amplifier guniner's primary sight

gunner's auxiliary sightGroup 2 - Crew commander's gps ext.commander hydraulic reservoirgunner main hydraulic pumploader race ringdriver slip ring

main gunGroup 3 - Electrical ammoturret networks boxhull distribution box Group 5 - Propulsionbull networks box driver's master panel

alternatorpower turbineair cleaner

electronic control unittransmission, mlain bodyfuli

These 26 components over the 48 tests produce 1218 comparisons between the( model predictionsand the field re'.ult s. Of these. 960 (781(-) were complem e mat ches, A compflet e miatch occur, when all1000 SQuASH outcoiiie> piedict thle observed field out conme. Thiirtv-.-ixI\ (3(-) of thle com parisonsresulted in complete iuj .muatchves: thatif -. S~u,-VSII inever )in its J000 replications . predicted theconmponent I(a niage observed. The rein a ii g 2-1.3 (I 9CC) coipanisons w~ere broken down bY t Ii ra t and

David W. Wphlt. Tr fo for oio~t~ro-q o7f V lirb~i 1 ~dIo/~ I1)tiv RJesenrcli Laboratory Teri1aI Report#3030. Anuiot 19,99

component into 34 statistical tests. The OP Test was applied to these groupings. Twenty-two (65%) ofthese tests accepted the hypothesis that SQuASH predicted the component PK correctly. Theremaining 12 (35%) failed the test for consistency.

Combining the complete matches and those components subjected to the OP Test. we get a 90%consistency in predicting individual component PKs for tile twenty-six components evaluated.

SQUASH had the most difficulty predicting damage to cables. The twenty-six componentsevaluated above did not include cables. It is not surprising that SQuASH would have difficultypredicting damage to cables since they have a very small presented area and the shotlines are infinitelythin. An analysis of all components is needed to assess fully SQuASH's ability to predict componentdamage.

7.3.2 Initial Ranking of Component Discrepancies: Table II summarizes the components havingthree or more mismatched shots. i.e. where < 25% of the SQUASH outcomes predict the field result. Itwas noted that crew members were four of the top five components having significant mismatches.Investigation of the crew data revealed an incompatibility between the field data collected and the dataexpected by SQuASH. As noted above (Section 2.), the SQuASH model performs a binning of allcomponents following a shot into crisp killi'no-kill states. However in the case of the LF personneldata, the original assessments were based on the notion of continuous fractional incapacitation (0.0 <LoF < 1.0). This incompatibility results in incomparable data for the individual crew components,component damage states, and the Mobility-, Firepower- and Mobility/Firepower Loss-of-Functionmeasures of effectiveness.

Table II. Components Showing Three or More Mismatched Shotsof the Twenty-Six Components Investigated

Number ofComponent Number of Complete

Mismatches Mismatches

Gunner 10 4Gunner's Primary Sight 8 6Driver 7 6Commander 7 2Loader 5 3Main Hydraulic Pump 4 4Hydraulic Reservoir 4 3Main Gun 4 1

Turret Networks Box 3 0

7.3.3 Revised Individual Crew Data: In order to make comparisons on how well the SQUASHmodel predicts crew incapacitation, we must first have comparable scoring between the model and thefield results. Since OQQuASH expects components to be either functional or nonfunctional after a shot,we asked the organization responsible for personnel vulnerability to convert the fractionalincapacitations observed in the field into these categories. An assumption had been made originallythat if the loss of function was greater than zero the crew member was totally incapacitated (old bins).The personnel vulnerability experts categorized fractional incapacitation greater than or equal to 0.75as nonfunctional (new bins). Table Ill reports the agreement between SQuASH and the field data usingboth the old bins and the new bins. Although the SQuASH model does agree more with the field datain predicting crew incapacitation, we believe that there are other factors that need to be investigated

for all components.

, !

Table III. Improvement in Predicting Crew Based on Binary Field Data

OLD BINS" NEW BINSt RESULTS

54%c 59% Complete match

27% 29c Mtost likely outcome predicted by ,QiiASlI

10%c 9(1,; Not most probable outcome, not a rare-----.-.--- event (probability > 0.05)

91% 98% Subtotal

3(-( 2% Rare event (probability , 0.05)

7%- 2%- Complete mismatch

9% 4% Subtotal

t If LoF 0.0, Outcome - Total Incapacitation

If LoF > 0.75, Outcome = Total Incapacitation

7.3.4 Component Damage States: On a given shot, damage of components is not independent.Predicting individual component damage over a set of tests gives no indication of how well we predictcomponent damage state or loss of vehicle functions. All vulnerability measures derived from field testsare a function of the component damage state of the vehicle since that is the field observable. Becauseof the dependency, the distribution of component damage state must be derived through a Monte Carloprocess using SQuASH. The critical components were grouped by system categories (Crew, MajorElectrical, Armament, Propulsion and Other) because the vehicle-wide damage state distributionin many cases was too large to compute even using the Cray-2. For each live-fire shot, a .Monte Carloprocess was invoked (1000 replications) using SQuASH. The results were used to derive the empiricaldistributions for the (five) sub-system component-damage states. The field result from each test andfor each of the five system categories (48 X 5 - 240) was then compared with the empiricaldistribution. If the probability of observing the field result within the empirical distribution was lessthan 5%, the hypothesis that the SQuASH model correctly predicted the component damage state wasrejected. This procedure is detailed in the Modified Ordering of Probabilities Test. 8 Since SQuA',[ onIyprinted the 200 most. frequent damage states and occasionally the number of outcomes exceeded thisnumber, there were 14 caes where conclusions could not be drawn: 42 (19%) out of the 226comparisons resulted in rejection. That is, SQuASH predicted component daiiage state con-istentlvwith the field results in 81% of the cases tested.

7.3.5 Revised Crew Component Damage States: The above analyses on component damagestates was based upon the old bins for the crew members. Rebinning ihe dat j using he 0.75incapacitation criteria, we find that SQuA.-II improve at prelicting crew component d(Iin.ag ,' " , IIin Table IX. The per'entage of rare evens (probl)bility of "wcief < 0) ,''' fri i27" I,

18'( in predicting crew comlponent damage state over all 48 test.

8 David \V. \\A,. .1t lodtifi ation to tht Ordtr by Probabiity 10'/ Pro ,,d ,r. Ih li.tli c [Heenrcht I It)Ornlor\ 'i e'Ii c ikiiReport, To be Pubishpi.

10

Table IV. Improvement in Predicting Crew Component Damage State

OLD BINS NEW BINSt OBSERVED FIELD OUTCOME

33%-( 35% Predicted on all 1000 SQuASH replications(('omplete Match)

27% 31% Most likely outcome predicted by SQuASH

13% 15c Not most likely outcome, but not a rareevent (probability > 0.05)

73% 81% SUBTOTAL

4c 8% Rare event (probability < 0.05)

23%. 10% Never predicted in the 1000 SQuASH replications

27% 18% SUBTOTAL

If LoF > 0.0, Outcome - Total IncapacitationIf LoF > 0.75, Outcome = Total Incapacitation

7.3.0 Analysis of Loss-of-Function: M-, F- and M/F LoFs have not yet been analyzed using thenew binning for crew members. Analysis of LoF for the old bins confirmed the SQuASH predictions for\lobility Kills in 41 (85%') of the 48 shots. The field results confirmed the SQUASH predictions forFirepower Kills in 16 (33%) of the 48 shots. Because many different component damage states can mapinto the same LoF. agreement here is not a sufficient condition to infer consistency of the SQUASHpredictions. This is a case where it is possible to get the right answers for the wrong reason. SQuASHis a component-level model and if the component damage state predictions agree with the observed fielddata it necessarily implies agreement of the LoF measures. That is, agreement of component damagestates is both a necessary and sufficient condition to validate the models. LoF analyses are summarizedhere only to give a complete accounting of the usual vulnerability measures reported.

7.3.7 Secondary Kill Mechanisms: Traditionally, component-level vulnerability models, in themain. calculate damage due only to the main penetrator and behind-armor debris (BAD). Thesemechanisms are normally termed the priniary-kill mechanisms. There are well-known conditions underwhich other phenomena such as blast, shock, etc. (often termed secondary-kill mechanisms) contributesubstantially to AFV dysfunction. Due to the time constraints for developing the SQUASH computerrmodel and generating the Abrams pre-shot predictions, only the primary-kill phenomena wereniodeled.*

In the actual field results, the secondary-kill mechanisms, when observed, were nearly always (therewas but a single exception) accompanied by damage due to primary-kill mechanisms. Thisobservation, if borne out by future tests, indicates that. in the main. secondary-kill mechanisms, whenpre-;ent. tend to kill (redundantly) components already killed by the primary phenomena. Clearly.future work is neded to weigh the true importance of secondaryv-kill phenoniena.

. i :wi, t:iv,. I.-n ,I in thf- SQUASH ,ode to "r:,juit otltr ,lanage pIvhnonin ; - n,-\v algorithins and ;,jpp.,,rting IJa:,

bop'0[1 availatde

8. SUMMARY

This sum miary revijews thle tw%%o manjor t lieni,. oft t, paper Fi rst. we give t 1w Itailed nat tire of themodleling paradigmis it ilized iniSii~ and reqii ired of the L1F field a'ieitProedire- forcomparability to exist. Second, we summlarize our, efforts to compare sttsti ll odel and t -T' datal

8.1 Similitude of Abrams LF Modeling & Field Assessment:

In Sections 2.-4. we diSCU.,Sed the Construction of thle SQuA Il m lodlel. The chiief iiir, are- Iwhat const itult e, a critical coimponen t antd how miany stic li teil pro01pry Cli~rACtV-7 :ri1e an.\'2 bow.should the decisiotn process be, construrted leading to Thle )Ost-hdot aset~itof Bernoulli kill no-killcomponent states, and :1 wvlat is the proper.(.1 coihigirt ion of lie fauilt t ree, wit bin which thle criticalcomponents reside?

Without st rict adherence to this p~art icular view of thle vuilnera bility world. the field-basedassessments cannot be compared properly with the model predictions. We make two relatedobservations: based onl the held ass essmient reports to date, we cannot ascert aml that indeed thloseprocedure., are comparable. WXe quickly add that we are not inferring that to asses s a .XFV in a miannerinconsistent with our model is wrong, only inconlsistent!

It is worth noting thatr both the dlescription of the model hirocesses given in Sections 2.-4. and themianner in which the SQuA.';H computer model perfornis it' cal1culations are bottomn-up in fas;hion.However, the way in which the Abramis field assessors p~erformed their invest igat ions was top-dowin inmanner. Following a shot, the assessors generally attempted to operate all major systems in order toflag possible dysfunction. If abnormal function was observed. then further invest igat ions wereperformed. This procedure could result in missing killed components for which redundant. (parallel)backups existed.

8.2 Statistical Comparisons - Field & Simulation Data:

This paper reports our first cycle of comparing LF field and simulation data. The Live-Fire test-result in mans' measures that can be analyzed to give insight, into the modeling process. Thleinvestigation of modifications that should be made to 'SQuASH to improve its predictive capability arecomplex. Where disagreements are observed in the measures of performance, many sources for thevariance exist and must be investigated systematically.

8.2.1 Perforation and Catastrophic Kill: All Live-Fire data hias been analyzed for perforationand catastrophic kill. SQuASH predicted perforation consistently in greater than 05% of the field tests.In every case SQuASH predicted as the most likely outcome the catastrophic kill result observed in thefield.

8.2.2 Individual Components: In this first set of comparisons. twvent)-six of the most importantcritical components have been analyzed to evaluate SQuASH's ability to predict individual componentdamrage. S-QuA.ShI predicted b~etter thain ~)%of the coniponent damnage correctly. Siili estiintiotiabilities are important to the Army studies supporting spare parts inventories and repair para nie'1ers .

Over all components SQUA.SH had the most diffhCUhty p~redicting damage to cables. IPossile catls(,,include but are- not limit ed to geomlet iic Sa mpling problems related to thle ver 'y smlall presenitedl area,.component P K H characterization, or lie fragment rlensi ties used for belinid-a rmor debris Thisproblem and its effect on thle comlponient (lanlage state and LoF measures are under itivestigat ionl.

Theailt-ilty to preFdict individual comiponienit damlage, althioiigi ncessary for agreeloetit betweimiodel anid t-'t ouitcomet i, itifortuiiiot.lY 11(1 sitfficietnt lSsteIII- Wide (oiiloneifitdtng's e.SU In n13iat7ed below, provide that. sii licieiicv.

8.2.3 Secondary Effects on Crew Members: Secotudary kill niiechatiiii (e,.g bl't. "hiock.aporitics) as, iiiea-ui.' oil one of t lie. tiiOst critical and sensiltive of .- F\' conliponiient- CreW, do nt,)

appear significant. In nearly every case where seconidary kill plienontena 'ouild he' oh-erved. coflipolli011ikilt hid already o--urr-d rta priary tuechiaiwiiss. it w\ould app),ar that thc cot iimniiio fo iiof

damnage characterization should remiain onl the primarY kill iicitits

12

8.2.4 Component Damage State: This measure of performance is both the prime characterizationof post-shot damage from which the other measures of performance (e.g. Mobility LoF. Firepower LoF.and \Mobility Firepower LoF) can be inferred as well as the most difficult to predict. Thedlimensionality of the damage vector can be very high. For conditions where the munition overmatchestile armor, we infer typically between one million and 30 million discrete damage-state possibilities at agiven location. And yet an actual test gives us only a single field damage state for comparison with allof these possibilities.

We also note that, given a consistent mapping of component damage state to the LoF measures,agreement between the field and SQuASH component damage state is both nece.sary and sufficient totest consistency of the SQuASH model predictions with the test data.

SQuASH currently predicts component damage state correctly in approximately 81% of the casestested. Considering the dimensionality of the problem and the fact that these were the first predictionsmade using a newly developed stochastic model, 81% agreement is remarkable. Component damagestate is under further investigation for improvements to the SQuASH model.

8.2.5 Loss-of-Functions: The LoF measures have been analyzed for all the Live-Fire test results.Although the LoF measures have not yet been analyzed using the new binning for crew incapacitation,the expected improvement is unlikely to significantly change the overall result. Mobility LoF waspredicted consistently in 85% of the Live-Fire shots. Only 33% of the predictions for Firepower LoFwere consistent with the field data. The dimensionality of the Loss-of-Function space is twenty bins.\lanv component damage states map into each LoF bin. Considering the dimensionality of this space,we reject the hypothesis that SQuASH predicts Mobility or Firepower LoF consistent with the observedLive-Fire data.

8.3 Current Status & Follow-on Effort.

On balance, considerable progress has been made in the analysis of the Abrams LF data. From thisinitial analysis our predictive capability is good in some areas. In other instances, for example certainindividual component kills, it is clear that we have not done well, but that good, or at least better,agreement can be achieved by modifying certain component PKs. In other areas of the analysis,particularly in the vehicle damage states, we encounter both the damage characterization of greatestimportance and the greatest statistical complexity.

We will continue to study carefully the statistics of these damage states. Their number anddiversity taken together with the mapping process to various Loss-of-Function metrics lie at the heartof the vulnerability assessment process and the use to which these related Measures-of-Effectiveness(e.g. \1 LoFs. F LoFs) can be utilized dependably. The uses, of course, include the assessment of Live-Fire tests, and the application of vulnerability data to wargames, lethality optimization, vulnerabilityreduction, and spare-parts estimation.

9 For a discussion of siuffi'iencv eonditions for vulnerability model validation, see Michael W. Starks, .4sefs.-ing th -ccuracy ofI'ulnerahility Model., by ('omparion with 'ulnerability Ezperiment. Ballistic Research Laboratory Technical Report#3018. J1ly 198)

13

APPENDIX: SAMPLES OF OUTPUTS FROM SQuASH

Figure A-I gives a histogram showing the distribution of residual-penetrator overmatch. Thcwarhead is unspecified in order to keep these results unclassified. In general. these curves exhibitcomplex shapes, sometimes with multi-modal distributions.

Behind Armor Penetration

100Mean Penetration= 8.2

- -Std. Deviation= 4.9

C- 70-:36GC_)

LC--

0 50-

0 40-

U 30-

a)

L:3 0-

1 12 11 112102224 28 30

Residual Penetration (in.)

Figure A-i. Histogram of Frequency of Occurrence vs. residual penetration. Because ninedifferent shot lines are used (typically encountering different armor types) together withvariable warhead performance, different levels of overmatch are derived.

This is a natural consequence of the randomness of the overmatch together with the grid ray dataderived over nine sample rays. Even though the rays are separated nominally by three inches, differentcombinations of armor are often encountered. The difference in effective protection levels can lead tosignificantly different residual magnitudes.

For one sample calculation over the course of 1000 code replications, some 60 critical componentswere assessed to have been killed at least once. Table A-I lists these components. The remainder of thefigures and tables in this appendix were taken from Ref. 3.

14

Table A-I. Listing of all components killed in at least one of 1000 replications of theSQUASH vulnerability model. The columns give the component identification, the totalprobability of kill, the probability of kill from the jet alone, and the probability of killfrom fragments alone, respectively.

Relative Frequency of DamageComponent

pal P, P,

commander 0.399 0.000 0.399gunner 0.995 0.883 0.594loader 0.301 0.000 0.301cable lw 100-9 0.018 0.000 0.018cable Iw101-9 0.011 0.000 0.011cable 1w104 0.008 0.000 0.008cable 1w104 0.137 0.00 0.137cable 1wL00- main branch 0.008 0.00 0.008cable lwL07-9 0.007 0.000 0.007cable 1w108-9 to main gun 0.034 0.000 0.034cable lw200-9 0.552 0.000 0.552cable 1w201-0 0.011 0.000 0.011cable Lw202-g main branch 0.017 0.000 0.017cable 1w203-9 0 012 0.000 0.012cable Lw208-0 0.309 0.000 0.300cable 1w209-9 0.2183 0.000 0.210cable 1w210- 0.337 0.000 0.337cable 1w301 0.158 0.000 0.158cable 1w304 0.039 0.000 0.039cable Iw360 0.017 0.000 0.017cable 1w309 0.070 0.000 0.070cable tw310 0.027 0.000 0.027cable 1w31l 0.008 0.000 0.008cable 1w312 0.012 0.000 0.012cable lw31S 0.033 0.000 0.035cable Tw "0,- 0.044 0.000 0.044cable 2w107-0 0.009 0.000 0.000cable Tw 108 0.006 0.000 0.00cable 2w112 0.002 0.000 0.002cable 2wL54-2w155 0.012 0.000 0.012hull distribution box 0.003 0.000 0.003hull networks box 0.012 0.000 0.012turret networks box 0.048 0.000 0.046Sumer's primary sight 0.025 0.000 0.025commander's gpe extension 0.107 0.000 0.107thermal image control unis 0.208 0.000 0.20=thermal rev'er 0.001 OO.00 0.001intercom amplifier 0.024 0.000 0.024guner's intercom control box 0.104 0.000 0.1041oader's intercom control box 0.018 0.000 0.018cable 2w117-9 0.003 0.000 0.003h.llne au pump to filter mani 0.003 0.000 0.003filter manifold 0.013 0.000 0.013hinta ffiter manffold to HDM 0.018 0.00 0.018haines filter manifold to 5DM 0.007 O.O0 0.007Unmm TDM to azimuth srvo 0.003 0.000 0.003

hines TDM to aximuth wrvo 0.011 0.000 0.011azimuth gearbox 0.004 0.000 0.004manual azimuth gearbox 0.004 0.00 0.004manual azimuth gearbox 0.008 OO00 0.008manual elevation pump 0.M 0.000 0.015manual elevation pump 0.005 0.000 0.005gunner's control handle 0.016 0.000 0.016commander's control handle 0.073 0.0O0 0.073race ring 0.013 0.000 0.013h.ine TDM to man elev pump cd 0.004 0.000 0.004hbine check valve to HDM bypa 0.020 0.000 0.020caial ready ammo box 0.052 0.000 0.052azimuth gearbox - ewe 0.022 0.000 0.022commander's vision block 3 0.003 0.000 0.003commanders vision block #2 0.005 O.O0 0.005commander's vision block #1 0.004 0.000 0.004loader's sight 0.017 0.00 0.017

I ffine riht bow to manirold 0.001 0.000 0.001P. - Total Damage due to all mechaismsP- Damage due to jetP; Damage due to fragments

The next two tables ,how how SQUASH output departs radically bey ond other point-btir-t models.

Here two classes of components are examined separately by category. This procedu re h:s been adoptedbecause of the great difliculty in interpreting the results of damage states across Ihe complete vehicle

Table A-I1 lists the category' of CREW. For this group. the calculated damii >t, Ifr,> apply to tlepersonnel located in the turret-basket area. The damage states derived from the 1000 replications weresorted together and then ranked from the most to the least likely in occurrence Tail, A-l -.hows thatthe most likely crew casualty state is for the commandtr and loader not to be inapacitated and for thegunner to be incapacitated. That outcome occurred -161 of the 1000 replications, for a net probabilityof 46%. The next most likely crew casualty state is for the conimander and gunnwr to be in.apacitated

but not the loader. The likelihood of this outcorne is asse-sed at 24%. For thi', romionent ,tubset.SQuASH predicted probable outcomes for only six of the eight possible combination- of 'onimander.

gunner. and loader.

Table A-I. Damage states from the SQuASH simulation for the subset CRE'. Open

squares (c) indicate no component kill. Bullets (o) indicate a component kill. Thecomponent numbers correspond to the listing below the table. The relative probability ofeach damage state is given in descending order of likelihood (column state). Thecumulat. e sum is given in the last column (sum).

Group: CREWDamage States, sorted by likelihood

Damage States Relative

I OccurrenceComponent Number state sum1 2 3 _

o . 0 0.461 0.461* * 0 0.237 0.698

• • 0.1932 0.890

[ 0 . 0.103 0.993O1 0 0 0.005 0.998* E] 0 0.002 1.000

o - component undamaged* - component damaged

Number Component

I commander2 gunner3 loader

The component damage states for ARMAMENT, shown in Table A-Ill, reval the greatest

complexity in damage states. This is probably to be expected since nearly" half of all the criticalcomponents killed during the 1000 replications wer part of this group. ks seen in otht, groupings, the

most likely damage state assessed for the 29 components in ARMAMENT i> no damage. this for 2"'of the outcomes. The most likely -tate exhibiting damage occurred for five components (numbers 6,10-12. 15) on 78 of the 1000 replications for a 7.8%(, probability. From here on. the 29 components areinvolved in a slow convergence to the 99th percentile (sumn) at the 223rd damage statl

The final stages of calculation of vulnerability involve the various categories of kill First.catastrophic kill represents the complete loss of the system, which generallyv occurs in encounter with

large-caliber ammunition (warhead and or propellant) or fuel. The probability of thi> Pvent is shownin Fig. A-2c. For this particular shot. the probability of a catastrophic event i,. a...sed a s zero. Note

15t

-Z0

~0000000000000 000

C 000OOOOOOO000O0O 100

C-000000000000*00 000

O00000000000000 000

C-O COMIOO D O00 2

V 000OD0000000000 000

7&i000000000000000 000 .S

U2 0 0 0

I4 _M ' - VD

~iooooooo~oo~o 000

0 -2 p

-j :j C)~

F=00C00000 00 0 .0oz o0 a -a , t Sm0 hQ

0nl c 0 l0000000000c O

ca =10 0000 00000 000 00ca ED -c -0 1-~ 1000 -Co -l0c , -wa

-,000000000000C0000 co

~-000000000000000 c0oo

Q~L. ~ 1000000 000000000 000

- -= 17

that the histogram associated with KI( ill can be populated only in the first and last bin,. In otherwords, catastrophic failure either occurs or it does not; the outcome is either zero or one.

The other kill categories are assessed by mapping each of the thousand damage states Via th,. l).over to the appropriate M- and F-Kill values. The category labeled NI F (read M OR F). by long-standing agreement with the TRADOC community, represents the larger of the two values. It i. notthe OR of the logical (Boolean) operation.

We examine the M-Kill plot in Fig. A-2a. Here we find the most likely outcome is for about 0 57Mobility Loss-of-Function (M LoF), assessed at, about 30% probability. lowever the dist ribut ion isextremely broad with approximately 18% of the outcomes near the 0.0 bin. The expected \1 LoFoutcome is 0.36: inspection of the histogram shows that. there are approximately 26%- of the outco||e,near this value. However the distribution is broad, and there are a significant number of occurrencesaway from the mean. The corresponding results for Firepower LoF are given in Fig. A-2b. In thtshistogram, the mean LoF occurs in a bin with a low population. There is also a significant probability(--+ 18%) that the F LoF will be zero. The MF LoF histogram is given in Fig. A-2d. The \I F value.by definition, is the larger of the M and F LoFs on a shot-by-shot basis. The F LoF tends to dominte

in this case.

Mobility Kill Firepower Killt0- tO0-

Mean L.O.F.-O.36 Mean L.O.F.-O.45Std. Deviation-0.23 Std. Deviation-O.2B

go-U UC C

L C-L- C-60 D60C. uU- Uo 0

0a40 0 40

C- C

60

0 40 0 40,

LC

0.0 0.2 0.4 0.6 O.B 1.0 0.0 0.2 0.4 0.6 0.8 1.0Loss of Function Loss of Function

Catastrophic Kil in ob t e My/Firepower Ki l1O0- laO-

Mean L.O.F.-O.OO Mean L.O.F.-O.53

v Std. neviation-O.OO a Std. eviaton-.30

080 0

U U

S0 o 0

u Uo

C C

i - "

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0Loss of Function Loss of Function

Figure A-2. Histogram-s of various kill caItegories derived from the SQUASH simulation.The Mobility Kill Loss-of-Function (LOF) is shown in a), the Firepower Kill in b), theCatastrophic Kill in c), and the Mobility/Firepower Kill in d). The means (expectedvalues) and stand-ard deviations are given for each plot, but are considered relatively

immaterial for these non-parametric (i.e. non-gaussian) statistics.

19

INFENTomALy LEFF BLANK.

20

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unlimlted)12 Administrator I Commanderlimi.td) 2 Defense Technical Info Center US Army Missile Command

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and Technology ActivityAmes Research CenterMoffett Field, CA 94035-1099

21

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1 Kaman Sciences CorporationGTRI-RAL-\L-kD ATTN: Timothy S. PendergrasATTN: Mr. Joe Bradley 600 Boulevard South. Suite 20SCRB 577 Huntsville, AL 35802Atlanta, GA 30332

35

DISTRIBUTION LIST

No. of No. of

Ketron, Inc. I Logistics Management Institute

ATTN: Robert S. Bennett ATTN: Edward D. Simns Jr.

696 Fairmont Avenue 6.100 Goldsboro Road

Towsontown Center Bethesda. ID 20817-5886

Towson, MD 212041 Los Alamos Technical Associates. Inc.

Keweenaw Research Center ATTN: John S. Daly

Michigan Technological 6501 Americas Parkway, #900

University Albuquerque, NN'I 87110

ATTN: Bill ReynoldsHoughton. MI 49931 1 LTV

ATTNi MS 19.1-51, Mike Logan

Lanxido Armor Products PO Box 225907

ATTN: Dr. Robert A. Wolffe Dallas. TX 75265

Tralee Industrial ParkNewark, DE 19711 1 LTV Aerospace and Defense

ATTN: Daniel M. Reedy

2 Lincoln Laboratory PO Box 225907

MIT Dallas, TX 75265

ATTN: Dr. Robert ShinDr. Chuck Burt 2 Martin Marietta Aerospace

P.O. Box 73 ATTN: VP-113. Dan Dorfman

Lexington, MA 02173 MP-433. Richard S. DowdPO Box 5837

3 Lincoln Laboratory Orlando. FL 32855-5837

MITSurveillance Systems Group 3 Mathematical Applications Group. Inc.

ATTN: R. Barnes ATTN: M. Cohen

G. Knittel R. Goldstein

J. Kong H. Steinberg

244 Wood Street 3 Westchester Plaza

Lexington, MA 02173-0073 Elmsford, NY 10523

Lockheed Corporation I Maxwell Laboratories. Inc.

ATTN: R. C. Smith ATTN: Dr. Michael Holland

PO Box 531 8888 Balboa Avenue

Burbank. CA 91520 San Diego, CA 92123-1506

3 Lockheed-California Company 1 McDonald-Douglas Astronautic

ATTN: C. A. Burton ATTN: Nikolai A. Louie

R. .. RiMci 5301 Bolsa Avenue

M. !tr nebrg Huntington Beach, CA 9.26 17

Burbank. CA 915201 McDonnell Douglas. lnc.

2 Lockheed-Georgia Company ATTN: David Hamilton

ATTN: Ottis F. ,Teuton PO Box 516

J. Tulkolf St. Louis. M1O 63166

Dept. 72-91, Zone 419Marietta, GA 30063

36

DISTRIBUTION LIST

No. of No. ofcopie Organization Coies OrganizaLion

McDonnell Douglas. Inc. I NAVIR DEVCONATTN: Alan R. Parker ATTN: Frank Wenograd3855 Lakewood Blvd., MC 35-18 Code 6043Long Beach, CA 90846 Walminstor, PA 18974

McLean Research Center, Inc. 1 North AircraftATTN: Robert D. Carpenter ATTN: Dr. Athanosis Varvatsis1483 Chain Bridge Road, Suite 205 Mail Zone 3622/84McLean, VA 22101 1 Northrop Ave

Hawthorne, CA 90250Megatek CorporationUnited Telecom Computer Group I Northrop CorporationATTN: J. Phrohaska Electro-Mechanical Division7700 Leesburg Pike, Suite 106 ATTN: Engh R. ByronFalls Church. VA 22043 500 E. Orangethorpe Ave., 7270

Anaheim, CA 92801Memex CorporationATTN: Charles S. Smith 1 Northrop Corporation91 Belleau Ave. Research and Technology CenterAtherton, CA 94025 ATTN: James R. Reis

One Research ParkMicro Electronics of North Carolina Palos Verdes Peninsula, CA 90274ATTN: Gershon KedemPO Box 12889 1 Norton CompanyResearch Triangle Park, NC 07709 ATTN: Ronald K. Bart

I New Bond StreetMIT Worcester, MA 01606-2698ATTN: Dr. S. BentonRE15-416 I The Oceanus CompanyCambridge, MA 02139 ATTN: RADM Robert H. Gormley,

(Ret)The MITRE Corporation PO Box 7069ATTN: Edward C. Brady, Vice President Menlo Park, CA 940267525 Colshire DriveMcLean, VA 22102 1 Okalahoma State University

College of Engineering, ArchitectureNASA-Ames Research Center and TechnologyATTN: Dr. Alex Woo ATTN: Thomas M. Browder, Jr.Mail Stop 227-2 PO Box 1925Moffett Field, CA 94035 Eglin AFB, FL 32542

NASA-Ames Research Center 1 Pacific Scientific/Htl DivisionATTN: Leroy Presley ATTN: Robert F. AldrichMail stop 227-4 1800 Highland AvenueMoffett Field, CA 94035 Duarte, CA 91010

37

DISTRBUTION LIST

No. of No. ofCop i es Organization Copies Orgnit n

Perceptronics, Inc. 1 Sachs, Freeman Associates, Inc.ATTN: Dean R. Loftin ATTN: Donald W. Lynch21111 Erwin Street Senior Research PhysicistWoodland Hills, CA 91367 205 Yoakum Parkway. #511

Alexandria, VA 22304Physics InternationalATTN: Ron Gellatly I SAIC2700 Merced Street ATTN: Dr. Alan J. ToepferSan Leandro, CA 94577 2109 Air Park Drive. SE

Albuquerque, NM 87106PRI. Inc.ATTN: W. Bushell I SAICBuilding E4435, Second Flo( ATTN: John H. McNeilly.Edgewood Area-APG, MD 21010 Senior Scientist

1710 Goodridge DriveRGB A-ssociates, Inc. McLean, VA 22102ATTN: R. BarakatBox B 2 SAIC\Wayland, MvLA, 01778 ATTN: Terry Keller

Robert TurnerRockwell International Suite 200ATTN: Dr. H. Bran Tran 1010 Woodman DriveP.O. Box 92098 Dayton, OH 45432Department 113/GBOILos Angeles, CA 90009 1 SAIC

ATTN: David R. GarfinkleRockwell International Corporation Malibu Canyon Business ParkATTN: Keith R. Rathjen, 26679 W. Agoura Road, Suite 200

Vice President Calabasas, CA 913023370 Miraloma Avenue (031-HA01)Anaheim, CA 92803-3105 1 Sidwell-Ross and Associates. Inc.

ATTN: LTG Marion C. Ross,Rome Air Development Center (USA Ret)ATTN: RADC/IRRE, Peter J. Costianes Executive Vice PresidentGriffis Air Force Base, NY 13441-5700 PO Box 88531

Atlanta, GA 30338

Rome Air Development Center I Sigma Research Inc.RADC/OCTM ATTN: Dr. Richard BossiATTN: Edward Starczewski 8710 1.48 Avenue. NEBuilding 106 Redmond. \WA 98052Griffis Air Force Base. NY 13-1,11-5700

1 Sikorsky .AircraftS-Cubed Division of United TechnologiesATTN: Michael S. Lancaster ATTN: R. Welge1800 Diagonal Road. Suite 120 North Main StreetAlexandria, VA 2231.1 Stratford, CT 06602

38

DISTRIBUTION LIST

No. of No. ofOrganizat ion Cop P Or-Ti7nization

Simula, Inc. 2 TASCATTN: Joseph W. Coltman ATTN: Charles E. Clucus10016 South 51st Street Darrell JamesPheonix, AZ 85044 970 Mar-\Valt Drive

Ft. Walton Beach, FL 32548Alan Smolen and Associates, Inc.ATTN: Alan Smolen, President 1 TASCOne Cynthia Court ATTN: Harry I. Nimon, JrPalm Coast, FL 32027-8172 1700 N. Moore Street, Suite 1220

Arlington, VA 222093 Southwest Research Institute

ATTN: Martin Goland 1 Technical Solutions, IncAlex B. Wenzel ATTN: John R. RobbinsPatrick H. Zabel P.O. Box 1148

6220 Culebra Road Mesillia Park, NM 88047San Antonio, TX 78238

1 Tradeways, Ltd.3 Sparta, Inc. ATTN: Joseph G. Gorski,

ATTN: David M. McKinley PresidentRobert E. O'Connor 307F Maple Avenue WestKaren M. Rooney Vienna, VA 22180

4901 Corporate DriveHuntsville, AL 35805-6201 2 TRW Operations and Support Group

ATTN: K. Dankers3 Structural Dynamics Research T. Heim

Corporation (SDRC) One Space ParkATTN: R. Ard Redondo Beach, CA 90278

W. McClellandJ. Osborn 1 United Technologies Corporation

2000 Eastman Drive Advanced Systems DivisionMilford, OH 45150 ATTN: Richard J. Holman

10180 Telesis CourtSyracuse Research Group San Diego, CA 92121ATTN: Dr. Chung-Chi ChaMerrill Lane 1 United Technologies Research CenterSyracuse, NY 13210 ATTN: Dr. Brian J. McCartin

Senior Research MathematicianSystem Planning Corporation East Hartford, CT 06108ATTN: Ann Hafer1500 Wilson Blvd 1 University of IdahoArlington. VA 22209 Department of Civil Engineering

ATTN: Dr. Dennis R. HornSystems Science and Software Assistant ProfessorATTN: Robert T. Sedgwick Moscow, ID 838,13-4194PO Box 1620La Jolla, CA 92038-1620

39

DISTRIBUTION LIST

No. of No. ofCopies Oranization Co Organizaion

University of Illinois at Lrbana-Chainriaign 2 University of WashingtonDepartment of Civil Engineering 409 Department of Electrical

and Environmental Studies Engineering, FT-I0ATTN: Dr. E. Downey Brill, Jr. ATTN: Dr. Irene Peden208 North Romine Dr. Akira IshimaruUrbana. IL 61801-237-1 Seattle, WA 98105

University of Illinois Van Es Associates. Inc.Department of Electrical and Computer ATTN: Dr. John D. Christie

Engineering Vice PresidentATTN: Dr. Shung-Wu Lee Suite 1-107, 5202 Leesburg Pike1.106 V. Green Falls Church, VA 22041Urbana. IL 61801

1 Virginia Polytechnic InstituteThe Johns Hopkins University and State UniversityApplied Physics Laboratory Industrial Engineering Operations ResearchATTN: Jonathan Fluss DepartmentJohns Hopkins Road ATTN: Robert C. WilligesLaurel, MD 20707 302 Whittemore Hall

Blacksburg, VA 24061-8603University of NevadaEnvironmental Research Center I Vought CorporationATTN: Dr. Delbert S. Barth ATTN: Paul T. Chan

Senior Scientist PO Box 225907Las Vegas, NV 89154-0001 Dallas. TX 75265

University of North Carolina I XMCO, Inc.ATTN: Professor Henry Fuchs ATTN: LTG Robert J. Baer,208 New West Hall (035A) (USA Ret), Senior Vice PresidentChapel Hill, NC 27514 11150 Sunrise Valley Drive

Reston, VA 22091-43993 Ohio State University

Electroscience Laboratory i XONTECHATTN: Dr. Ronald Marhefka ATTN: John Dagostino

Dr. Edward H. Newman 1701 N. Fort Myer DriveDr. Prasbhaker H. Pathak Suite 703

1320 Kinnear Road Arlington, VA 22209Columbus, OH -13212

1 Zernow Tech Services, Inc.3 University of Utah ATTN: Dr. Louis Zernow

Computer Science Department 425 \Vest Bonita, Suite 208ATTN: R. Riesenfeld San Dimas, CA 91773

E. CohenL. Knapp 2 SURVICE Engineering

3160 Merrill Engineering Bldg ATTN: Jim FoulkSalt Lake City, UT 84112 George Lard

1003 Old Philadelphia RoadAberdeen. MD 21001

40

DISTRIBUTION LIST

No. of No. ofCoie Organization C~pj&es Organization

1 Georgia Technical Research Institute 1 Dr. Edward R. Jones,Systems and Technical Laboratory Private Consultant

ATTN: Dr. Charles Watt 9881 Wild Deer Road1770 Richardsons Road St. Louis, MO 63124Smyrna, GA 30080

1 MG Robert Kirwan (USA Ret)1 Duke University 10213 Grovewood Way

Department of Computer Science, Fairfax, VA 22032VLSI Raycasting

ATTN: Dr. Gershon Kedem 1 Donald J. Krejcarek236 North Building US Army Field Artillery BoardDurham, NC 27706 4717 NE Macarthur Circle

Lawton, OK 735111 Dr. Robert E. Ball

642 Tyon Drive I Mr. Robert B. Kurtz,Monterey, CA 93940 Private Consultant

542 Merwins Lane1 Mr. Michael W. Bernhardt Fairfield, CT 06430-1920

Rt. 1, 12 Arthur DriveHockessin, DE 19707 1 Dr. Roy A. Lucht

Group M-B MS-J960I Mr. H. G. Bowen Jr. Los Alamos, NM 87545

408 Crown View DriveAlexandria, VA 22314-4804 1 Mr. Donald F. Menne

617 Foxcroft Drive1 Mr. Harvey E. Cale Bel Air, MD 21014

2561 Meadowbrook LaneCarson City, NV 89701-5726 1 MG Peter G. Olenchuk (USA Ret)

6801 Baron Road1 Mr. Robert L. Deitz McLean, VA 22101

Perkins Coie1110 Vermont Avenue, NW 1 Mr. Albert E. PapazoniSuite 200 1600 Surrey Hill DriveWashington, DC 20005 Austin, TX 78746-7338

1 Thomas Hafer 1 Dr. A. E. Schmidlin1500 Wilson Blvd. 28 Highview Road14th Floor Caldwell. NJ 07006-5502Arlington, VA 22209

1 Mr. Arthur Stein,I Mr. William MI. Hubbard, Consultant

Consultant 30 Chapel Woods Court613 Eastlake Drive Williamsville, NY 14221-1816Columbia, MO 65203

1 Dr. Dora StrotherI Mr. Charles E. Joachim 3616 Landy Lane

PO Box 631 Ft. Worth, TX 76118Vicksburg, MS 3%I180

41

DISTRIBUTION LIST

Aberdeen Proving Ground

Dir, USAMSAAATTN: AMXSY-A, W. Clifford

J. MeredithAMXSY-C, A. ReidA.MXSY-CR, M. MillerAMXSY-CS, P. Beavers

C. CairnsD. Frederick

AMXSY-G, J. KramerAMXDSY-GA, W. BrooksAMXSY-J, A. LaGrangeAMXSY-L, 3. McCarthyAMLXSY-RA, R. Scungio

M. Smith

Cdr, USATECOMATTN: AMSTE-CG, C. Drenz

AMSTE-LFT, D. GrossR. Harrington

42

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