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Technical Report 419 L ANALYSIS OF MANUAL THREAT EVALUATIOk SAND WEAPONS ASSIGNMENT (TEWA) IN THE C AN/TSQ-73 AIR DEFENSE SYSTEM 0 Charles C. Jorgenien and Michael K. Strub ARI FIELD UNIT AT FORT BLISS, TEXAS SS-P2 U. S. Army Research Institute for the Behavioral and Social Sciences ~ j October 1979 , Approved for public rmleese; distrlbulon unlimited. _ 80 9 25 064 ý4• : . . . .. , , , .

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  • Technical Report 419 L

    ANALYSIS OF MANUAL THREAT EVALUATIOkSAND WEAPONS ASSIGNMENT (TEWA) IN THEC AN/TSQ-73 AIR DEFENSE SYSTEM

    0 Charles C. Jorgenien and Michael K. Strub

    ARI FIELD UNIT AT FORT BLISS, TEXAS

    SS-P2

    U. S. Army

    Research Institute for the Behavioral and Social Sciences

    ~ j October 1979, Approved for public rmleese; distrlbulon unlimited.

    _ 80 9 25 064ý4• : . . . .. , , , .

  • U. S. ARMY RESEARCH INSTITUTEFOR THE BEHAVIORAL AND SOCIAL SCIENCES

    A Field Operating Agency under the Juri-ýdiction of the

    Deputy Chief of Staff for Personnel

    ~ I FRANKLIN A. HARTJOSEPH ZEIDNER Colonel, US ArmyTech niCL Director Commander

    .................... . ........

    [ NOTICESDISTRI BUTi ON: Primary distributior. of this report him been made by ARI. Please address correspondenceconcernin% distribution of reports to: U. S. Army Research Institute for the Behavioral and Social Sciences,ATTN: P-:RI-TP 5001 Eisenhower Awint.., Alexandria, Virginia 22333.

    F INAL DISPOSITION: This report may be destroy'ed when it is no longer needed. Please do not return it tothe U. S. Army Research institute for the Behavioral and Social Sciences.

    PjQT The findings in !his report are not to be construed as en official Department of the Army position,

    unless so designated by other authorized documents.

  • ~,h.

    UnclassifiedSECURITY CLASSIFICATION OF THIS PAGE (WFMan De. Bnt*er0

    REPORT DOCUMENTATION PAGE BEFORE C TO.7. REPORT NUMBER I MGOVT ACCESSION NO. S. RECIPIENT'S CATALOG NUMRER

    Technical Report 419 -/ )"'

    NALYSIS OF-MANUAL D REAT IDVALUATION ANDr,•. /-APONS-.SSMNIMENT IZEW IN THE A•NITS73 Z To r"- • .R F'.p],

    WiR DEFEMRE SYSTEM . • . ... r-.'"-=- , _"•..""•* • '""" • "'lm 1. CONTRACT ORGRANT NUMmEP00'o)

    S. PErRFORMING O11GANIzATION NAME AND ADDRE[SS 10. PROGRAM E[LEME[NT.r PROJE[CT. TS4KU.S. Army Research Institute for the Behavioral A -A"• UNO IUm[

    5001 Eisenhower Avenue, Alexandria, VA 22,f33 XQ; ~~~11. CONTRLKI.NG OFFICE N AME[ AND ADDRESS$ 131'• ' '"9. .....

    7O 1/979~R

    U.S. Amy Air Defense Schoo • •/ C _97/ "

    Fort Bliss, TX 79916 ••:;•-"'"'e--23

    4MONITORING AGENCYE NAME AORF.S(II differen from ContrainO Olf) 15. SECURITY CI.ASS. (o fl thisrepot)

    "- 0• • ,•::I--T "-/-:I-i /Unclassified

    ' ~~1S*. DECL.ASSI FI CATION/ DOWN GRADINGSCHEDrULE -

    IS. DISTRIBUTION STATYSENT (of this Report)

    Approved for public release; distribution unlimited.

    17. PISTRIBUTION STATEMINT (of the, absrct AnD tred In Block 20, PO differet from Report)

    IAR. SUPPL.OM.NTAIY NOTTS

    r .IUS. K AY WORmS (Continue fn tovorso sid o It ncessary ad Identify by block number)

    U.S. Air defense systemsFot lisHuman factors

    i')l• Mnull weapons assignmentM.DITRI 1UI threat evaluation

    20""J(. A" ACT renhw as ara eneswebb N noem aind 1l 6hl7 by loc* nueebni,)

    As tactical ai.r threats have increased, so has the need to efficientlycoordinate ground defense. With the advent of computer aided command .Andcontrol systems, the identification of human strengths and limitations has

    become critical to the success of the Army air defense mission.

    7 SThe research reported in this paper was conducted in 2075 during thef

    " ~~early development of the AN/TSQ-73 missile minder. The missile minder is \S, , I(Continue]) ,

    L% I " FORM 3 am -nO nO F ,I o v e ,sisO mW .•E-'T U n c la s s if ie dg SECURITY CLAYO CiCATRODR OF THiIS PAGE (libra. Dat Ennered)

    Huma fator

  • UnclassifiedSICUMITY CL.ASSIFICATION OF THIS PAGE(I~ Deita Bnrm*

    Item 20.(Continued)

    representative of a class cf emerging air defense systems which place unusualdemands on the processing capabilities of the human operator. The purpose of

    the research was to evaluate human operator performance under realistic taskloading, aircraft threats, and manning configurationsi. As a result of thisstudy, procedures were developed which can effectively be applied to assessoperator performance ,"r.dr a wide variety of emerging air defense systems.The procedure can also be utilized to aid in firing doctrine development,assist human factors specification, and improve interoperability decisionsin linked air defense systems.

    I

    .I

    Unclassified

    JSjECUNITY CLASSIFICATION OF THIS PAGE(Wten Date Bnte-d)

    I .. L.¶a . . .. " .

  • Tinhclnial Report 419

    ANAYLSIS OF MANUAL THREAT EVALUATIONAND WEAPONS ASSIGNMENT (TEWA) IN THE

    AN/TSQ-73 AIR DEFENSE SYSTEM

    Chaeles C. Jorgensen and Michael H. Strub

    Submitted by:Michael H. Strub, Chief

    ARI FIELD UNIT AT FORT BLPSS, TEXAS

    Approved by:

    E. Ralph DueekPt.RSONNEL AND THAININGCESEARCH LABORATORY

    U.S. ARMY RESEARCH INSTITUTE FOR THE BEHAVIORAL AND SOCIAL SCIENCES5001 Eisenhower Avenue, Alexandria, Virginia 22333

    Office, Deputy Chief of Staff for PersonnelI' Department of the ArmyOctober 1979

    Army Project Number Human Factors In2Q762722A?65 Air Defense Systems

    Approved for public release; distribution unlimited.t ! iii

  • ARI Research Reports and Technical Reports are intended for sponsors ofR&D tasks and for other research and military agencies. Any findings readyfor implementation at the time of publicationare presented in the last partof the Brief. Upon completion of a major phase of the task, formal recom-mendations for official action normally are conveyed to appropriate militaryagencies by briefing or Disposition Form.

    iv

    'A

  • FOREWORD

    The Army Research Institute Field Unit at Fort iliss is actively engagedin a research program designed to improve the evaluation of human per-formance in air defense 3ystems. As ta:tic..fl air threats have increased,so has the need to efficiently coordinate gro~und defense. With the ad-vent of computer-aided command and control systems, the identificationof human stv'engths and limitations has become critical to the success ofthe Army air defense mission.

    The research reported in this paper was conducted in 1975 during theearly development of the AN/TSQ-73 missile minder. The missile minderrepresents a class of emerging air defense systems which place unusualdemands on the processing capabilities of the human operator. The pur-pose of the research was to evaluate human operator performance underrealistic task loading, aircraft threats, and manning configurations.As a result of this study, procedures were developed which can effec-tively be applied to assess operator performance under a wide varietyof emerging air defense systems. The procedure can also be utilized tohelp develop firing doctrine, assist human factors specification, andimprove interoperability decisions in linked air defense systems. Thisresearch is in response to requirements of Amy project 2Q762722A765and special needs of the U.S. Army Air Defense School (USAADS), FortBliss, Tex.

    EPH ZNER

    hnical Director

    Ii

    II

    !, V

    WqII 1

  • Analysis of Manual Threat Evaluation and Weapons Assig ient in theAN/TSQ-73 Air Defense System

    BRIEF

    Requirement:

    To investigate human performance under varying air defense threats.

    To determine human overload points requiring transition from manual toautomatic operational modes.

    Procedure:

    Air defense crews were evaluated over a six-day period under changingconditions of crew configuration, number of available fire units, andattacking aircraft threat. Switch action times were reccrded by theAN/TSQ-73 computer and matched against event times in predeterminedthreat scenarios. Analysis of operator actions utilized switchactuation latencies and operator errors (identified via incorrectswitch sequences). Results were subjected to advanced multiple regress-ion analysis modeling in order to generate predictive formulas foroperator performance under load.

    Findings:

    Hostile aircraft engagement latency averaged 3,47 minutes for systemcontact, identification, and weapon assignment during the simulatedcombat exercise. The chances were at least 50 percent that the air-craft would complete its run if it was in - major assault wave. Amanning configuration in which the officer implement, decisions directlythrough the weapon assignment console significantly improves assignmenttimes. Wave size of aircraft had the greatest effect on the weaponassignment operator although the aircraft identification operator timesincreased linearly as a function of the number of aircraft. Manualweapon assignment operators tended to overload at eight Pircraft andreaction times increased rapidly. Greater numbers of fire units improvedweapon assignment times but only if eight or more were available.Operator fatigue may be a siqnificant factor in weapon assignment underheavy task demands.

    Utilization:

    The techniques developed in this report can be applied in any air defensesystem having built in microprocessors that can record operator switchactions, such as the developing PATRIOT system. The resulting improvedestimates of operator actions and re~ction times can be applied tofiring doctrine evaluation, system software development, the man/machineinterface,-and interoperability studies involved in linking togethercommand and control systems.

    vii.Preceding Page Blank

  • TABLE OF CONTENTS

    I Introduction.......... ................................................. .1

    II Procedure .. .. ....... . ........ .. ... . .. ...... .. ....... 3

    III Results and Discussion. .. .. ........ .. ... . ....... . .....

    IV Conclusions........ ...... . .... .. . .. .. .. .. .. .. .. ... 14

    Appendix. .. ...... .. ... ........ ... ... .................................. 21

    Distribution .. . . . . . . . . . . . . . . 25

    LIST OF TABLES AND FIGURES

    fable Accuracy Data (days 5 and 6).......................... 8

    Figure 1 Experimental Design .................................. 5

    Figure 2 Mean R'-action1 Times for ID as o Functionof Six Wave Sizaes ................................... 15

    Figure 3 Mean Re~action Times~ for WA as a Functionof Six Wave Sizes................................... 16

    I 4Figure 4 Mean Reaction Times and Estimated ReactionTimes for Total Reaction to a HostileAircraft as a Function of Wave Size................... 17

    Figure 5 Best Fit Estimated ID Reaction Times asY.a Function of Day of Test............................ 18

    Figure 6 Bist Fit Estimate of WA Reaction TimesasdFunction of Day of Test..................... 19

    ix

  • I. INTRODUCTION

    The Army is fielding a new air defense system for command and

    control of Hawk and Hercules Fi,'• Units. Called the AN/TSQ-73 (Missile

    Minder), the system contains software which will automatically perform

    threat evaluations and weapon assignment (TEWA). The chief advantage

    of the automatic TEWA is its speed in assigning hostile aircraft to

    available fire units. Given sufficient time, it is likely that the

    tactical director, by virtue of being able to take into account complex

    information and recognize event patterns, would make more "intelligent"

    TEWA than the machine since the machine TEWA is software limited.

    The tactical director performing manual TEWA is subject to increased

    information loading and stress as the number of aircraft in an attacking

    wave increases. The present research sought to investigate human TEWA as

    a function of wave size to assist in the determination cf a manual satura-

    tion point. Such a point would suggest the level at which the system

    should transition from manual/semi-automatic control to automatic control

    as the intensity of a battle increases and the number of radar tasks

    become too numerous for manual weapons assignment. While some argue for

    exclusive manual/semi-automatic mode operation and others for an alli1,"

    automatic mode, it is more likely that the system will reside in the manual/

    semi-automatic mode until the operators and tactical directors are over-

    loaded by the sheer volume of tracks requiring attention. At this point,

    the operators and tactical directors would transfer the system to the

    automatic mode but still maintain constant monitoring and override

    capabilities.

    'if

  • The purpose of this experiment was to collect baseline data from

    which overload points could be determined. It was judged that such

    points would be a function of the number of hostile aircraft in an

    attacking wave or scenario, the number of fire units under direct control

    of the Q-73, and the rate at which the attacking wave approaches. The

    first two variables were systematically changed in the experiment, while

    the third was fixed. Also, a key conmmand and control question concerned

    whether the tactical director could coordinate activities better from behind

    the console operators or at the weapons assignment console where he could

    implement his fire unit assignment decisions directly through the console.

    Thus, the third primary variable in the experiment was the manning

    configuration. In one configuration the officer was behind the console

    op~eraitors, while in the second configuration the tactical director-sat at

    the weapons assignment console. Also included for control purposes were

    three minor variables. They were the specific raid scenario, the kr*est

    day, and the crew.

    2

  • 11. PROCEDURE

    Personnel participating in the experiment (crews) consisted of

    three Air Defense officers and six enlisted men from the US Arm~y Air

    Defense School (USAADS) recently detailed to Ft MacArthur. CA, in

    connection with the TACS/1ADS effort in 1975. (Pilot data were collected

    from an "expert" team of one officer and two enlisted men who had been

    assigned to the TACS/TADS project for over a year.) While the crews did

    not receive a formal training program on the AN/TSQ-73, their arrival at

    the testing site approximately three weeks prior to the start of the

    experiment allowed sufficient time for them to become familiar with the

    functions and operations which would be required of them in the experiment.

    Although some practice effects were expected to be found over the six

    experimental sessions, all crews were Judged to be qualified for operating

    in the Q-73 at the start of the experiment.

    The testing environment consisted of the interior of a prototype

    Q-73 van. The principal items of equipment were two operator consoles,

    identical in configuration, which were placed side by side at the front

    of the van. The console on the left side was used for track identifica-

    tions and the right console for weapon assignments. Other equipment

    included cc'nuunication lines for cross talk between the simulated Group

    73 and Battalion 73, and between the Battalion 73 and the fire units.

    An officer from USAADS served as Group 73 and issued directives to the

    Battalion 73 as required. Four experimenters rotated in the role of

    simulating "Squawk" from the fire units, e.g., acknowledgment of assign-

    ment, etc.

    3

  • Data collection occurred during six consecutive evenings between

    2200 and 0600 as shown at the bottom of Figure 1. Data was collected

    for the expert team on the morning of the seventh day between 0600 and

    0800. Each team served for a two-hour period each evening. Each period

    consisted of two one-hour sessions. (Simulation equipment constraints

    precluded simulated raid tapes from being over one hour in length.)

    USAADS prepared scenarios from which twe raids were scripted and two

    raid tapes were developed for use in the Q-73's simulation mode of opera-

    tion. To assure comparable group data, all video viewed by operators on

    their radar screens was generated from the tapes rather than from live

    radar signals. The simulation package also included the capability for

    periodic recordings of the status of all actions taken by the operators

    and the times of these actions. In addition, the system periodically

    recorded the status of all fire units under control of the Battalion Q-73.

    During each one-hour session, a team would be exposed to three different

    assaults or waves of varying size. As soon as an aircraft track entered

    the system and three simulated radar sweeps verified its presence, the

    track became available to the ID operatnr seated at the left console. All

    tracks entered with an unknown identity. Simulated messages into the Q-73

    resulted in change of status symbols replacing unknown symbols on the

    operator's screen. When the ID operator observed this special symbol, he

    "hooked" the track by placing his cursor over the syinbol and pressing the

    appropriate function switches to reveal whether the track was friendly or

    hostile.

    14

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    8 8 182 Yes8 ' 8 ii8

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  • When a track symbol changed to hostile, it became the duty of the

    weapons assignmen~t officer to select a fire unit to engage the track.

    The Q-73 system has limited software to provide automatic assignment of

    fire units, but it was the purpose of the presevit experiment to ass.,ss

    human performance capabilities in the manual weapon assignment mode.

    For each two-hour session, there were either four, six, or eight

    fire units under control of the Q-73 (see Figure 1). The manning config-

    uration consisted of having the tactical director behind the console

    operators or seated at the weapons assignment console. Thus, each

    combination of fire unit number and manning configuration resulted in

    six different conditions constituting the six experimental se-sions.

    I6

    6

    'I _____

    I ~¶r - ~ - -

  • IF ___________________________

    III. RESULTS AND DISCUSSIONS

    The analyzed data consisted of 383 sets of reaction times corres-

    ponding to complete actions taken by AN/TSQ-73 operators on hostile

    aircraft during days 1 through 6. Thirty-three additional sets of times

    were obtained from the expert group and were used in non-parametric

    analysis of operator training and familiarization. Each set was composed

    of three values for a given hostile aircraft: (1) the total time to identify

    an aircraft and assign a firing unit; (2) the proportion of the time required

    by the ID operator; and (3) the proportion of the time required by the

    weapons assignment operator. As an estimate of terminal system effective-

    ness, percentages of successfully engaged aircraft were tabidlated for

    days 5 and 6. A breakdown of these percentages into detailed categories

    of actions, e.g., number of friendly aircraft incorrectly engaged, was

    precluded due to extraneoL factors such as uncontrolled instructions to

    the ope~rators, system problems, and errors on the radar track tapes. It

    was still possible, however, to estimate overall performance against

    7 hostile aircraft. These percentages are reported in Table 1.

    This -fable shows the percentage effectiveness of the operators. It

    -is based on ratio of the average number of completed identification/

    ;~ weapon-assignment sequences to the average number of completed identifica-tions in a wave. Effectiveness remains at about 70% for low- and medium-

    I~ size waves. It drops to about 49% for high-wave sizes. In this experimentShigh-wave size was 25 or more aircraft. It is possible that these

    estimates may be conservatively low. Effectively completed sequences

    7

  • LA C

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  • may have been restricted by uncontrolled instructions issued during the

    experiment to reduce extraneous noise on the operators' screens, such as

    bogus track identifiers created by rapidly turning aircraft.

    A detailed investigation of operator reaction times added insight into

    the variables influencing overall effectiveness. By examining operators'

    switch actions on the AN/TSQ-73 console, it was possible to accurately

    determine ID and weapon assignment times. These times were analyzedin relation to the experimental variables of manning configuration,

    number of fire units, number of aircraft in an attacking wave, training

    group, day of test, and raid-tape scenarios. To maximally explore the

    relationships ri-esent in the data, times were subjected to multiple linear

    regression analysis using an IBM 360-65 computer. The data were tested

    against 90 different models corresponding to plausible psychological

    outcomes. Multiple F-tests were then used to choose the most parsimonious

    models with the greatest degree of explained variance.1

    F The following conclusions were supported by reaction time data. Theaverage total time to identify and successfully engage a hostile aircraft

    was 208 seconds. (Start thime was estimated at about 24 seconds after the

    system first contacted the radar track.) The average time to correctly

    It should be noted that the degrees of freedom used in these Fstatistics represent model comparisons and are not always directly relatedto the number of experimental variables as is the case in the usual ANOVATable. The reader is referred to the appendix for reference detailingthis procedure.

    r 9

  • identify a friendly aircraft was 57 seconds. The iD and weapons assign-

    ment (WA) operators did not always respond in the same manner to the

    experimental variables. Manning configuration had a significant effect on

    UA reaction times (F(l, 31 8 )'9.49 P'ý.01). When the officer implemented

    decisions through the console his mean reaction time was 91.6 seconds

    versus 131.4 seconds when he served as tactical director. This wds an

    average improvement of 39.8 seconds, or about 30%.

    Number of fire units also effected WA time (F2 ,380)=4.14 P

  • -. OMI II9

    values for ID times are plotted in Figure 2 as a function of wave size.

    For WA the linear trend seen in ID times was not evident, F:gure 3 shows

    mean reaction times already rising rapidly at eight aircraft, suggesting

    that the WA operator was already overloaded. Latencies reach a peak

    of 176 seconds per aircraft at 16 aircraft and recede to a steady state

    level of 100 seconds thereafter. Though dropping from the highest value,

    terminal WA times are still well over a minute longer per aircraft than

    at a wave size of eight. This decrease coincides with a loss in overall

    effectiveness and may be due to the forced adoption of faster but less

    optimal WA strategies for assigning hostilc targets to the most appropriate

    fire units. Comparisons between possible wave models-showed the WA data

    was best fit by a cubic equation:RTwA= 3.23w-.012w3 -29.37

    The cubic fit was a significantly better predictor than either a linear

    or a second order equation (F(1 ,380)=4.29P

  • more sensitive to the attacht configuration than -the ID task, since

    the raid tapes generated different numbers of artificial tracks on the

    radar screens depending on the aircraft maneuvers utilized in the raid.

    Reaction time data show a significant effect over days on ID and WA

    times (FID(5,377)= 2 .59 P

  • Due to the low number of expert scores and the possible violation

    of normality assumptions, a non-parametric Wilcoxen matched pairs signed-

    ranks test was chosen. The results showed no significant difference for

    ID times (Z=1.03 p

  • IV. CONCLUSIONS

    Tentative conclusions may be drawn for some of the original research

    questions. First, TEWA in the semi-automatic mode is not instantaneous.

    Average time for system contact, identification, and weapons assignment in

    the AN/TSQ-73 system was 3.47 minutes. Second, manning configuration in

    which the officer implements decisions directly through the WA console

    significantly improves assignment times. Third, wave size has its greatest

    effect on the WA operator, although ID times do increase linearly as the

    number of aircraft increase. Fourth, WA is overloading at eight aircraft

    and reaction times increase rapidly. Increased numbers of fire units do

    improve WA times but only if eight or more are available. Finally, oper-

    ator fatigue could be a consideration in WA under heavy task demands.

    L I REFERENCES

    Ward, Joe H. and Jenninqs, Earl, Introduction to Linear Models, 1973,

    Prentice-Hall, Inc.

    i

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  • APPENDIX

    The techniques used in this report to determine predictive formulas

    involved a multiple linear regression program modified by Jorgensen to

    permit rapid generation of model vectors. A discus;ion of the statistical

    logic, model construction, and general programing methods is available

    in "An Introduction to Linear Models" (Ward & Jennings, 1973).

    Briefly the technique involves solving for parameters in a theoretical

    equation previously defined by the experimenter to reflect specific

    psychological'assumptions. This is done through a least squares fit of

    the equation parameters to raw or transformed data. The program then

    generates the standard beta weights and regression constant for that solution.

    The predictive power of the equation is specified by M2 , the squared multiple

    correlation coefficient. M2 is mathematically equivalent to the percent

    of explained variation. Through the use of alternate equations, F ratios

    can be set up to compare various assumptions in terms of their explained

    variation. Analysis of variance and factorial analysis of covariance are

    two of the many possible model formulations which could be utilized within

    the regression framework.!n

    Usually the most efficient strategy for finding optimal moaels

    consists of postulating a general all-encompassing equation which takes

    -into account a linearly independent set of predictor variables based on

    conditions used in the experiment. The M for this model serves as a

    maximum against which the predictive power of other simpler models is

    06. 21 p' .c-W'. i.- .... 3¶*iSS

  • judged. The simplest possible predictive model is the mean of the

    distributions. An F ratio formed between the general model and the

    mean model tests the usual null hypothesis for equality of means. By

    using the same technique with more complex models, F tests can be set up

    comparing various models to the general model and to each other. This

    is analogous to analysis of covariance. The pattern of significant F

    ratios as well as the M2 efficiency of the models quickly points out the

    most efficient and parsimonious equations for a given set of assumptions

    and predictive power.

    For example, in this experiment the three general models were all

    predictive equations taking into account raid tapes, low, medium, or

    high wave sizes, days, manning configuration, groups and fire units.

    A different general equation was generated for total, ID, and weapons

    assignment times. In this analysis four types of models were condidered:

    orthogonal component models for each variable of interest (these are

    equivalent to a one-way analysis of variances for each variable), linear

    models (equivalent to simple linear regression fits), second and third

    order polynomial models (which investigated parabolic curves) and mixed

    models, such as a linear model going second order at a specific point.

    The following are examples of a general 12-element orthogonal model for

    [ .total times, a model based on six wave sizes, a linear model, and apolynomial model:

    22

    a7i P 77

  • 7I

    Time (total) " aoXI a1S2 Ja2 13 " ". l7

    Time (total) -aoYI+aIY 2+a2Y3Y4+a4Y5 +a5Y6Time (total)

    Tite (total) U+aW

    2 3Time U+aWI~aW +a W

    where X1... X12 are colrmn vectors of O's and I's partitioning total data

    times into orthogonal sets as a function of such variables as days, t *ves

    or raid tapes.

    Y...Y 6 are column vectors of O's or l's partitioning total times

    into sets for wave size one through 6, respectively.

    U is a unit vector of l's.. W is a column vector containing the

    numbers one through 6 corresponding to the size of the wave.

    W is the direct product of W with itself.

    a is a beta weight for the regression.

    Though many models were considered and fit, only the most parsimonious

    and experimentaly meaningful are reported in this paper. The equations

    derived represent best fits for the available data. Their generalizability

    assumes the generalizability of the experimental situation to the combat

    usage of the AN/TSQ-73.

    23

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    1 THF ARmY LlbRAHY

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