An Analysis Plan For The Arcoms Ii Experiment Di Giorgio, Emilio 1983-06

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Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 1983-06 An analysis plan for the ARCOMS II experiment Di Giorgio, Emilio Monterey, California. Naval Postgraduate School http://hdl.handle.net/10945/19638 Kvvit,':. :• Dudley Knox Library, NFS Monterey, CA 93943 NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS AN ANALYSIS PLAN FOR THE ARCOMS II EXPERIMENT by Emilio Di Giorgio June 1983 • Thesis Advisor: T Jayachandran Approved for public release; dist:ribut:ion unlimited T210090 Dudley Kaox Library, NPL Uonterey, CA 93943 SCCUXtTV CL ASSiriCATlOM Of TntS PACC (Wttmn Dmtm gnl»r>d) READ INSTRUCTIONS BBPORE COMPLETINCi FORM REPORT POgjMENTAHO N PAGE 1 4 ffl^OMT NUMSCK TiTue (tmd OOVT ACCKMIOM NO. a. Suhllllm) ncci^iCNT's CATALOG NuMaen s. Tv^e or RCPowT Master An Analysis Plan for the ARCOMS il Experiment 7. ). pcrioo coveneo k ' Th^?7i?l J^n^ 19 8 3 • PcnPonMiNG one. nt^onT numbch • AuTHonro CONTHACT OM chant NUMSCnCa) . Emilio Di Giorgio • PCnronMINO ONOANIZATION NAME AND AOOAIII 10. PnOCHAM CLEMENT. PHOjCCT. TASK AHEA * MOHK UNIT NUMSEMS 12. nEPOHT DATE IS. .June 19 8 3 NUMBEH or PAGES IS. SCCuniTY CLASS, Naval Postgraduate School Monterey, California 93940 n conthollino office name ano aooress Naval Postgraduate School Monterey, California 93940 U MONITOMINC AGENCY NAME * 74 AOOnESIfll 4l»«r«if Irom Cantrollint Offlecj \%m. IS. DISTNiauTlON STATEMENT (ol thlm t^tort) OCCLASSiriCATION/DOMNGNAOiNG SCHEDULE (oi ihia Kmpmrt) Approved for public release; distribution unlimited. 17. tS. OlSTHiauTION STATEMENT (of ihm a^atrmcl anttmd In af«e* 30, 1/ Mllmtmit Irmm Ram^rt) SUPPUEMENTARY NOTES Travel expenses and data support were provided by the United States Army TRADOC Systems Analysis Activity. It. KEY WOMOS (Contii-M an f99f ml*» H nmc»amfr ••* Idmnlllr »r WoeA nuM*«rJ Armor field experimentation Experimental effects and interactions Distribution of times to acq^uire and engage Conditional line of sight time and path segment lengths, and aim errors. , ao. ABSTRACT (Conllmf mt fvm»» mt*» II n«e*a««wr •»* Idmrntllr *r *!••* i>um^ M) The purpose of this thesis is to examine and recommend methodologies that will support the analysis of the ARCOMS II field experiment. This is done in three parts. The first is to determine the methods with which to analyze the experimental effects and interactions. This is followed by a discussion of data analysis techniques for representing the DO ,:°r„ 1473 EDITION or I NOV AS IS OaiOLCTE SeCURITY CLASSIFICATION OF THIS PAGE (Whtn Dmim Enfrmd) data. Thirdly, an examination of the techniques for determining the significance of certain questions relating to the Armor Combat Process is discussed. S N 0102- LF- 014- 6601 SECURITY CLASSIFICATION OF THIS PAGEfWh«n Dmim Enfrmd) Apfrcved for public release; disxribution unliait'Sd an Analysis Plan for the AfiCOHS II Experiment by E.S., Emilio Di Giorgio Captain, United States Army United States Military Academy, 1974 Submitted ir. uartial fulfillment of the requirements for the degree of MASTER Of SCIEHCE IN OPERATIONS RESEARCH from the NAVAL POSTGRADUATE SCHOOL June, 1983 ABSTBACT The purpose of this t.hesis is ro methccolocies that will II field experiment. is tc examine and reccmmend support the analysis of This is done in three parts. the ARCOMS The first determine the methods with which to analyze the exper- and interactions. This is followed fcy a discussion of data analysis techniques for rapresenting the Thirdly, an examination of the techniques for deterdata. imental •effects mining the significance of certain questions relating to the Armor Ccmtat Process is discussed. TABLE CF CONTESTS I. INTRCDUCTION A. 9 EACKGRGONL 9 1. Scenario 10 2. Data Ccllection 11 3. Dependent Variables 11 12 B. Independent Variables OBJECTIVE C. SCOPE 13 U. II. III. IV. 13 ANALYSIS OF EXFEHIMSNTAL EFFECTS 15 A. EACKGRODD DISCUSSION 15 B. ANALYSIS CF THE EVENT MATRIX 17 1. A 2*- 2. 2x2 1 Half Fractional Factorial 17 ANCVA With Replications 19 CAIA ANALYSIS 25 A. GENERAL 25 3. DATA STRUCTURE AND CATEGORIZATION 26 C. FITTING THEORETICAL DISTRIBUTIONS TO DATA . . 26 1. Methodclogy 26 2. CLOS 30 3. Acquisition Data 33 4. Engagement Data 33 Data METHCDS FOR DEALING WITH QUESTIONS OF SIGNIFICANCE 37 A. GENERAL E. THE EFFECT CF BOUNDING BY THE DEFENDER ON HIS 37 DETECTABILITY C. QUICK DASHES BY ASSAULTING VEHICLES D. E. ENGAGEMENT AND ITS SIGNIFICANCE ON ATTRITION ROUNDS EXPENDED CN TRUE VERSUS FALSE TARGETS F. FALSE TARGET DETECTION RATE 37 39 . UO . 41 42 FEEQUENCY CF OVERHATCHSR DETECTIONS G. V. CCNCIUSIONS AND RECOMMENDATIONS U3 U5 A. CONCLOSIONS 45 B. RECOMMENDAIIONS 45 APPENDIX A: DEPENDENT VARIABLES 48 A. OFFENSIVE OPERATIONS 48 B. CEPENSIVE OPERATIONS 49 APPENDIX E: 2X2 ANOVA WITH REPLICATIONS 50 A. ANOVA MODEL 50 B. COMPUTER PROGRAM COTPUT OF ANOVA RESULTS 52 DATA ANALYSIS RESULTS 55 C. APPENDIX C: 5u A. CLOS DATA 55 B. 55 C. AQUISITION DATA AIM ERROR CAT A D. SCATTER DIAGRAMS FOR TIME AND PATH SEGMENT 55 LENGHTS APPENDIX E: GLOSSARY AND 55 A aBREVIATIONS 70 A. ABBREVIATIONS 70 B. GLOSSARY 70 LIST CF REFERENCES 73 INITIAL DISTRIBUTION LIST 74 LIST OF TABLES I. FOPCE COMPOSITION 10 II. PACTCR LEVELS 12 III. EXEZRIMENTAL CESIGN MATRIX 16 IV. CCCED EXPERIMENTAL DESIGN MATRIX 16 V. THE POSSIBLE 2x2 ANOVA SUB-MODELS 20 VI. ANALYSIS CF VARIANCE DATA 21 VII. RESOITS OF ATTACKER TO DEFENDER TACTICS ANOVA VIII. RESULTS FOR PCCLED SUM OF SQUARES IX. RESULTS OF FIITING ATTACKER TANKS CLOS DATA ... 31 X. GCCDNESS-OF-FIT RESULTS FOR ACQUISITION DATA . 3U XI. RESULTS OF AIM ERROR FITS 36 XII. 2x2 ANOVA TABLE 51 XIII. RESULT OF FITTING CLCS DATA 56 XIV. RESULTS FOR TIMS TO ENGAGE DATA 60 XV. RESULTS FOR TIME TO DETECT DATA 6 . . 22 24 . . 1 LIST OF FIGURES :.1 Critical Region for the F Statistic 23 2.,2 Critical Region for 3,.1 Data Structure 27 3.,2 Fitting Procedure 28 3^,3 Fitted and Empirical CDF Plots 32 C,.1 Tank CLOS Time and Path Segment Histograms C.,2 Tow CLOS Time and Paxh Segment Histograais C.,3 APC CLOS Tiie and c.,4 Attacker Tark to Defender Tank Acquisition Eata c. 5 Attacker Tank to Defender Tow Acquisition Data c.,6 Attacker Tark to Defender Dragon Acquisition F 24 (1,9) Path Segment Histograms ... ... ... 57 58 59 62 . 63 Data 64 c.,7 Eefender Aim Error Histograms 65 c. 8 Attacker Aim Error Histograms 66 c.,9 Tank CLOS Segment Scatter Plots 67 c.,10 Tew CLOS Segment Scatter Plots 68 c. APC CLOS Seament Scatter Plots 69 1 1 !• A. INTBODUCTION EACKGECOND Decision-making within the Armed Forces has evolved into complex process an extrenely dependence upon and computer Defense requiring an ever increasing quantitative tools such as combat modeling siiruiation. xhis situation view of In Department recognized the importance the data of the required as input to these models. Consequently, the Army has undertaken a program of models improvement supported by field exferimentaticn. In Training and Doctrine Command response to as the proponent for experiments to provide Improvement Program the required support. series of field directed the Tradoc Ccmbined Arms Fort Hood, This Armor the Army Model Furthermore, Test Activity a (TCATA) It at Texas to conduct the first of these experiments. initial experimentation Operations Ccirbat Experiment Phase II force the designated the TRADOC (TRADOC) Systems Analysis Activity (TRASANA) this effort was quickly Support Model (ARCOMS II) engagement experiment followed by was designed II force-en- to provide modelers to better understand that would enable Field (ARCOMS) The ARCOMS . the data the direct fire comtat processes in both offensive and defensive opera- tions; the result eventual improvement in cf which is the Armor comtat modeling, combined arms ming. time Ancng the critical issues and range dependent simulation to be addressed distributions variables" during the force-on-f orce were the "dependent of the engagements as well as the experimental effects and interactions [Ref. thru 1-10]. and wargam- 1: pp. 1-1 Sce nar io 1 . this scer.aric for The series cf ccmbined " a meeting engagements betwe-rn ATTACKER aiirs shown in Table and DEFZNDEE forces ccnfigured as p. consisted cf experiaient I [Ref. 1: 1-5], The force configuration depicted here is typical of an Armor heavy team attacking an Armor platoon supported by The specific quantities of anti-tank weapons. each force element were allocated in order to provide the Attacker with the minimum force ratio of three to one. TABLE I PORCE COMPOSITION ECUIEMENT OVERWATCH BOUNDING TYPE Tank, DEFENSE OF FEN SE M60 APC 2 platoons 1 platoon AT 1 platoon 1 platoon 1 section 1 element « Tte scenario was designed to play OS and CPFOR tactics in both offensive and defensive op'^rations. The opposing forces were given initial briefings and operations orders. The test officers acted as both the controllers and headquarters for the higher the participating players were permitted to conduct of their experience and consistant selected with to the The the operation to the best, ability so tactical represent. units. The 10 long as doctrine attacking they remained that fores they were ccaaenced one cf from deploymsr.-t avenues of two salected approach. Their objective was to seize pcsizions being defended by the flowing. free the tactical This permitted Artillery, smoke, realistic as possible. of the meeting engagement was Froc this point opposing force. play to be as mines and the use trenches were not played. £§ia Collect icn 2* Pricr to the conduct of the experiment data on xhe following environmental areas was collected. 1. Meteorological data. 2. Player demographics. 3. Eguipment demographics. U. Historical guestiona ires. This was followed, phase in short time later, a employment of which the by the experimental automated measuring and recording devices enabled data coiisction to be performed in this method of data collection Additionally, "real time". amass an enormous quantity of data pertaining to position locaxion, firer and -arget identifiprovided a means cation, range, and a tew. The data tc a record of hits and misses, collected consisted of five types. on the dependent Line-of -sight data (intervisibility) 2. Target aquisition data. 3. Target distribution data. 4. Tarcfst engageiEsnt 5. Attrition data. . results. Cep gnd ent Va riable s The dependent variables that pp. are, variables They are 1. 3 just to name were measured [Ref. 1-20 thru 1-33] are too numerous to be listed here. however, provided in appendix A. 1 1 1: They Four independent variables were chos=n at measure th* dependent or response variables. variables consisted cf two levels as fixing each of the distinct variable levels, Each cf these shown in Table II. By combinations of rhe independent an experimental trial was determined. entire experiment consisted of a which to eight rrials each replicated total cf three tim?£. TABLE II FACTOR LEVELS INCEFENDENT VARIABLES LEVELS ATTACKER TACTICS -Fire and .Movement -Rapid Approach -Deliberate Defense DEFENDER TACTICS -Hasty Defense -Hilly TERRAIN (avenue of approach) (Avenue -Flat (Avenue HATCH POSITICN (visibility) -Open -Closed 12 The ' 'A') B» OEJECTIVE B. It is the objective of this paper to examine those" ireth- will hest support odologics that the data analysis effort reduction. This is to be The first is an examination of following the coirple^icn of data accomplished in three parts. the experimental second is The effects. to discuss analysis techniques to describe the data. by discussion of This is followed the analysis techniques that determine the significance of data will help to certain questions relating to the Armcr Ccmbat Process. SCOPE C. will be limited to specifically The scope of this paper addressing the questions of "What should be analyzed?" as well as "Shat method should be employed to perform the anal- ysis?". In the preceding paragraph it was stated that a primary concern of experimental analysis is to determine the effect that the independent variables have upon dent variables. effect that equally important It is the interactions upon the dependent variable. between these This the depen- to examine the variables have is to be accomplished in the following manner. 1. of current procedures in An examination analysis of factorial design analysis will variance and be mada to decide upon the best method with which to estimate the experimental effects. 2. Cnce an appropriate method has be used procedural example will analytical prccess involved in been selected, a to illustrate the the derivation and interpretation of the experimental effects. the data Combat Modeling, upon the methods which transfom the In order to facilitate analysis should focus data into descriptive or Armor predictive 13 models. The models include regressicn models as well as many well known profca- Procedural methods will be discussed in order tc obtain answers zo specific questions regarding the combat process reflected by this experiment. conducting Included in this discussion are proposals for bilisxic cr stochastic models. te-weer. these results and experience as well as ether experimentation. comparative analyses 14 historical n. A, ANALYSIS OF EXPERIHENT&L EFFECTS BACKGEOOD DISCUSSION The four independent variables each at two levels form of sixteen total urique combinations. variable for dependent to conduct possible factorial design. forth, be factors through analysis of an referred to as II and while their appr cpriare C nated as plus( + this coding will a variables will, be used throughout the particular facror, or This was due prima2: each combination was replicated three times. employed. proven tc utilized the 2* factorial be an efficient effects, contributions that , were 2-3]. look at A actually Terrain method error. combination of two, estimate the as well The main effects Tactics, as an ar^ the Defender Position nave upon the experi- Hatch mental yield (the dependent on the ctier hand, by which to the factors Attacker ar.d design would have interaction effects and the estiirats cf ^experimental Tactics combinations xhat p. If all possible combinazions of the control vari- ables had been irain been desig- using only eight rily tc the prohibitive cost of resources [Ref. the A factor-level ccmbinaticn. treatment combinations. show The thesis when refer- of the sixteen IV will hence- been coded levels have experiment was performed by Table 2* a factors. have III The AECCMS II Yet, using is For clarity and simplicity or niinus(-). ) variance the experimental Tables the combina-icns it these The independent listed in ring to each of measuring 3y a variables) ccnsist of . The interactions, the simultaneous effect of three or four factors a upon the yield. This is valid sc long as the factorial model assumptions are valid. 15 TAELE III 2XPEEIHENTAL DESIGN MATRIX CCNTECI VARIAELE LEVELS Attacker Tactics Defender tactics Terrain of (avenue a p pr o a ch Hatch Position SIGN COD Fire and Movement A Rapid Approch A Deliberate B Hasty B Hilly C flat C Open D Closed D TABLE IV CODED EXPERIMENTAL DESIGN MATRIX TRIAL A B c D + 1 2 3 4 5 6 + + + -f •f •f > •f 7 8 No. of Ho. of (*) {-) 4 4 f + 6 2 6 6 2 2 16 NO. OF REPS 3 3 3 3 3 3 3 3 B. AUALISIS OF THE EVENT MATRIX Given the event matrix in Table "How should it determine experiHaving already excluded the 2* factorial tecause of the reduced number of trials, tility of using ether known te examined. is -her order to analyzed in be mental effects?" design IV the question This types of factorial designs will involve a viill the feasi- at fractional facxo- loolc confounding of the interactions tc produce sub-mcdels cf a 2* factorial design. Although the use of rials, and blocking variables was considered, in this faper. does not exist be generated. will not be included it This is primarily due to the a fa.cz that there which blocks could physical variable from The introduction of a dummy blocking variable would only serve to compound the analysis of the confounding that wculd normally cccur due to blocking. 1 • i il'L fractional Factor ial M^l Cften there exists redundency with amount of main effect^-. the in a factorial design negligible effect especially trje when the design [Sef. 3: notion one may it possible of freedom factor is it. that gained is ^.o That cost is in terms of a has prior information the little interaction cr a attached tc cost one knows If from experience of such a negligible effect, there will be little or no loss of information. the other hand, if no a pr iori knowledge exists, 17 a loss of information regarding interaction. the effect of the omitted cr seme are used in However, when an assumed tc be negligible is Capitalizing upon this reduce the number of 374-375]- pp. find The latter large number of factors trials and still obtain valid results. bit interaction cr the particular factor. a or be attributed to either of a higher ordar cf a certain the interactions respect to This reduncency may negligible effect a a On less of liJcely Rather than regarding occur. "cc infer maticr. it would , attributed to is ncrmaliy inf or maticn *hat be confounded wirh effect normally attributed to Thus an combination nation. now confounded with is is less of a say that some other r,he affect. the omitted factor some other factor combi- now indistinguishable effec-cs are two The xhi? as more appropriare -c has been information the effac-. from one-another Reduction in the requisite number of trials may also half-repiicate of a 2* factorial. A half-replicate of the 2* factorial is merely a 2*- I or 23 factorial. This requires only eight or half of the original sixteen trials. Thus, it only remains to determine those eight combinations that produce the best results. acccmplished by be considering confounding comes from proper choice The a a interaction with other factor combinations. generates called complimentary two fcld-ovar. a sets of higher This procedure combinations eight is equally useful Either set order for the analysis provided that measurements are taken using the selected half- replicate. Clearly, it is important to obtain as much informa- purposes of tion as possible with regard to the main effects. it necessary to generate is higher order interactions. respect the to interacticns an attempt was fold-over sets AB, AC, AD, BC, Unfortunately, . match. ABC, An attempt ABD, ACD, It BD using and CD were generated and , match the resulting treatment ccmbiused in the experiment (Table none of the fold-over sets produced a with each of the third order interactions BCD, and ABC D was also fruitless. tecame readily apparent that the imbalance in the occurrence of have fold-over sets The naticns to the eight actually IV) by confounding This precludes any ambiguity with main effects. made to To do this factors at the upper an over-riding effect in 18 and lower level using any subset was to of a 2* (S6€ Tabl€ IV) factorial design sub-mcd=l -hat The only . could produce the proper treatment combinations for analysis 22 factorial is the This design . severely reduce the amount of useful informa- will, however, tion about the 2x2 ANOVA design or interaction effects factors and the -hat would have otherwise been available. 2x2 ANOVA With Replications 2.. The imbalance in the treatment combinations selected for the experiment dcss not allow for the examination of all the 2x2 sub-models that are possible. combinations are indicated in Table the four independent variables as the ether two be held at a will possible to be Choosing any two of V. factors will require that fixed level. examine only possible The Once this is done it effects of the the chosen factors. of an example, if Attacker Tactics is consid- Ey way te the second, the 2x2 design for V may be derived. at least four Since factors level, it and Defender first factor ered to B, C, of that this configuration requires the proper and D th? factors "A AND B" shown in Table Notice trials tactics as plus-minus combination. never occur together at the lower will not be possible variance table using factors 3 D. 19 to construct an analysis of and C, or B and D, or C and TABLE V THE POSSIBLE 2x2 ANOVl SaB-MODELS "A AND B" A+B+OD+ A+B-C+D+ • A-» Trial 1 Trial a A- Trial 2 Trial 6 "A AND D" A+ E+C+D> " A-I-E4C-D4- A AND B" A^B^C^•D + A+B+C+D- A+ Trial 1 Trial 3 A+ Trial 1 Trial 5 A- Trial 2 Trial 7 A- Trial 2 Trial 8 The model for a 2x2 analysis of variance with repli- cations is relatively (Ref. pp. 568-570] simple. 4: Assuming that an cbsevaticn of the response variable is a functicn of the fcllcving affects -the grand mean, -the row effect where i=1,2 6. 1 -th€ cclumn effect where j=1r2 -the interaction effect -experimental error for the observation at the kth replication where the )c = 1,2,3 observation in -he ijth call mcdel representing the kth may then te written 'ay. The error + 6 + 1 terms in Y . 'J + 'i^ ' . . ij the model + (2.2) £ i jk are assumed distributed with mean zero and variance 20 a"^- to be noraially The fictitious data in Table trate the analysis of variance determine interest tc Tactics, and Suppose it procedure. effects the will serve tc illus- VI factors of Attacker the mean time Defender Tactics upon is of for the Defender to detect an attacker. The data in each cell repretime for the defender to sents the mean for replications the three each of treatment ccmbinations in Table analysis of variance is provided BMDP2V, subroutine, the as a solution using the Bicmed table for this model as well computer corresponding to An V. detect an attacker in Appendix C summary of the results is listed in The results of the analysis may serve to answer Table VII. questions concerning the existence of effects or interac- [Ref. 5: p- tions. 359-386]. A relevent three The questions relate column (Defender Tactics), rcw (Attacker Tactics), to and inter- action effects. TABLE VI ANALYSIS OF VARIANCE DATA DEFENDER TACTICS 2 1 1 ATTACKEE TACTICS (j) 60 82 80 74 70 3a 86 90 90 76 SH 92 (i) 2 The null and alternative .on hypotheses on the intsrac- effects are stated as KG: There is no interaction eff ect ( -b . HA: There is an interaction eff ect ( \b . 21 .= 0) y^ 0) Where "i" and gc between " j" hyposthesis null is (KG) levals one and rwo. indeed true then If the tss^ ths statistic, IS = MSI/f?SE, is distributed as an "F" with" 1 , degrees cf freedcai. The probability that an "F" variable 8 will exceed the computed value of the test statistic is used ( ) detemine to rejected. It the if null hypothesis is customary will be to reject Ho if accepted or this computed probability is less than a preselected value, a , called the level of sigr.if icance. a represents the probability that the null hypothesis is rejected given that it is in fact true. This relationship is depicted in Figure 2.2. For example, if the value of the test statistic greater, it would lead to at an alpha cf . 1U07. is equal to 2.67 or rejection of the null hypothesis At an alpha of 0.1, we would fail to a reject the null hypothesis; it would then be concluded that there is no evidence to suggest the existence of a significant interaction effect. TAELE 711 BISOITS OF ATTACKER TO DEFENDER TACTICS ANOVA (HYEOTHETICAI EXAMPLE) SOURCE SOM OF SQUARES D. F . «EAN SQUARE MEAN ss:i = Err rCT 79707 MSM = 79707 ATTACKER TACTIC SSA = 507 MSA = 507 DEFENDER TACTIC SSD= MSD = 27 27 INTERACIICN EFFECT SSI = MSI = 147 147 ERRCR EFFECT SSE = U4 MSE = 3 55 22 TEST STATISTIC 1449. 22 TAII PROE 0.00 00 9.22 0.0162 0.49 0.5034 2.67 0. 1407 When the null hypothesis is not rejected, cf squares sum VIII) analysis of often modified by is squares tc to test in the the adding the modified error it; hypothesis on the main the =rror variance table -che Table ( interaction sum of mean square is then used effects. The resulting mean square values ard the values of the test statisxic shown in Tatle VIII. in If a = 0.1 one can conclude as depicted rhat "Attacker Figure 2.3 effect on the mean time to Tactics" has a significant detect a target by the defender "Defender Tactics" does while the are not. Of course, this example was contrived for illustrative purposes and does not necessarily reflect reality. will te possible to perform response variables Once the data is a collated it similar analysis on using the ANOVA configurations all the in V. Figure 2. 1 Critical Region for the 23 F Statistic. Tatle " ' " " " TABLE 7III JESOLTS FOR POOLED SUM OF SQUARES I MSP FA (S£E > £SI)/(DFe + DFi) 4ao + ia7)/(8 1) — 65.22 = MSA/MSP 507/65.22 F (1,9) = 3.36 .^ 7.77 FC = MSD/MSE 27/65.22 F c(1»9) = 3.3 6 -^ .4 14 (1,S), F .9 Figure 2.2 7.77 3.36 0. 414 Critical Region for 24 F (1,9). III. DATA ANALYSIS GEMEEAL A. The manner and method by which often dsterniined by for the express an event to tion. its intended ise. If it is purpose of assessing the will occur, tabulate the data is analyzed is mcst to be used probability that it would be desirable , at a minimum, empirical distribu- results based upon -he On the other hand, if the data is intended to be used for further analysis, it would be more desirable to fit a The latter method has theoretical distribution to the data. some distinct advantages over the former. Tabulation of empirical results are not as versatile as the fitting of a distribution. The fitted distribution allows for the study of the and ters of changes in the values of effect indapendent the especially important in variables. combat both the parameThis modeling aspect is must be which situations. Mere importantly, have been theoretical probabality distributions, extensively studied, and their properties are well responsive to known. a vari=ty of scenarios and This makes them extremely useful in analysis as well as modeling. Ir many situations, a problem may be more easily modeled mathematically than by laboring over an elaborate ccmcuter simulation. in light of the preceding discussion, the remainder of this chapter will cover the methodology for fitting theoretical distributions to data and testing for goodness-cf-fit. 25 DA1A STBXTORE ANE CATEGORIZATION B. B€fore any attempt is mads at analysis, appropriate detsririre the to data data structure provides the Figure 3.1 level of it is necassary to be for the used. ARCOMS II experiment. Since the appropriate level of data is dependent upon the issues and analyses to be performed, its determina- conjunction with made in will te tion the discussion of analysis techniques. FITTIUG THEORETICAL DISTRIBUTIONS TO DATA C- '' -lethcdolcqy • methodology for The fitting probability tions fellows the sequence shown in Figure 3.2. begins with tion data. mated from the data. then compared parameters The distribution are either is hypothesized the of known in advance or they are esti- The empirical distribution (histogram) with the hypothsized distribution "goodness of fit" test. This provides an distribution The process educated que ss as to the underlying distribu- an the of distribu- will using a determine if the fitted approximation to acceptable the distribution of the data. a. Estiirating Parameter Values Once a decision has been bution tc b€ It fitted, e.g. made as to the distri- exponential, gamma, normal stc. will te necessary tc estimate tne parameters. eters determine the estimates of experience. specific shape the parameters If this then serve tc of is not the case, derive an estimate for The param- the curve. are available the , Cften from historical data itself may the parameters. The appropriate estimates for many of the standard distributions may be fcund in Reference 6. 26 AflcoNt :i 0*1 A ._....J DATA TTl^! TtlAL u ^'i'i rr-^ 3 i I «-l -I I ' I I < . I I ^ V % ^f tr DCPf«C¥T v*AIA«l£S ATTAClfB TTPC Figure 3.1 Data Structure. 27 STAflT CONSTHUCT A MlSTOCaAM SELECT ,^_ TC$ CSTIMTP PMUMCTERS oENCfurE TMttajfTICAL pnoM«iLiTiES COMKtCT COOOMCSS Of FIT* TEST arxc Figure 3.2 Fitting Procedure, 28 "Goodness of Fit" Tests fc. the most Two of goodness-of-f it for Kolomcgcrcv-Smirnov are the tests. (K-S) statistical tests widely used Chi Under . Square and the certain conditions, each of these tests has attributes which makas it preferable to the ether. The test may K-S continuous distributions when the only be used parameters of the distri- bution tc be fitted are assumed to be known. have beer, distributions, and exponential the normal ccnstructed However, special which permit the K-S test when the parameter have been extension of the for fitting tables to be used estimated from the data. K-S test is known as for This the Lilliefors test. The K-S and Lilliefors test are often preferred over the Chi Square test when the sample size test, en the other distributions, and it The Chi Square small. is applicable hand, is is to all especially good when types of moderate to large samples are available. useful but A distributions is less rigorous the technique of plots. This graphical method tiles of indicates requires plotting the percen- theoretical distribution the empirical distribution. a against A the straight line good fit. Variables Selected for Analysis c. While data analysis should every dependent variable measured, Sight (CLCS) fitting constructing probability the percentiles of plot method of , Acquisition, be accomplished on the Conditional Line of and Engagement data were selected to provide procedural examples. 29 CIC3 Data 2. Sight data consisted prima- The Conditional Line of rily cf the time duration and path segmenz length over which between an attacker vehicle and line of sight was determined to exist. element cf the opposing force time segment duration was measured defender ar.d defender to attacker categories. fact that to the path The were measured only for the distance over which the attacker is due The for both the attacker to on the other hand, segment lengths, least one at: vehicle traveled. the attacker forces were This moving throughout the entire period of the engagement, whereas, the forces would defender only expected to be defensive positions. alternate decided tc For this theoretical distributions fit between attacker vehicle types move between reason it to the was CLOS data (Tanks, Tows, and APCs) , and the aggregate of all the defender forces. Histograms of the data sets indicate that the CLOS Time and Path segment lengths might be represented by cne of distr ibutics. five Weibull, They the are Beta and Lcgnormal distributions. curve grams. were fit that is "sinilar" The Exponential, to the in shape By varying the to that of the histo- and Weibull distributions Gamma, time and path segment lengths. shows the results of this fit for two of these sets. the number of data pcints in each the Chi Sguare test was used X2. By ccmparing distribution the X2 > of the two sets 1 -a Since is 829, the Chi Square following rejection criteria may x^, Table IX to compute the test statistic, X^ to the l-aquantile of Reject the null hypothesis of Gamma, it is possible to obtain parameters cf these distributions, a Exponential, a (D.F.) 30 "good fit" if be used. 1 TABLE IX EESDLTS OF FITTING ATTACKER TANKS CLOS DATA TYPE CELLS n DIST PARAMETERS (N) TIME £29 (K) CHI STAT D.F. (K-N) X 1-a (DF) ' 5 EXf ^=.01935 194. 1 4 9.488 5 GAK. 9=. 00686 7.539 3 7.814 WEIB. r=.3478 v=0.0 5.52 2 5.99 688.4 6 12.59 2.407 5 11.07 8.67 4 9.488 SEG. 5 1 a=31.5l4 B=.5714 PATH S29 7 BXF. 7 GAM. SEG. X=.0118 9=.0027 r »EIB. 7 =0.231 v=0.0 1 a=44.505 6=.5128 1 _ A tila cf J ccmparison of rhe test statistic ro the .95 guanthe Chi Square distribution, showed that for all time segment lengths the hypothesis tha* the data represents an exponential both the fits. provided distribution is Gamma and the For an path soundly rejected. Weibull distributions provide good Gamma distribution segment lengths obviously However, tha better fit than did th€ Weibull exception to this is the Tow path segment lengths. Figure 3.3 shows the plots of the Weibull cummulative distributions function and the empirical CDF for distribution. The only tank tiie and path segment data. 31 For rime Segment lengths (A < Q m O — o < Figure 3.3 Fitted and Empirical CDF Plots. 32 distributions are virtually identical. This indicates that the Hsibull provides a good fit for Time segment lengths. Ir the second case the Weibull fit was not as good Gamna fit. as the The results for the remaining sets of the two CLOS data are enclosed as Appendix C. 3 Acq uis ition . Cata Acquisition data Attack€r weapons The Defender force, was devided into two acquiring or of sight, the From this data, twc depen- analysis viz. "Time to target given that there exists conditional line and "Time to Engage" a target given that it has dent variables a those of and the Defender force wsapons acquiring and engaging Attacker weapon types. Acquire" engaging data grcups. were selected for , been acquired. The histograms for both "Time to engage" cne mcst the pointed to the likely to provide data sets had Lilliefors test was used. a good fit. number in Table In those cases where data points, the of tabulated been of Reference A16 as the The Lilliefors quantiles for the distribution have exponential found exponential distribution small a to acquire" and "Time and may The results 7. be Tanks acquiring or engaging Defender Tow weapons is shown in Table X. They indicate that the exponential distribution provides a good fit to Attacker the those for the both the data on "Time to Engage". 'Time to These remaining data sets are Acquire" and for results as well as provided in Appendix C. ^ • Enqaqsm ent Data Engagement range to engagsment, data consists of aim errors in measurements on the both vertical and hori- zontal angular shifts originating from the target's center 33 __ _ , TABLE X GCOENESS-OF-FIT RESULTS FOR ACQOISITION DATA ATTACKEB TANKS TO DEFENDER TOWS TYPE n DIST EARAMETEES TilDQ 15 EXP. X =.0092 .1642 a < 0.5 15 EXP. X =.08 15 .3202 a < TEST STAT CRITICAL VALUE tc Acq. TiiD^ .999 tc Eng. — - of mass, well as as a 1 indicator variables deli- series of neating target exposure, aspect angle, whether it is moving, whether it is firing, and whether it was hit, missed or killed. Since all the variables, except for aim errors, are indicator in nature, figure number of the Consequently, they will aim of times marely yield they occur errors are the only a proportional in the data. dependent variables selected for fitting a distribution. An examinaticn of this data revealed that aim errors were only recorded for Attacker and Defender Tank weapons. The data was, therefore, formed into four sets corresponding to the "X" and " Y" Histograms for Defender larks. suggestid that to coordinates of aim error for Attacker and a xhese coordinates each of Normal distribution is a likely candidate Since the aim error distribution is bi-variats, fit. a bi-variate normal distribution must be fit, unless it can be coordinates is Ths correlation between "X" and "Y" for Attacker and shown that zaro. the correlation between 34 the two were computed to Defender Tanks assume that the correlation to be between the small enough to two variables is handled separately. The results cf XI -O.OU respec- 0.15 and With this assumption the "X" and "Y" coordinates can zero. be are appear These valuas tively. be the Chi Square test listed in Table show that the Normal distribution does not provide the data. fit tc shaped), when the Khile they are similar in empirical distribution is cciEfared to the Further investigatioi: cf theoretical shape of zero Normal (bell distribution. the data showed this was aim errors may good extremely "peaked" due tc a large number of zero error points within the data set. excessive number a be the This result of rounding to the nearest integer mil when the data was recorded. Since the significance of a one mil error depends upon the range to the target, might prcvide far toe coarse a measuring to the nearest iril measurament scale. The end clustering of data points on the integer values, especially at zero. was not possible to fla a consequence it obtain a good fit tc the aim error data. result is a 35 TABLE XI RESDITS OF Aia ERHOH FITS DATA SET Attacker (X-cccid) NDMBEE OF CELLS PARAMETER ESTIMATES y =-0.331 a^ = Attacker CHI SQ VALUE 61.75 1.01 0.053 80.67 (Y-coord) 0.982 Defender .0167 111. 385 (X-cccrd) .572 Defender = (Y-cocrd) 2 .428 =1.09 36 294.564 DEGREES OF FREEDOM IV. MEIHCPS FOR DEALING WITH QUESTIONS OF SIGNIFICANCE A. GFNEfiAL improve combat modeling within Ic order to increased understanding of the Without the knowledge cf one-another, engange combat process is essential. how ccmbar units operate, manuever, terminate engagments, combat expected to represent reality. or scarcely be modeling could Thus, the primary focus of this those analysis methods combat processes. Each question will UTili2ed to be the significance The questions to issues that upon the chapter will be to discuss which may questions regaring answers to the Army an provide of certain be examined are based TRASANA determined to be important. addressed separately, be by briefly the most appropriate method discussing the pertinent issue, of analysis, and the experimental dara that will support the analytical method. B. THE OF EFFECT BOUNDING THE BY DEFENDER ON HIS DETECTABILITT It has, for the most part, defender were to stealthily sive positions, him. he counter A that if a move between alternative defen- might prolong the time it takes to detect that any argument is stationary tackgroud is more movement against likely to queue the a visual, electronic detection ability of the searcher, thereby, increase the probability that the attacker thermal, and been assumed detects or a defender target. Defender movement into and The question is then, between alternate tions significantly increase the rate force is able to detect him?" 37 at "Does the firing posi- which the Attacker may be viewed The question the notion supports alternate An asking whether the number that as positions increases detections. hypotheses that exists versus the alternative that the data of moves between the number the so does approach to answering the statistical test as of this question is to no increasing trend an increasing trend dees exist. The data required each defender must relate the number of times that vehicle moves between defensive positions to the corresponding the number of times that he is detected by any member of the atxacker force. A set of data trial will consist of the paired observation Xj for each (Xj,Yj), where is the number of moves for the jth defender vehilce, Yj is the total A and number of detections scored against him. method nonparametric for detecting increasing or trends is the Cox-Stewart test [Ref. 7: PP.133-13S]. Although this test is adequate for determining whether or not a trend exists, it provides no specific information as to how this result is to be used for modeling decreasing or analysis. therefore, It is, more useful to in addition to answering method which will, employ a the question, estimate of the magnitude of the relationbetween the t *o variables of interest by means of also provide an ship nonparametr ic regression [Ref. 7: pp. 272-277], Assuming the linear regression model Yj first the = A (U.l). a BXj (U.l) ncnparametric estimates of ranks are determined; tions may + he obtained The slope "B" in an "A" and "B" estimate of the based on number of detec- substituting these estimates in C^.l) will determine whether or not by relationship exists between Xj 38 and Yj. The magnitude and sign of the slope will determine the degree and direction of The Spearman's the relationship. [Bef. 7: 252-256] may be pp. Rho test for correlation used no test the following hypothesis He: t = bo Ha: t > bo This is the null hypotheses equivalent to testing correlation exits correlation does the versus exist. A regression positive that a must be pointed out that It using least squares that will indicate rejection correlation does indeed exist. a alternative that no could be used, provided distributional assumptions are satisfied. least squares regression is extremely sensitive to However, the existence of outliers. If it is suspected that outliers that all the are present, it is best to regression. such as use a mora "robust" the one just described method of or the Median regression. confidence interval for the slope in equation U.I may be derived by using the "two point" slope method [Ref. 7: p A 266-267]. QOICK DASHES BY ASSAULTING VEHICLES C. make quick It vulnerability, to reduce In order dashes from one is suspected is asked, significantly defilade position to that these quick dashes to detect defender targets. tion assaulting " their ability the next. reduce its ability the following ques- by assaulting quick dashes Do reduce Therefore, vehicle to detect weapons defender targets?" As in the previous section we may test for increasing Cox-Stewart test; or perform a hypothesis test on the slope of the regression to determine if a posi- trend using the tive correlation exists. Because of the advantages prvicusly 39 enumerated, the nonparametric regression method is preferred in this analysis as either In case precisely the it is of constructed in must be taken tc insure sets data the Care same manner. that the length that well. are precisely defined and "quick dash" is a consistent tactical current with doctrine. Assuming that the quick dash lengtn is 200 meters, it is now the number of times that 7«5hicl€ "j" possitle to define Xj, corresponding tc moved less than or equal to 200 meters; Xj determine the number of detections scored by vehicle "j". The result is the bi-variats data set (Xj,Yj). This type of data may be collected, specific to a particular we may new battle run, trial or aggregatted for the entire experiment. D. EHGAGEMENT AND IIS SIGNIFICANCE ON ATTfilTION question here The engagements occur attacker?", or "Does engages the "Does is defender the hurt frequency the opposing force increase and decreases the kills it kills it recei ve3(Zi) derived. A total of . 24 with which a the force it achieves attacker force, two sets of engagements initiated by that force (Yi) engagements initiated by than the kills bi-variate data must be analyzed. kills attributed to it more which receives?" Fcr either the defender or point. frequency with the One set is the number of and the number of (Xi) The other set is the number of . that f orce (Xi) and the number of Each battle run represents one sample sample points may, therefore, be The analysis procedure is the test for trend using the Ccx-Stewart test, or the method of nonparametric regres- sion discussed in section B. 40 B. BCONDS EXPENDED CN TROE 7EBS0S FALSE TARGETS issue tc The b€ addressed the number of rounds relationship between true false targets. or a Attacker force, weapons fire fewer there exists is whether the expended against the stand From question can point of posed "Do be a rounds per target against the Attacker false targets true ones?" The same question may in turn be asked with respect tc the Defender force. It may, in addition, te more detailed in scope so as tc concern a particular weapon type, battle run, or trial number. than against The issue involves a comparison of the distribution of are specifically interested in deter- two sets cf data. We iiining whether net we can expect one set or to have higher expected value than the other. The data required for this analysis consists of of observations. One set representing expended against true targets (Sj) . the number cf rounds The other set number cf rounds expended against false targets The expected value expected value of An appropriate cf consists cf assigning the sun where >E (S j) } Sk is lass than the {E (sk) Pn The hypotheses normal test statisxic [Ref. (gf-Pn) Z= / pp. 378-384] 8: Q.O - Pf (1-Pf) Pn (1-Pn) Nf Nn Y a by constructing a standardized may be tested rejection occurs statistic the test if interval nay now be established for 0< Pf-Pn < Z / I For each Overwatching bivariat€ , (Pf-Pn) Pf (1-Pf) Xi , target is firing, and Yi, and Pn= confidence as (1-Pn) ?n(1 ?n (U.S) Nn the number The elements a of the detections when the the number of detections when the target is not firing. The proportions ?f and Xi/(Xi-«-Yi) A Z or stationary attacker target point is constructed. point are ^ -^ Nf r bivariate data exceeds the normal distribution. quantile of the standard 0. (4.2) Yi/(Xi+Yi). constructed for each battle run, of the entire experiment. 44 The Pn are then Pf= sample may be trial or as an aggregation CONCIOSIONS AND RECOMMENPATIONS ?• CCNCIOSICNS I. Whil€ the ARCOMS collection of the processes, it field experiment forged II experimental data did net provide experimental effects the Armor on The choice eight factor-level combinations at which ured failed to provide the balance used is the 22 of the the data was meas- needed to perform a 2*-i The only model which could be factorial analysis with this is not an applicable Combat for an efficient analysis of and interactions. fractional factorial analyis. the way in replications. Even sub-modal for all factor combina- tions. In fact, there are only three combinations of factors that provide suitable models. They are Attacker Tactics to Defender Tactics, Attacker Tactics to Terrain, and Attacker Tactics to Hatch Position. The fitting of theoretical distributions is possible for a great d«=al of the data. Preliminary data analysis suggests that CLCS time either Gamma or aquire and are distributed as and path segment lengths Weibull distributions time to engage appear while to be the tima to exponentially distributsd. B. EICCMMENCATICNS Based upon these conclusions the following recomenda- tions are made. 1. Variance for the dependent variables A should be accomplished using a listed in Appendix 22 factorial design ANOVA) with three replica2x2 This model is provided in Appendix tions per cell. An Analysis of ( B. The Model assumptions should 45 be verified by cf -he error terms. checking for rcrmality If this consideration shculd be given to the Friedman nonparametric analysis of variance cind its extension for the case with replications assumption is not reasonable, [Ref . 7: pp. 299-308 ]. it is recommended that a Fcr future experimentation, 2. detailed experimental design be determined collecting any The design shculd data. prior to specify the issues tc be addressed, the analysis techniques to be employed, and structured to An early identification of the how the data support the analysis. analysis techniques will is to be help define the type and quantity of data to be collected. CLOS Time The 3- segment lengths when ploted against both Time to Clos and Range to the initiation of CLOS reveal the presence of plotted against the a bi-modal relationship. range to initiation of representing longer duration modes, frequent occurrences, meters. as were located This phenomenon occurred '^hen CLOS the well as more at 1500 and 3000 for both Time and Path segment lengths. Figures showing this phenomenon are in Appendix D. It is recommended that an investi- gation of this phenomenon be pursued with small scale experiment. the ARCCMS Prior to little data experiment, there has been generated from field experimentation very which can realistic combat scenario. Combat models have relied heavily historical data. upcn engineering and generated well ccntrclled Engineering data is from "labcratcry-like" experimentation. The interactions involved represent in a a ccmtat evironment with a engagement are not reflected in be obtained tion is frciD as free flowing such data. f orce-cn-forcs Some idea must to how different data from field experimenta- engineering or historical data. 46 The objective the field experimenration data provides is to datermine if more realistic representation of the combat data a than the ether two. It is recommended that 1. A comparative ABCOKS data analysis and that be performed of the between Balistic the Research Laboratory and the Night Vision Laboratory. 2. Regression Analysis should be performed using the engagement data discussed in Chapter III to predict A the parameter "t". Nigh"!: for probability of detection in time This should be compared with the resul-s of the Vision Laboratory experiment. This comparative provide an analysis may between engineering insight into the differences data and field experimentation. HI that collected from APPENDIX A DEPENDENT VABIABLES The dependent are variables listed according their contribution to combat processes in A. OFFENSIVE OPESATICHS Attacker vehicle LOS ti ice and pat.h Segments. Number of Defensive position scanning lasers with LOS to single attacker vehicle. Number of atracker vehicles with LOS to single defensive position scanning laser. Defender vehicle CLOS time and path segments during exposure. Number of defender vehicles wi-ch CLOS to single attacker vehicles. Number of targets acguired by the attacker force. Time tc acguire true targets by the attacker. Number of false targets acquired by the attacker. Number cf true targets with CLOS and rounds expended by the attacer force. Number of true targets engaged by the attacker force. Time tc engage true targets by the attacker. Target engagement results for true target engagement by the attacker force. Number cf false targets engaged by the attacker force. Time to engage false targets by the attacker force. Reported target engagement results for false target engagements by the attacker force. Time, distance, and movement rate between bound positions for the attacker force. 48 Time of occupaticn of the bound position and rounds fired by the attacker force. Number cf hits received by attacker vehicles. Number cf kills cf attacker vehicles. B. DEFEHSIVE OPERATICNS Defender vehicle LOS time segments. Kean number of defender vehicles with LOS tc offensive scanning lasers. Attacker vehicles with CLOS time and path segments during exposure. Number of attacker vehicles with CLOS to single defender vehicles. Number cf true targets acquired by the defender forces. Time tc acquire true targets by defender vehicles. Number cf false targets acquired by the defender forces. Number cf true targets with CLOS and rounds expended by the defender forces Number cf true targets engaged by the defender fcrce. Time to engage true targets by defender vehicles. Target engagement results for true target engagements by the defender forces. Number of false targets engaged by the defender force Time to engage false targets by the defender vehicles Pepcrted target engagement results for false target engagements by the defender force. Time, distance, positioits and movement rate between bound for the defender force. Time cf occupaticn of the bound position and rounds fired by the defender fcrce. Number cf hits received by defender vehicles. Number cf kills cf defender vehicles. 49 APPEHDIX B 2X2 ANOVA WITH REPLICATIONS ABOVA HCDEL I. The 2x2 analysis variance modal with of three replica- tions per cell is where i = 1,...,n ; n=2 j = 1,-..,in ; m=2 k = 1 , . . . , p ; p= 3 The model parameters are the grand mean n = 3. = the y. = the second factor affect ^^. - the interaction effect £. = The error term ., first factor effect error terms are independent and This model assumes that the Normally distributed with It a mean of zero and variance of a\ may be used to test the following hypotheses 1. All 3. no affect = 0. (There is =0. is no due to the first factor) 2. All y. (There affect due to the second J factor) 3. interaction effect) The clarify the fcllcwing terms are defined in order to ANCVA table on the following page. All \b . = 0- (There is no ID 50 ^: w , CO c ^ < *; ^^ p^ rz! < CO s.j 00 CO • (— < CI C/7 CO C'J CO CO 00 i < CQ 00 GO CO 00 II II 00 23 < M >-• I < . I o M 1 1 •H i e C CM •-I ^.^ l-i '-: " 1-^ •^ N.-^ •^1 •H ;^ t 1 >- ;:ti •n • 'r-\ <-^ 1 1 > i cuw S C w t-i ^~^ ^ "^ n i-0 j»: (= t-j -I— •H r" ^ 1 I ' 11 < 7^ i 00 CO II II 00 1— :o 1 1 CO 1 II II L-3 an CO 00 CO C-i O f— < C_) c.: CJ ex r) o 00 CQ < < -v r~i o < j-H O < c^ < tx 51 b -H CCMFDTEB PEOGRAM E. NAV41 POSTGRADUATE SCHOCL FILE: TESTAE fROGRAM //CIGIORGI (1928,1159), •CIGKAGI OR 360«,CLASS=A JCe Al //MAIN CRG=^PGVMl.i928F //* //* SA^FLE CF AMOVA HYPCThtlJCAL TEST CATA // // // ATTACKER TACTICS TC DcfE^CEf TACTICS. //* EXEC BI^EC,fR0G=8MDF2V //GC.SYSiN CC /PRC3LEM TITLE IS 'AREITRAFY h>PCT hET I CAL TEST DATA* V-fiRl;iBLES ARE 5. /INFLT fCRN^T 15 3F3.C)* . bAf*E^ ARE OEFT/C T AT^C T IC ,CET TIME . /VARIABLE CEP£NDE:\T IS DETTIMt, /DESIGN CPCLiFING ARE CEF T^CT , / T AC 1 IC • /GRCLP 2. CCDEMli ARE 1, h/MES(i) ARE DELidfHAiTY. CCCES(2) ARE i, :. fAME£i2> ARE FIRcMVT , F ;? I C . /END // * , ec ec 70 2 66 2 9C 2 9^ 1 82 74 1 5A 1 2 9C 2 76 2 92 1 1 1 2 2 2 2 2 2 /* // 52 PAGE 1 EM0F2V - AN/LYSIS OF VARIANCE AhC COVARIANCE WITH REPEATED MEASLi^tS. BMOP STATISTICAL SOFTWARE, INC. 196^ WESTWCCC BLVD. SUITE 202 (213) 475-57CC FkCGRAM REVISED APRIL 1982 ^'A^UAL REVISEC 1981 CQPYRIGhT (C) 1^82 REGENTS CF UNIVERSITY CF CALIFORNIA TO SEE REMARKS /NO A SUMMARY OF NEk. FEATURES FCR THIS PRCGRA^, STATE N'^US. IN THE fRI^T PARAGRAPH. — JUNE li, 1«83 AT 22:23:08 FRCGRAM CONTRCL INFORMATICN /PRCELEM /INPUT TITLE IS 'ARBITRARY H YPCTl-ET ICAL TEST DATA'. \,;!RIA3LES ARE 3. FCRN/T IS (3F3.C)' . NAMES ARE DEFTAC .ATACTIC ,C£TTIME . CEFENCENT IS DETTIME. CRCUFING ARE DEFTACT ATAC TIC . CCDESd) ARE 1, 2. NAI^ESdJ ARE OELie, HASTY. CCCcS(2) AKc 1, 2. NAMESi2) ARE FIREWVT , f API C. • /VARIABLE /DESIGN , /GRCLP /END FRCBLEM TITLE IS ;!R8ITRARY t-Y FCTI-ET ICAL TEST CATA ••.••.•• NUMBER CF VARIABLES TO READ IN. NUMBER OF V/PIAELES ADOEC 5Y TRANSFORMATIONS. '. . TOTAL NL^'3£F ZF VARIABLES . NUMBER CF CASES TO READ IN CASE LABELING V/RIABLES M5SING VALLES CHECKED BEFORE CR AFTER TRANS. BLANKS ARE INPUT UNIT NLMBER RSrtlNO INPUT UNIT PRIOR TO READING. . DATA. • NUMBER CF WCfCS CF DYNAMIC STORAGE NUMBER CF C^icS CESCRIBED BY INPUT FCRMAT TO END • NEITHER MISSING • NO 9c254 5 ... 3 DETTIME 9 ChARACTERS. 3 . ..... VARIABLES TC BE USED DEFTACT 1 2 ATACTIC INPUT FCRMAT IS 3 . 1 (3F3.0) MAXIMUM LENGTH CATA RECCRD IS INPUT VARIABLES VARIABLE RECORD COLUMNS INDEX 1 2 NA^E DEFTACT ATACTIC NO. BEGIN 1 1 1 4 flELC HDTH ENC 3 3 3 6 TYPE VARIABLE INCEX NAi'E *F * 3 CETTlME F DESIGN SPECIFICATIONS =12 GPCUF DEFEND = 3 EASED ON INPUT FORMAT SUPPLIED VARIABLE NO. NAME 1 2 MINIMUM LIMIT MAXIMUf< LIMIT fECOPDS READ PER CASE. 1 MI SSI NG CCDE CATEGORY CATEGORY NAME CODE DEFTACT l.GOOCO DELI8 2.00GOO HASTY ATACTIC 1.00000 FIREMVT a.OvOOO RAFIO 53 INTERVAL GREATER L£ THAN C C. 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UJ a. h-UJ a UJ LULL. < m .-4»4i-l>^GO C£.UA 00 LU xac :> LULU • • < 00a LUQ i-CJ UJ < >z —ILU lU^en G> < — z - 00 :oo 300 ••00 " O r—— o rO ui . f OB-mLP QB>j (O * >j»— ^j«— r--i lO »j ^ -< 1/1 1/) s s m O o n O > 5 o > o z > 8 NC OF SAMPLES *00 200 300 400 bOO xxx2^'-''x CrTiO; •OTJ'rar- r-r- 35ZgOu<.-n02ir"-. -> — ^ z z z— -. -. > -n 2 — — — r-.J mm n Q Z o O u» r— -I ?; I mo m o m to g O s X O > o > 2 Figure C. 1 Tank CIOS Tine and Path Segment Histograns, 57 c (/I o to X < !? »- !^ Ui UJ -i — o t- Z ^— eo ^ ^» if» >c\ 3 U^ UI ^ .^ o Q. — t^ K1 >^ "^ - - <, a u < m 2 O 5 L^ -< WJ > _) UJ UI —1 ^ ^• UJ •— • h~ ,^J i/i 1/1 - ? tn Z u/ — uJ LJ UJ Ui Pi^ —i* ^- ^- r 2 UJ UJ UU _ ^ UI Lo Z ^fe5^251^S ^m < Ui q: or (_> L^ x2 X 2: 0 SjIdi^VS JO ON o o 1 2 tr Ui \ tn X < o UI a: o 2 o UJ c 2 O Ut Z ? UI 9t in (/> O 1/1 rx i£> (5> fX >^ ao "^ cw "• (N to Ui — — r 3 tn 5" UI uJ UJ to O U m^ Z uj ui UJ — UI U OU 2o£-j UJ cu l/l _ J l: 2: 09 09 • . v/ix2XtnCii:iric>*3f^o»x :x 0» SjIdr^VS JO ON Figure C.2 Tow CLCS Tiae and Path Segment Histograms. 58 in o a < I§ cc UI CO X CI < !£ ^ S »— o Uj DC o 8 ^ z 3 O Ui o lyi ^. -^ UI O Irt yi — X £_r^'r' "^OXJ — tNO m — f^'~-or^'^<3>-»0'^ > X to Ui u< -i ^^ -z: ;/i i/i Z ^ ^ 0,^2i -* -^ u. QJ Q. X 02 0» 09 O ^ 01 a^ '3 C »^ 0' - ^ u z 2 -1 09 c'l Z uj ^ .^ 1^ -> •'_' X r 0. X '/I SoO— 5r^2r.rx-^ a" 2 4 x^'^'^i*'''"'''^ 1-" 0. Ot SJIdrNVS jO Figure C.3 -. Q xi/ix zx>/ii/i:tuicN5'^o>xx 3= :i: 08 — UI on APC CLCS Time and Path Segment Histograms. 59 TABLE XIV RESULTS FOR TIME TO ENGAGE DATA DATA PCR ATTACKER TO DEFENDER VEHICLES: TYPE Tack tc CIST. FORM l_e^(t-2) X .076 CRITICAL VALUE TEST TYPE TEST STAT D. F. Chi 5.41 5 a< .75 NA a< .30 Sq. Tank (87) 1-e-^t .328 Lilfor. .1497 l_e^(t-3) .2414 Lilfor. .2857 Tack to Tew (15) Tank tc Drag. l-eA(t-3) Tew to Tan k i23) l_eA(t-3) Tow to Tow . 146 Chi 3.34 3 SA .7< ^<, 8 4 .7 * O lO CO o• O 43 — ^O - 5 UJ — s«J ^^ •-• •— »— >- •— 2. z. « 3^ Ui < r. S — —^ UI p— — y- ^ •< — :z >(/i(/)Zui — Uj(_) — UI —I Ui -> -J ^ui UIO Lt,0O t-uiu20uj(/>ucrZa:a: Z _ 0: Ui « < l^ ui UI _ — a Q. — ^ — ui a .jj i-i rfS wS . c£ X 02 OC X (/I t/^ (7i 5 ^ ^ ' 'iS rn ./> fN /> vw 3 "^ I »X 3< 01 S31cl>NVS JO ON z < I- q: Ui a UJ o z OC a c to < o o 4 lO < 2 < o— »- (B ^ — Ui > (/1 (/I Z Ui Ui i/> — Ui O u t-uiu.z;ou-jj(_!5za:-r u. z; O u- JJ CJ S r-i£^3_juiZ> ^-u.a — u.< u. 3 . w r^ i^^ _ r 2£ X ~ o» X X • uaO< ix"i . o<; ot oi: oc i") >i^ Oi SjldhVS JO ON Figure C.a Attacker Tank to Defender Tank Acquisition Data. 62 o Ui a z. o z o 5 rfl UI t3 < UI 2 'i O O UI lij 5 ^K it UJ i . u> UI 2 2 < Ui 2 O — _, wi _1 S Ui UI ut __ — < ^ Z >«/l(/lZui _— UJ'/* 'Jv* t- . — UJ(_> h- r- 2 Z ujui ^_i5ouiaa^Q, 33 W1X ZX(/>Crt:^irtxx O »— oc u> a UJ u. UJ O Z UI S3 a < OC o < IN i z < o: V* «N <. * >- f- i^ o (N <<»— — — —— — 0(N«^— O^ to u < u 6 i ! Figure C.5 I r T T i •< > U^ i/i t/> t/l nr u* UJ im LJigO< ^iSui<: Z. < — « T ~ "^ O o - » 1 >~ N. «) «3 (>» 1/1 2 ^ o < a — UJ Ui .^ UI UI ^* ..J »-• .^t -• .^ «• « CO '— Ui U- *1 A, ;^ IX < UJ UJ 2 X Q xaix2xi/ii/ii:«ocM3p^o»xx — c!3;u?^«^ Ui Oi SI O'l SjIdl^VS JO 5 ON z o o < a a: Ui a UI o o o O O UJ < 2 8 o Q O o -i O- — 5 ^^ - Z Z Ui — Ui Ui Z Z i/l l/> I/) >-uiuZOuiuiu»iiZJ:iZ_ (^ iroa:v*j«uiuiZ ua3C< ^ -» I— ^^ UJ 5 — aa — a ^ ^i-uiO. '^_/ hAJ -« l^rf k*J .£. -^ **. X wi X 2 X ^/i ?t i u^ y< 41 lO 41 (N (J> 5 X X Sjidi^vs jO on Figure C-6 Attacker TanJc to Defender Dragon Acquisiticn Data, 64 :. a: o a: cr C, Ui < en o o cc C < < «/> 2 Z 2 00 lA -J Z Q ac o o o 5 ^ Ui a: a § o « a> -J — a o —— ><<^0 o O* O O O O to trt 2 r<4 I I > > (/) X tn Ui Z 2 Ui Ui -Lju.z25Lj'yioCt2ccJc a cr ui < — Ui _ uj< *>— uia."— 0. —a — —3 M ^ umo< q: O q: J- 021 08 • - J. 0» S3"ldWVS JO ON q: 2 < - u< z ^ zz Ui LJ l/l omO-* Z05ui-uiQ.—'a-a.'22 -.-i-SQUiaaiOi ui Q — xJl'^i*^*'!'! xi/>xzxi/»OT^iocMar^ O z r- Z >cn-u.a.— So. — < Lj-< "-^^^ujUIwi Q 9^5 rv XI/>X2XW1(^^iOCn3 Ui q: J. O q: J. 09 08 001 (j» 0^ >t X 02 S31dWVS JO ON UJ UJ u < E o [ q: Ui —J 2 2 2 < 3 Z ai < 2 o O IK O O U O a: UJ 2 < s !; Jr Q O X %. _j _. •< _ — oOo 3 — O —O < — • rfl f^ f^ '- • I I 'T I OOO— I I x (/I [ 2 S UI !i :: bid .— >- < > 2 —2o2 ^^ X u S Oy 2 ui ^ 5 ^ —a —< U u — -.^SoCJuq. o 2 3 ^ 6 Ij UJ UJ i/i UJ 1/1 :2 UJ (^ o: -J "I UJ Ui .Z a. .^ I- u- a. g^ q. tA tn r^ a> I [ 09 09 Figure C.3 Ot xuix2xi/iCnSintN 3 Oi attacker Aim Error Histograms. 66 ' > X X LJ (_)Cbo< w >- (x>; x: oo» 002 oot Ul >~ to t/l Z — — >- z L- z r zoa-j'*»^^CMtf1— — 3 O Ul «/i Ul 3 Z 3 UJ uj L^ »n O -J u UJ UJ r- _i — I- < — — uj ui — — — — - • . — z n: - z wjuj >U^(/)ZuJ — UJ u, sJ y zoujtnuaZSa U -^ "'OiXuj^ujujZ CD O oujin'/> Q, — S O / 5 —• i/i '_) <_) X 00* OOv yi X? X £xi/iCnit>r)tN3'^(T>x 00 COC SJldm-S jC ON Figure C.9 Tank CLCS Segment Scatter Plots, 67 o -I *o c V) o »— on it o < X 3 O O CD 2 Z (jj a 2 O UJ U1 _j X ^ kO « OO • oO "^ - o- OO o — ^ < — > »- Ui 02 2 »- z — u u* o O (/> O <_> i^ *X X Or 08 1 UJ U (/I I/I 1/1 SSIdAVS JO CN ^8 O t/1 5^ 2 or o IS UJ 01 o 3 O 00 UI 1/1 ^ "* ij < ^SS O "* iT — — t- »o — 1^ »r so <0 tM (SI CJ> •» (N — — to rd lJ 1/1 O O — > ^ -< 2 UJ U1 — UJ Loo 20uJUlO(Z 2 a. (t < Uj ;0£-J 1^ 7 X (_jCbO< U. UJ D ^ U^ u, C XV/>X2Xt/'0''i£infN 3 '^ X X Ui i/i UJ 1/1 _J f-uiu. L • I u") C7> 09 09 Ot cc S31driVS jO ON Figure C. 10 low CLOS Segment Scatter Plots. 68 • 1/1 o 0. < . H o o U3 UJ — I r K— c r<. 3 3 O (<^ .fci o C/l (/I X *• ;^ a> 5 _^ < o 'O in -o u ^— (/I (/> Ui tn S* :? •-•• O n !Sf Ci X ui * CN Ui Ul UJ •— •-• •—• p^ •< •— UJ Z 2 >— ^ a. a. '^ -J — -- Urf UJ ^ ^ -J -J NVS JO ON o a. •4. !- C/1 (/I o ^3 o5 O C3 2 O UJ s 1/1 l/> >— a, l^ 9 — 3 o f^ - u. u- ^ ucDO«< 3. — UJ -J -- -• < —; t^ •;; UJ — uJ UJ O >J 5 I" V' - ^ ^ 2: zci-*j<-ju.;:x .*) «< Uj •_) >-> Q -X— Xi/ix2xi/Ii/i^^cn5'^?ackerly, C. Mathematical Statistics W ith Applications, 2ed Ed. " ~ . No n op ar a m etric , TJulFuiy Press7~"!^Tr"' 73 Statis tics , INITIAL DISTRIBOTIOH LIST No. Copies 1. Defense Technical Information Center Cameron Station Alexandria, Virginia 2231U 2 2. Library, Code 0142 Naval Postgraduate School Mcnzersy, California 93940 2 3. Professor T. Jayachandran, Coda 53Jy Naval Postgraduate School Monterey, Califorria 93940 4. LTC. £. Paek, Code 55Ph Naval Postgraduate School Monterey, California 93940 5. CFT Emilio Di Giorgio, FA, USA 22-21 Crescent Street Astoria, New York 11105 6. USA Tradoc Systems Analysis Accivity ATTN: ATOR- TGM White Sands Missile Range, New Mexico, 74 1 1 1 4 88002 202098 Thesis D5T3T c.l Di Giorgio An analysis plan for the ARCOMS II experiment. 15 MT 84 13090 / 202038 Thesis D5737 c.l Di Giorgio An analysis plan for the ARCOMS II experiment. thesD5737 An analysis plan for the ARCOMS II 3 2768 000 98519 6 DUDLEY KNOX LIBRARY exper