Develop and demonstrate a methodology using Janus(A) to analyze advanced technologies.

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(1)Calhoun: The NPS Institutional Archive Theses and Dissertations. Thesis Collection. 1991-06. Develop and demonstrate a methodology using Janus(A) to analyze advanced technologies. Wright, Jerry Vernon Monterey, California. Naval Postgraduate School http://hdl.handle.net/10945/28117.

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(6) NAVAL POSTGRADUATE SCHOOL Monterey, California. THESIS Develop and Demonstrate a Methodology Using Janus(A) to Analyze Advanced Technologies by Jerry Vernon Wright. June, 1991. Samuel Parry James Hoffman. Thesis Advisor: Co- Advisor:. Approved. for public release; distribution is. unlimited. T256332.

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(8) SECURITY CLASSIFICATION OF THIS PAGE. REPORT DOCUMENTATION PAGE REPORT SECURITY CLASSIFICATION. 1a. 1b RESTRICTIVE. MARKINGS. Unclassified. 2a SECURITY CLASSIFICATION. AUTHORITY. 3. DISTRIBUTION/AVAILABILITY OF REPORT. Approved. for public release; distribution is. unlimited.. 2b DECLASSIFICATION/DOWNGRADING SCHEDULE 4. PERFORMING ORGANIZATION REPORT NUMBER(S). NAME OF PERFORMING ORGANIZATION. 6a. 5. 6b OFFICE. Naval Postgraduate School. (If. SYMBOL. applicable). MONITORING ORGANIZATION REPORT NUMBER(S). NAME OF MONITORING ORGANIZATION. 7a. Naval Postgraduate School. 360. ADDRESS. 6c. Monterey,. (City, State,. CA. 7b ADDRESS. and ZIP Code). 93943-5000. Monterey,. 8a NAME OF FUNDING/SPONSORING ORGANIZATION. ADDRESS. 8c. (City, State,. 8b OFFICE SYMBOL (If. (City, State,. CA. and ZIP Code). 93943 5000. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER. 9. applicable). and ZIP Code). 10. SOURCE OF FUNDING NUMBERS. Program tlement No. Protect. Work. No. Unit Accession. Number. 1 1. .. TITLE (Include Security Classification). DEVELOP AND DEMONSTRATE A METHODOLOGY USING J ANUS) A) TO ANALYZE ADVANCED TECHNOLOGIES PERSONAL AUTHOR(S) WRIGHT, JERRY. 12. 13a TYPE OF REPORT. 13b TIME. Master's Thesis. From. V.. COVERED. 14. DATE OF REPORT. JUNE. To. (year,. month, day). 15. PAGE COUNT. 101. 1991. SUPPLEMENTARY NOTATION. 16. The views expressed Government. 17 COSATI. in this thesis are those of the. CODES. 1. GROUP. FIELD. author and do not reflect the. SUBGROUP. 8. official policy or position of the. SUBJECT TERMS (continue on reverse. if. necessary. Department of Defense or the U.S.. and identify by. block. number). Janus(A), Central Composite Design Experiments, Response Surface Methodology, Advanced. Technologies. 19. ABSTRACT. (continue on reverse. if. necessary and identify by block number). This thesis presents a study of a methodology for analyzing advanced technologies using the Janus(A) High Resolution Combat Model. The goal of this research was to verify that the methodology using Janusl A gave expected or realistic results. The methodology used a case where the results ). were known: the addition of a long range direct fire weapon into a force on force battle. Both the weapon characteristics and force mixes were used as input parameters/variables. A Central Composite Design experiment was conducted in Janusl A to examine the relationship between the Long Range Tank (LRT) and the other tank killing systems in the force. The results of the research indicate that weapon system range is critically important in the Janus (A) model as is competant tactical positioning of the forces. The LRT significantly increased the destructive capability of the force as long as it was positioned in a tactically sound area. But, when overwhelmed by enemy forces, the LRT still contributed to the number of enemy kills, but the contribution to the survivability of friendly forces was not as evident. Response Surface Methodology was used to build a mathematical model of the relationship between the response and input variables of the experiment. ). 20 DISTRIBUTION/AVAILABILITY OF ABSTRACT. Q. UNCIASSIIIED/UNLIMITED. ]. SAME AS REPOR1. 21. |J. [JliC. USERS. NAME OF RESPONSIBLE INDIVIDUAL Samuel Parry. 22a. DD FORM. 1473. 84. MAR. 83. APR edition may. ABSTRACT SECURITY CLASSIFICATION. Unclassified. 22b TELEPHONE (Include Area code). 22c OFFICE. (408)646 2786. OR/Py. be used until exhausted. All other editions are obsolete. SYMBOL. SECURITY CLASSIFICATION OF THIS PAGE. Unclassified.

(9) Approved for public release;. Distribution is unlimited. Develop and Demonstrate A Methodology Using Janus(A) To Analyze Advanced Technologies. by Jerry Vernon ^Vright Captain, United States Army B.S., United States Military Academy, 1981. Submitted in partial fulfillment of the requirements for the degree of. MASTER OF SCIENCE. IN OPERATIONS. RESEARCH. from the. NAVAL POSTGRADUATE SCHOOL June 1991.

(10) ABSTRACT. This thesis presents a study of a methodology for analyzing advanced technologies using the Janus (A) High Resolution this research. was. to verify that the. or realistic results.. The methodology used. where the. weapon. direct fire. results. were. into a force on force. A Central. Composite Design experiment was conducted. Janus(A) to examine the relationship between the Long Range Tank (LRT). and the other tank indicate that as. a case. Both weapon characteristics and force mixes were used as input. parameters/variables. in. goal of. methodology using Janus(A) gave expected. known: the addition of a long range battle.. Combat Model. The. is. killing. systems in the. force.. The. results of the research. weapon system range is critically important in the Janus(A) model. competent. tactical positioning of the forces.. The LRT. increased the destructive capability of the force as long as a tactically sound area. But,. contributed to the survivability. Methodology was used. was positioned. when overwhelmed by enemy forces, the LRT. number. of friendly. it. significantly. of. forces. enemy. kills,. was not as. to build a. in. still. but the contribution to the evident.. Response Surface. mathematical model of the relationship. between the response and input variables of the experiment.. in.

(11) el THESIS DISCLAIMER. The views expressed the. official policy. in this thesis are those of the. or position of the. author and do not reflect. Department of Defense or the U.S.. Government.. The reader. is. cautioned. further. that. certain. vehicle. system input. parameters used and portions of the computer program developed in this research are not valid for. made, within the time free of computational. Any. all. scenarios of interest. While every effort has been. available, to ensure that the. and. logic errors,. computer programs were. they cannot be considered validated.. application of these programs without additional verification. of the user(s).. IV. is. at the risk.

(12) TABLE OF CONTENTS I.. INTRODUCTION. II.. ANALYSIS METHODOLOGY. 4. A.. EXPECTED RESULTS. 4. B.. SCENARIO. 5. C.. WEAPON SYSTEM CHOSEN. 6. D.. INPUTS. 7. E.. MEASURES OF EFFECTIVENESS. III.. EXPERIMENTAL DESIGN A.. IV.. V.. 10 12. EXPERIMENTAL DESIGNS CONSIDERED. CENTRAL COMPOSITE DESIGN EXPERIMENT. 13 18. A.. DESIGN CENTER POINT AND FACTOR RANGES. 18. B.. FACTORIAL COMPONENET OF CCD. 20. C.. BUILDING THE EXPERIMENTAL RUNS. 21. DATA ANALYSIS METHODOLOGY AND RESULTS. 23. A.. RESPONSE SURFACE METHODOLOGY. 23. B.. RESPONSE SURFACE ANALYSIS AND RESULTS. 26. C.. CONCLUSIONS. 38. D. V.. 1. FURTHER TESTING AND ANALYSIS. CONCLUSIONS AND RECOMMENDATIONS. A CONCLUSIONS. 40 47 47. v.

(13) RECOMMENDATIONS. 49. APPENDIX A. ANALYSIS FRAMEWORK. 51. B.. A.. BACKGROUND. 51. B.. APPROACH. 53. C.. JANUS(A) SIMULATION. 65. D.. CONCLUSIONS. 70. APPENDIX. B.. JANUS(A) TACTICAL SCENARIO. APPENDIX. C.. FIVE FACTOR CCD EXPERIMENTAL DESIGN MATRIX..78. 71. A.. DESIGN VALUE NOTATION. 78. B.. LRT MAXIMUM RANGE LEVELS. 78. C.. DESIGN MATRIX. 78. APPENDIX. D.. RANDOM NUMBER GENERATION PROGRAM. 81. A.. FORTRAN RANDOM INTEGER PROGRAM. 81. B.. SUBROUTINE RANNUM. 82. C.. ASSOCIATED SYSTEM LINE NUMBERS. 85. APPENDIX. E.. SAS. OUTPUT. 86. A.. SAS. OUTPUT RED KILLS. 86. B.. SAS. OUTPUT BLUE KILLS. 88. -. -. REFERENCES. 90. INITIAL DISTRIBUTION LIST. 91. VI.

(14) LIST OF TABLES Table. 1.. CCD FACTOR LEVELS. Table. 2.. EXPERIMENTAL RESPONSE RED KILLS. 28. Table. 3.. RED KILLS REGRESSION MODEL SUMMARY. 30. Table. 4.. EXPERIMENTAL RESPONSE BLUE KILLS. 31. Table. 5.. BLUE FORCE REGRESSION MODEL SUMMARY. 33. Table. 6.. ANALYSIS OF VARIANCE TABLE. -. Table. 7.. ANALYSIS OF VARIANCE TABLE. -. Table. 8.. RESULTS OF ADDITIONAL RUNS. 21 -. -. Vll. RED KILLS. 34. BLUE KILLS. 36 41.

(15) LIST OF FIGURES. FORMBT AND LRT. Figure. 1.. SSPk CURVE. Figure. 2.. LRT KILLS. 42. Figure. 3.. LRTs KILLED. 42. Figure. 4.. M1A1 KILLS. 44. Figure. 5.. MlAls KILLED. 44. Figure. 6.. TOW KILLS. 45. Figure. 7.. TOWs KILLED. 45. viu. 11.

(16) I.. The Army. INTRODUCTION. of the 21st century will be a highly technical, flexible, and. lighter force than has. been seen. in the past.. While the. size of the. Army may. shrink, this reduction will not necessarily result in a loss in the destructive. and the number of units on. capability of each unit, only the size of that unit. the battlefield will diminish. To meet these changes, the. weapons that are more powerful, and require fewer. Army must. soldiers (reduced. develop. crew. size). with the goal of producing a force of adequate capability.. Reduced force. size. comes with demands for a reduced military budget. The. control of costs, always important, can be expected to dominate. Army. operations.. weapons. will. be. to control costs. Significantly, cost control for the. critical as. is. the. to provide. Army moves. an. before they are actually built.. efficient. to. to test. aspects of. development of new its forces.. One way. new weapon. concepts. modernize. method. all. Those concepts which prove useful are. likely. candidates for further development.. A framework. for analyzing. new weapon. advanced technologies was recently developed Center. (ORCEN). Military. Academy. of the at. concepts which incorporates at the. Operations Research. Department of Systems Engineering, United States. West Point. (see. APPENDIX. A).. The. ORCEN. is. used by.

(17) the. Army and cadets for. the analysis of system design, operations research, and. combat modelling. This framework. and outputs. to. consider. technologically advanced. The. a logical ordering of inputs, processes,. is. when conducting an. operational. is. to. demonstrate an. method for using a computer simulation that fits within the proposed. framework. to. perform conceptual analysis of an hypothesized advanced future. weapon system. The computer simulation This simulation for training. is. selected for this study. currently being used by the. and the analysis of weapons and. to teach cadets modelling. and. Army and Marine Corps as a tool. tactics.. It is. used at the. for using. supported by. ORCEN. Janus(A) as an analytical tool to. explore the operational implications of advanced technological First, it is relatively. was Janus(A).. analysis.. There are several reasons. it is. of a. weapon system using a computer simulation model.. goal of the research presented in this thesis. analytical. analysis. weapon systems.. easy for warfighters to use, not just programmers. Second,. Army. analytical agencies (Training. Institute for Defense Analysis,. etc.).. Third,. it. and Analysis Command,. uses straightforward attrition. based measures of effectiveness (MOE) and measures of performance (MOP). Also, Janus(A) uses well understood battle calculus (stochastic processes) in the. model. Using Janus(A) will allow analysts to evaluate technologies early on in the. research. and development phase to assess the. technologies. Furthermore, Janus(A). is. viability. of future. the primary high resolution analytical.

(18) model used the. at. Training and Analysis Command-Monterey (TRAC-Mtry) and at. ORCEN. This thesis attempts to model an advanced technological system placed in. an actual battle and analyze a whole.. The major. its. impact on the force's destructive capability as. objectives to accomplish this goal include:. 1.. Research, identify, and select those model input parameters for an advanced weapon system that could justifiably model the implications of technology in Janus(A).. 2.. Define a straight forward methodology (design an experiment) to be used to measure the effects of the technology on the force as a whole.. 3.. Build a mathematical model that approximates the relationship between a desired response (i.e., number of enemy kills) and the. system characteristic variables. (i.e.,. weapon. range)..

(19) II.. ANALYSIS METHODOLOGY. The methodology chosen. to. demonstrate this study was to take a case with. expected results, replicate that case in Janus(A), and compare the results. The steps to accomplish this are. to: 1). posit a case with. known. results, 2) select. an. appropriate scenario to analyze the advanced technology, 3) select appropriate input parameters, 4) select appropriate measures of effectiveness, 5) select an effective. and. analysis to. efficient. experimental design, and,. 5). compare the results against the expected. To check the. feasibility of. conduct thorough data results.. using Janus(A), a case. answers are already known. This. will. is. posited where the. enable the analyst to determine. if,. Janus(A) provides expected reasonable results. The case for this study. fact,. the addition of a long range direct. This. is. fire. weapon system. in. is. in a desert scenario.. an important case because the future of advance technologies. toward smaller units capable of destroying the enemy quicker,. is. leaning. at greater. ranges, and with less ammunition.. A.. EXPECTED RESULTS. The expected. results for a long range direct fire. range scenario seem kills.. trivial.. It is. weapon system. in a long. expected that there will be more long range. This will allow the force with the long range weapon to engage and. kill.

(20) the. enemy. first,. keeping the enemy further away for a longer period of time. and thus bring other weapons. to bear. weapon may not increase the Blue overwhelming odds, casualties.. It is. is. it. B.. (TOW). (friendly) Force's survivability against. expected that. will create. it. more Red (enemy). anti-tank. (MBT) and tube-launched. optically tracked wire. weapon system.. SCENARIO. The. (NTC) it. While the long range. expected that the long range weapon will be superior to the. current main battle tank. guided. on the enemy.. actual scenario chosen for the analysis. battle that took place in 1988.. is. a National Training Center. The reason. for using this battle is that. took place on ground where long range. an actual training. battle.. The. visibility is possible.. Also, this. scenario pits a battalion level tank heavy task. force in the defense (Blue Force) against an attacking Motorized Rifle. (Red Force). The scenario was replicated into Janus(A) by [Ref. 13].. A. CPT. brief explanation of the scenario can be found in. The main reason from the author. development of the scenario. Regiment. David Dryer. APPENDIX. for using this scenario is the fact that there are. in the. for the study.. with actual decisions.. Commanders and. The. B.. no biases. Developing. a scenario from scratch could lend itself to tactical and doctrinal errors. scenario actually occurred.. was. This. soldiers influenced the battlefield. scenario begins. converge, and engage in two separate battles.. where the units are separated, For this study, a simulation of.

(21) this scenario. was allowed. to. run until the middle of the. first battle.. This. allowed the collection of data for the long range portion of the battle to. determine the contribution of the long range weapon to the C.. force.. WEAPON SYSTEM CHOSEN. The advanced technological weapon posited in. this scenario is a direct fire,. high velocity, kinetic energy tank gun system with a of 6000 meters. This. maximum. effective range. weapon system would be mounted on an armored. and have the capability on. firing. chassis. an Armor Piercing (AP) round at a velocity. and range greater than that of an existing main battle tank.. The. operational requirement for this. hypothesis that. it is. feasible to develop a. enemy armored systems. weapon system comes from the. weapon system capable. at a greater range. of engaging. than current tanks, and achieve a. greater probability of kill given a hit from the increased velocity of the round.. The Defense. Science Board proposed such an advanced technology in 1984.. The envisioned system armored platform. to. fired a high velocity, kinetic. energy projectile from an. engage enemy targets at ranges up to 6000 meters with. roughly the same probability of hit/kill and armored piercing capabilities of a. main. battle tank. (MBT). at. 3000 meters. [Ref.ll].. Sensors and engagement. systems are assumed to be more advanced than the current main battle tank systems to allow the engagements at such extended ranges.. system. for this. weapon may. The guidance. either be heat seeking, magnetic, or laser guided..

(22) For this study, the system. will. be referred to as a Long Range Tank (LRT).. INPUTS.. D.. There are two types of parameters that were chosen. for this study:. weapon. system parameters and force mix parameters. Weapon system parameters are those weapon system characteristics that are varied throughout the experiment to. determine what. they might have on the response.. effect. Force mix. parameters are force ratios of one weapon system to another. The force ratios used for this study consisted of the number of new systems replacing the old. system divided by the replacement). of a. The. total. number. of old systems initially in the force (before. force ratios are varied, thus replacing different quantities. weapon with the system under. study. This allows the analyst to. measure. the effect of the weapon system in relation to the force mix with another. weapon system.. The input parameters. #LRT/(max #. of. TOWs),. tank opening range, range.. 4). (factors). 2) ratio of. TOW. chosen for this study. #LRT/(max #. opening range, and. 5). MTBs),. to. force. be discussed. advanced technological weapon system characteristic,. 3). 1) ratio. Main. LRT maximum. These were chosen because they represented the. and #2), the opening range issue (#3 and #4,. (#5).. of. are:. of. battle. effective. mix issue (#1 later),. and the. maximum effective range.

(23) A. LRT. into the force structure.. LRT. eliminates the interactive. contribution of the systems together in the force.. Therefore, ratios of the. question arose as to. Replacing. LRTs Also,. to. all. of the. TOWs. how. to put the. TOWs and MTBs with. and. MBTs. random replacement. the. were decided upon as inputs of each. TOW. MBT. and. Each. bias due to positioning in the scenario.. in the experiment.. by the. TOW. LRT removed. MBT. and. any. system had an. equal probability of being replaced, thus positioning and movements for the. LRT were it. predetermined based on the position and movement of the system. These. replace.. factors relate the. number. of. TOWs. and. MBTs. that were. randomly replaced by the LRTs. For each run, a specified number of. and. MBTs were. replaced randomly. This. means that keeping everything. constant (movement routes, firing posture, tactical position,. number. of. TOWs. same replacement. and. MBTs were. switched and. as any other run. This. number generation program distribution) to get a. that used the program. The program can be seen. in. Each weapon system was given a. The. forces. number. APPENDIX line. number. were numbered sequentially from one. 8. the. FORTRAN random. RANNUM. had not been previously. until the required. else. a certain. made LRTs. No run had. was done with a. integer, checked to insure that the integer. selected.. etc.),. (uniform. random number, converted that random number. and repeated the process. TOWs. of integer. into an. selected,. numbers was. E. in the Janus(A) data base.. to the. number. of elements.

(24) For this random replacement, each of the. in the force size.. numbered from the. MBTs. 1. to. 23 (the. initial. were numbered from. 1. number. of. TOWs. to 39 (the initial. The random number generator then. scenario).. integers from a specified range (1-23,. TOW systems were Each of. in the scenario).. number. of. MBTs. selected a desired. in the. number. of. This random replacement. 1-39).. eliminated bias due to positioning. Using this ratio as a parameter provided a. measure of effectiveness of the. LRT. versus the. The longer range. that range matters for this scenario. desirable and. the LRT.. TOW and MBT. for a. It is. expected. weapon. more. is. will. be advantageous to replace the shorter range weapons with. It is also. expected that the longer range weapons will dominate the. it. weaker weapons and therefore, replacement of the weaker weapons survivable) will occur. first.. The maximum opening range. of a. weapon system. is. a parameter that. thought to be sensitive in Janus(A) from previous studies the opening range of a weapon prevents firing at effectiveness). This restriction. shot but would allow the. occur:. [Ref. 2].. maximum. fire.. his position. If a. is. fire. weapon opens. within his fire at its. was. Restricting. range (minimum. would improve the P h and P k values. enemy to engage with. without exposure to return. two things. (less. for a single. maximum range maximum. range,. potentially detectable by the blast of the. weapon, and the small P h and P k values produce a minimal Introducing the opening ranges of the. effect. on the enemy.. TOW and MBT as inputs will hopefully.

(25) The LRT maximum range described above. incorporates both the opening range as. and the maximum. effectiveness of the. weapon system, which. includes the effect of the hyper-velocity kinetic energy round.. the. P h and P k. tables. were not changed from those. for the. The values. MBT. The range. bands associated with the values were altered to represent the effective ranges.. P k and P k 1. in. maximum. Improving the range of the weapon system, while keeping the. values the same, gives better results at the shorter ranges. Figure. graphically portrays the single shot probability of. (solid line) as a function of range.. kill. (SSPk) for the. The dashed and dotted. MBT. lines represent the. SSPk curves for the LRT at maximum effective ranges of 4500 meters and 6000 meters (the center point and Within Janus(A), the. experiment discussed. later).. maximum opening range was changed to coincide with the. P h and P k maximum range E.. axial point for the. band.. MEASURES OF EFFECTIVENESS. A measure. of effectiveness. (MOE). is. a measure of the contribution of a. factor to the overall effectiveness of the force.. (dependent variable) that output. 1.. 2.. The MOEs. Number Number. is. It is. the response variable. a measure to quantify the results of the model. selected for this experiment are:. of red kills of blue kills. MOE #1 gives a measure of destructive capability (lethality) and MOE #2 gives. 10.

(26) — —. mbT LRT. C. CPJ. •••+ 4---. Figure. 1.. RANGE C KN/O SSPk Curve for MBT and LRT.. a measure of survivability.. Both can. easily. be recorded and analyzed. These. allow an analysis to determine which of the previously discussed factors had a significant effect. on both enemy casualties and friendly. The number. MBT, and LRT, but contributors to the. study. is. of. RED. Kills include not only those kills. also artillery kills,. number. survivability.. machine gun. kills, etc.. of red kills other than the. by the. TOW,. While there are. TOW, MBT,. or. LRT,. this. interested in displaying the effect of the parameters on the lethality. of the force as a whole. selection:. keep. it. MOE. #1 obeys the two fundamentals. simple and bigger. direct relationship to the one. the force by replacing the. theme. is. better.. MOE. #2. is. of. MOE. simple and has a. of this study: the survivability effects of. TOW or MBT.. 11.

(27) III.. EXPERIMENTAL DESIGN. Experiments may either confirm knowledge about a system or explore the effect of. new. expected. to. technological. how. conditions of the system [Ref.. confirm. the. operational. weapon system.. to apply force ratios to the. ultimately. are. a. 1:. benefit. p.l].. This experiment. of. proposed. a. is. advanced. Additionally, this experiment will demonstrate. model as parameters. Models such as Janus(A). transformation of a set of inputs (the scenarios and. circumstances of combat) to a set of outputs. Using such a model equates to selecting the inputs. and then "running" the model. to. examine "what happens".. Because this analysis concerns the performance of a weapon which exists only in concept, the exact value of all inputs is not. inputs suggest parametric analysis which. is. known. Uncertainty. express. how. which. will identify. a future technology. model. often considered a problem of. experimental design. In the context of this research, the issue efficient design. in. is. to select. an. the sensitivity of scenario inputs which. weapon performs and how. it is. are questions of performance capabilities and force structure.. used.. These. Performance. capabilities relate to physical characteristics such as rate of fire, range or. weapons, and. ability of sensors to detect targets.. Force structure issues. concern the number and type of weapons which comprise a force along with 12.

(28) information about. how. these weapons are used.. As previously described, Janus(A) incorporates inputs which describe both. weapon performance and is,. force structure composition.. The. issue for analysts. therefore, to select an experimental design which will demonstrate. how well. a force performs given various combinations of these inputs. In this case, the objective. is to. of a future. determine how changes. weapon. will influence. in various. performance characteristics. the overall combat capability of the friendly. force.. A.. EXPERIMENTAL DESIGNS CONSIDERED. A. The. level is a specific value set for the input or. results attained. represent. factors. from several runs of a model. the. output. of. the. model. parameter being analyzed.. at various levels of particular to. changes. of the. factor.. Geometrically, this output characterizes a response surface as a function of. input parameters.. There. is. no reason. to believe that responses are linear,. therefore, at least three levels are chosen for this study. Several experimental. designs are available which provide a methodology to perform this type of analysis.. A few. will. be considered for this study:. and central composite designs. following reasons [Ref. 1.. factorial, fractional factorial,. Factorial designs are important for the. 3: p. 306]:. They require. relatively few runs per factor; and although they are unable to explore fully a wide region in the factor space, they can indicate major trends and so determine a promising direction for further. 13.

(29) experimentation. 2.. They can be. 3.. They form the. suitably. augmented. to. form composite designs.. basis for fractional factorial designs.. These designs and the corresponding fractional designs may be used as building blocks so that the degree of complexity of the finally constructed design can match the sophistication of the problem.. 4.. The interpretation of the observations produced by the designs can proceed largely by using common sense and elementary arithmetic.. 5.. For this experiment, due to time and resources, the interest. main 1.. effects of the inputs. on the. on the response with a manageable number of runs.. Full Factorial Design.. A full and. is. factorial design is. levels are considered.. one where. For. n. levels. all. possible combinations of factors. and k. factors, there are. nk. possible. combinations of experimental runs to consider. For this study, there are factors or inputs.. five. This would require 3 5 = 243 experimental runs to cover. all. combinations. However, time and resource constraints force the consideration of. some type 2.. of reduced factorial design.. Fractional Factorial Design.. A. fractional factorial design is one that considers certain high-order. interactions to be negligible. Therefore, those runs which provide information. about the negligible higher order interactions are eliminated. Thus a fraction of the. full. factorial. design. may be 14. sufficient. to. capture the relevant.

(30) information.. Fractional designs are widely used in screening experiments,. those interested in identifying those factors that have large effects [Ref.. As the goal of. p.325].. this research. is. 1:. to identify such cases, this design. warrants further consideration.. For this experiment, one half of the in. terms of. designs. effort. full factorial. and time (120 experimental. may be more manageable but. runs).. design. is. One. unmanageable. fourth fractional. the loss of some low-order effects. significant. Also, for fractional designs, the interactions that will. may be. may be. be eliminated. significant to this study. Therefore, another fractional factorial design. alternative will be considered and chosen. 3.. Central Composite Design (CCD).. An. alternative to the 3. k. factorial. system. called the central composite design (CCD).. is. a class of composite designs is. greatly used by. workers applying second order response surface techniques. [Ref. 4: p. 126].". The CCD specific. all. is. the 3 k factorial or fractional factorial design augmented with a. number. of axial points.. factor levels set half-way. [Ref. 5: pp. 9-10].". CCD. CCD. is. is. The. center points "are experimental runs with. between their minimum and maximum settings. Axial points are runs with a factor set at. maximum level and the. "This design. all. other factors set at their center point. a five level experimental design.. The preceding. its. minimum. level.. or. Therefore,. discussion of the. a very brief and general overview of a complex class of experimental. 15.

(31) For additional information, the reader. designs.. Response Surface Methodology Experiments. [Ref. 4]. is. encouraged to examine. and Understanding Industrial Designed. [Ref. 5].. The Central Composite Design reduces the number of experimental runs that would be needed. number. is. and 10 replications. significantly less. The CCD can. also. were used. The. a full or fractional factorial design. of experimental runs for this five factor experiment. points, 10 axial points,. This. if. fit. 32 factorial. at the center point [Ref. 4: p. 153].. than the 243 runs required in a. be used to. is 52:. full factorial design.. a second order response surface.. Since. it is. unclear what type of response surface to expect from this experiment, an. estimated response surface must be approximated. The. second order response surface. order effects. This design. is. It. CCD. approximates a. provides information about main and low-. rotatable, meaning:. A design is said to be rotatable when the variance of the estimated response the variance of y, which of course depends on a point of interest xlf - is a function only of the distance from the center of the design and not on the direction [Ref. 4: p. 139].. -. that. x2. ,. ...,. is,. xk. This means that "points in the factor space which are the same distance from the center point (origin) are treated as being equally important [Ref.. The experimental is. design chosen for this study was the. perhaps the most popular. in a second degree. model. class of designs. [Ref. 6: p.32].. 16. 4:. p.165].". CCD. The CCD. used for estimating the coefficients. It is difficult to. physically interpret.

(32) what. is. meant by. third,. fourth,. and,. this. for. experiment,. Assuming those higher order interactions. interactions.. supported use of the CCD. This (third, fourth,. and. is. fifth order). fifth. to be. order. negligible. reasonable because higher order interactions. are difficult to physically interpret and are. confounded in the main and second order interaction. effects.. This. is. reasonable. because models such as Janus(A) are intended to have orthogonal inputs. Also, the statistical techniques involved in response surface methodology are very similar to those associated with simple linear regression analysis. of the objectives for this research effects of a technology. to. were. to design. on a response and then. Recall,. two. an experiment to measure the. to build a. mathematical model. approximate the relationship between the response and the variable inputs.. Use of the objectives.. CCD. and the response surface methodology. Response surface methodology. Chapter V.. 17. will. satisfies. these. be discussed in more detail in.

(33) IV.. CENTRAL COMPOSITE DESIGN EXPERIMENT. This section describes study.. The CCD. is. how. the. CCD. design was implemented for this. a five level experimental design that assumes that higher. order interactions are confounded by the main effects and second order interactions.. The CCD. is. composed of three. the. parts:. full factorial. design at. the radial points (equi-distant from the center of the design), the single runs at each axial point (the. minimum and maximum points. of each factor),. and the. center point (average value component of each factor) replications. Given the. weapon, the scenario, the factors (parameters), and the MOEs, the levels each factor must be determined. The. first. step. is. to build the design, or. for. run. matrix which defines the levels of input parameters used for each run of the simulation.. A.. DESIGN CENTER POINT AND FACTOR RANGES. The experimental. center point (CP) for each factor. maximum and minimum. determined by the experimenter. For this design, the. _MINfa£tor+ MAX ~. 18. determined from the. The ranges. values for that factor.. L,r factor. is. factor. CP. of each factor are. is. defined. as:. Q).

(34) which. is. the midpoint of the range of values considered reasonable for each. The minimum and maximum. factor.. were obviously. set at 0.0. and. replaced for a given ratio. At. while at. 1.0, all. values for the. These. 1.0.. 0.0,. values for the force ratios (Xj and. no. relate to the. TOWs. of elements. replaced by LRTs,. TOW and MBT opening ranges were set at 500 meters. level.. for the. LRT. MBT, 3750 meters. range was determined using the current. range (3000 meters) as. its. This put. The maximum ranges were the AMSAA. values in the data base (3000 meters for the. LRT was. MBTs were. 2). TOWs and MBTs were replaced by LRTs. The minimum. of the. the center point at a reasonable. The CP. or. number. X. minimum opening. for the. TOW).. MBT maximum. range (hypothesizing that the. no worse that the current tank) and the hypothesized. maximum. range of 6000 meters.. The CP for the. CP. for the force ratios. (#LRT/#TOW, #LRT/#MBT). is 0.5.. The CP. TOW and MBT opening range was determined using equation (1).. values for each factor are as follows: CPlrt/tow = O.o CPlrt/mbt = 0.5 cp\1bt range = 1*50. CPtOW RANGE = ^1^5 = 4500 ^"lrt max range. The center. is. defined as (X„. X X X 2,. 3,. 4,. Xg) = (0.5, 0.5, 1750, 2125, 4500).. 19. The.

(35) B.. FACTORIAL COMPONENT OF CCD. Delta. the amount a factor. (6) is. factor portion of the design.. experimental 6. The. levels.. varied around the. is. This. is. CP which. is. the two. necessary to calculate the factor's. following equation. is. used to calculate the appropriate. value for each factor:. _. r. factor-. Alpha. (a) is. point [Ref.. number. MAKfactor-CPfactor _ = -. ^AX. factor' ^factor. (2). 2^78. defined as the distance from the design center point to an axial 5:. p.62]. of factors.. and. is. calculated by the equation (2. For this experiment, a =. (2. 5 1/4 ). k 1/4 ). ,. where k. = 2.378. The. 6. is. the. values for. the factors in this study are as follows: °LRT/TOW. = U.Zl. *LRT/MBT. = O.Zl. 'MBT RANGE. = 526 meters. 5 tow range. = 683 meters = 631 meters. "LRT max range. The preceding. discussion provides the necessary information for determining. the five levels for each factor listed in Table. Determining the. five levels for. the other levels in that each. the. P h and P k. 1.. LRT MAX RANGE was. table. 20. is. different. from. a function of range. Each table.

(36) is. The CCD. divided into five range bands.. range. Each table. maximum. was changed. range (the. levels only consider the. to reflect the appropriate range. minimum. range. is. zero).. maximum. band given the. JANUS(A) uses. a piecewise. continuous function composed of 4 line segments to describe the probabilities of hit. and. kill for. a given. weapon. the range bands are shown in. TABLE. C.. 1.. as a function of range.. APPENDIX. The CCD. levels for. D.. CCD FACTOR LEVELS. MIN. CP-ft. CP. CP+5. MAX. LRT/TOW. 0.0. 0.29. 0.5. 0.71. 1.00. LRT/MBT. 0.0. 0.29. 0.5. 0.71. 1.00. MBTRG TOWRG. 500. 1224. 1750. 2276. 3000. 500. 1442. 2125. 2808. 3750. LRT MAX RG. 3000. 3869. 4500. 5131. 6000. BUILDING THE EXPERIMENTAL RUNS. The number. of experimental runs required for this experimental design. with five factors (k = 5). is. 52 [Ref.. maximum. That. and 10 replications. factorial runs, 10 axial point runs,. axial point is. 4: p. 153].. there are 2 5 = 32. full. at the center point.. An. is,. an experimental run with a factor set at either. level. and. all. its. minimum. other factors set at their center point levels.. or. The 10. center point runs will allow an estimate of the experimental error to be made.. Thus, a check for model adequacy design matrix for this research. is. is. possible [Ref.. located in. 5:. pp.7-62].. APPENDIX. D.. The experimental runs were conducted by manipulating 21. The complete. specific portions.

(37) JANUS(A) data base. The. of the. different force ratios required that individual. weapon systems be replaced by the LRT. This replacement was done randomly for each. run. (as. mentioned previously). This random replacement removed the. bias due to positioning of the system in the force.. A. consequence of this random replacement was that certain key systems. (MBTs, TOWs) were element.. Some. noncombat or. killed. immediately due to poor. of the elements in the actual. tactically. unsound areas due. tactical. placement of the. NTC scenario were positioned in. to mechanical. breakdowns or poor. positioning by the force commander. In any event, certain systems were killed. immediately and others shortly after the battle began at long exposed ranges. If. those elements were picked by the random. by the LRTs, then the contribution have. to include the. The. sound. tactical. number generator. to the survivability of the. to. be replaced. Blue force would. employment of those weapons.. actual manipulation of the data in Janus(A) can be accomplished by. following the instructions in the. JANUS. [Ref. 7: p. 3-1 to 3-25].. 22. Documentation and Users Manual.

(38) V.. DATA ANALYSIS METHODOLOGY AND RESULTS. The methodology used experiment and the data. in. thesis consists of the. this. analysis.. design of the. This chapter contains a description of the. response surface methodology and the data analysis associated with the results of the experiment.. RESPONSE SURFACE METHODOLOGY.. A.. Response surface methodology (RSM) consists of a set of techniques used in the empirical study of relationships. group of input variables. methodology was applied. RSM. was used because:. between one or more responses and a. [Ref.6:p.l].. For this study, response surface. to the results obtained. 1) it. from the. assumes the residual errors. CCD. experiment.. to follow a. normal. distribution (thus permitting simple significance tests to be done), 2) least squares regression techniques allowing a. to. it. uses. mathematical model to be built. approximate the relationship between the response and the variables, and approximates a convex surface in which the optimum operating conditions. 3) it. are. met. (MOE) for this. [Ref.4:p.63].. The. result, or. response. is. the measure of effectiveness. associated with each experimental run. Recall, the two. experiment were the number of. kills.. 23. RED. kills. MOEs. selected. and the number of. BLUE.

(39) Response Surface Methodology (RSM). is. a set of techniques designed to. There are several reasons. find the "best" value of the response [Ref.6:p.l].. choosing. RSM. for. RSM allows one to. as a statistical technique [Ref.2:p.33]. First,. develop a mathematical model to approximate the relationship between a. measurable response and the input variables over a selected region. Second, with RSM,. it is. least effect. on the response. Third,. possible to identify the factors which have the. analysis, specifically the. method. most. effect. and. RSM is very similar to multiple regression. of least squares.. RSM. applies regression. analysis "in an attempt to gain a better understanding of the characteristics of. the response system under study [Ref.6:p.l].". CCD. Lastly, the. type of. experiment and the related response surface methodology results in greater precision. in. estimating the. regression. with. coefficients. a. minimal of. experimental effort [Ref.4:p.l26]. 1.. The Response. The response. is. the measurable quantity whose value. affected by changing the levels of the factors [Ref.6:p.2],. study are the force ratios of. ranges of. MBTs. LRTs. and TOWs, and. to. TOWs. The. "true response,. 77". LRT maximum. range.. The. means the hypothetical value. obtained in the absence of experimental error [Ref.6:p.2].. 24. assumed. to be. factors for this. and MBTs, maximum opening true value of the. response corresponding to any of the 52 experimental runs. The term. is. of. is. rj. denoted by. rj.. that would be. However, error. is.

(40) always present in experiments and the actual value observed for any given. combination of factor levels Recall the. the. MOEs. number 2.. is. Y=. r}. +. where. e,. e. is. the experimental error.. chosen for this experiment are the number of red. of blue. kills. and. kills.. The Response Function. The value. of the response. depends on the levels. r?. X. 1. ,X 2 ,...,X k of k. quantitative factors, f pf 2 >--f k- Therefore, there exists a mathematical function, 0,. of X^Xj,...^, the values of which, for any given combination of factor levels,. provide the corresponding value of. equation. The response. rj.. function. is. (3).. K ,...X. n=<t>(xxy. The response to. function,. <f>,. is. (3). k). 2. called the true response function. be a continuous function of the 3.. given by. X 's. and. is. assumed. [Ref.6:p.2].. ;. The Response Model and Fitted Response Surface. The second order response model. of k factors takes the following. general form:. i = p. +. EPA +. EE. 25. W. +. £ pX. <4).

(41) where the. fy's. are the regression coefficients for the first-degree terms, the. are coefficients for the pure quadratic terms, the. /?jm 's. fa's. are the coefficients for. the cross product terms and the Xs represent the experimental levels of the k factors.. The estimates and parameters The. least squares.. are then obtained using the. predicted response function. is. method. of. given by the following. equation:. t. where the. £. bpCj. b's are estimates of the. estimate values of. The. * +. =. 77. For. further. is. <5). +. /J. parameters. Equation. for given values of. discussion above. technique.. £ £ v^» E bX. X X x,. 2 ,...,. Xk. (5). can be used to. [Ref.6:p.2].. only a general overview of a complex statistical. information. concerning. the. response. surface. methodology, one should refer to Response Surface Methodology [Ref.4] and. How B.. to. Apply Response Surface Methodology. [Ref.6].. RESPONSE SURFACE ANALYSIS AND RESULTS. 1.. Model Response. The 52 experimental runs were executed and the. kills. and. BLUE. package SAS. kills. were tabulated. for each of the runs.. (Statistical Analysis Software). model and the. total. significance of the variables.. 26. was used. number. The. of RED. statistical. to calculate the. fit. of the. The experimental responses. are.

(42) tabulated in Tables 2 and 2.. 4.. The Fitted Response Surface Model. The. statistical. package SAS was used to perform the multiple. regression necessary to build the second order response surface model for both. RED in. Kills. response and. APPENDIX. F.. BLUE. Kills response.. The assumption. The SAS outputs. are displayed. of quadratic response surface allows for the. estimation of 21 model parameters, including the intercept [Ref.5:p.7-65].. 27.

(43) TABLE. RUN. 2.. EXPERIMENTAL RESPONSE RED KILLS -. RUN. RED. RUN. RED. RED. RUN. KILLS. KILLs. KILLs. RED KILLS. 1. 63. 14. 44. 27. 42. 40. 44. 2. 47. 15. 62. 28. 43. 41. 51. 3. 59. 16. 39. 29. 42. 42. 48. 4. 45. 17. 59. 30. 43. 43. 44. 5. 63. 18. 39. 31. 61. 44. 41. 6. 51. 19. 45. 32. 35. 45. 51. 7. 60. 20. 39. 33. 50. 46. 43. 8. 47. 21. 66. 34. 43. 47. 59. 9. 48. 22. 37. 35. 44. 48. 43. 10. 41. 23. 51. 36. 60. 49. 45. 11. 50. 24. 39. 37. 47. 50. 47. 12. 48. 25. 51. 38. 42. 51. 52. 13. 55. 26. 39. 39. 52. 52. 38. 3.. RED. Kills. The. regression analysis for the response. Response Surface Model.. RED. Kills. produced the. following model:. r?. R=. 47.754 + 2.425X + 2.075X 2 -0.125X 3 + 0.475X 4 +5.725X 5 + 0.906X 1 X 2 -. 0.094X. 1. 1. X. 3. -0.594X. 1. X. 4. -0.156X. 1. X 6 + 0.031X X 3 + 1.782X X 4 +1.344X X 2. 2. 2. 6. +. 2 2 2 0.281X3 X4 -1.531X 3 X5 + 0.344X 4 X 5 -0.881X 1 2 + 0.244X 2 + 1.244X 3 -0.006X 4 -. 0.256X5 2. (6). 28.

(44) where X, = #LRTs/#TOWs, X 2 = #LRTs/#MBTs, X 3 = MBT Range, X = TOW 4. Range,. and. coefficients,. X 5 = LRT max. Range.. Table 3 summarizes the estimated. standard error of estimate,. t-ratio,. and p-value. The. and. t-ratio. associated p-value are used to test the null hypothesis that the coefficients (the. are equal to zero against the alternate hypothesis that the coefficients are. /3s). not equal to zero. That. is:. H H If. a coefficient. is. :. a. ft. :. = 0,i =. ^0,1 =. l,2,.... 1,2,.... equal to zero at some significance level, this implies that the. variable associated with that coefficient has no effect on the fitted model. This. hypothesis test. would. reject. H. is. a two-tailed t-test and the significance level. is. established at a level of a = 0.05. Since the test. the significance level becomes (a/2 = 0.025).. The. represents the smallest level of significance,. for. a,. (a) at. is. which one two-tailed,. p-value listed in Table 3. which one would. The. rejection region for this hypothesis test corresponds to any value of. t a/2. The. .. Those. table value of. factors. marked. t. "*". 025. in. with 31 degrees of freedom. is. 1. 1. 1. .. >. approximately 2.04.. Table 3 are significant at a = 0.05.. 29. H. reject.

(45) TABLE. 3.. RED KILLS REGRESSION MODEL SUMMARY.. VARIABLE. COEFF. EST.. STD. DEV.. t-RATIO. p-VALUE. x,. 2.4250. 0.9241. 2.62. 0.0134*. x. 2.0750. 0.9241. 2.25. 0.0320*. -0.1250. 0.9241. -0.14. 0.8933. 4. 0.4750. 0.9241. 0.51. 0.6109. 5. 5.7250. 0.9241. 6.19. 0.0001*. 2. x3 x x x,. 2. -0.8810. 1.0164. -0.87. 0.3927. x. 2. 0.2439. 1.0164. 0.24. 0.8119. 1.2449. 1.0164. 1.22. 0.2302. x x2 4. -0.0060. 1.0164. -0.01. 0.9953. 5. -0.2560. 1.0164. -0.25. 0.8028. XjX 2. 0.9062. 1.0332. 0.88. 0.3872. X1X3. -0.0937. 1.0332. -0.09. 0.9283. XjX 4. -0.5937. 1.0332. -0.57. 0.5697. x,x5. -0.1562. 1.0332. -0.15. 0.8808. XX 2. 3. 0.0312. 1.0332. 0.03. 0.9761. XX. 4. 1.7812. 1.0332. 1.72. 0.0947. 2. X3. 2. 2. 2. XX XX XX xx CONSTANT 2. 5. 1.3437. 1.0332. 1.30. 0.2030. 3. 4. 0.2812. 1.0332. 0.27. 0.7873. 3. 5. -1.5312. 1.0332. -1.48. 0.1484. 4. 5. 0.3437. 1.0332. 0.33. 0.7416. 47.7540. 1.8182. 26.26. 0.0001*. 30.

(46) TABLE. RUN. 4.. EXPERIMENTAL RESPONSE BLUE KILLS -. RUN. BLUE. RUN. BLUE. KILLs. BLUE. RUN. KILLS. KILLs. BLUE KILLS. 1. 55. 14. 60. 27. 60. 40. 64. 2. 65. 15. 57. 28. 67. 41. 56. 3. 54. 16. 60. 29. 58. 42. 61. 4. 60. 17. 56. 30. 58. 43. 62. 5. 56. 18. 62. 31. 62. 44. 63. 6. 60. 19. 63. 32. 73. 45. 60. 7. 54. 20. 60. 33. 60. 46. 58. 8. 60. 21. 69. 34. 63. 47. 57. 9. 61. 22. 67. 35. 64. 48. 64. 10. 65. 23. 59. 36. 54. 49. 62. 11. 54. 24. 62. 37. 57. 50. 59. 12. 58. 25. 56. 38. 60. 51. 59. 13. 58. 26. 63. 39. 59. 52. 64. BLUE. 4.. The. Kills. Response Surface Model.. BLUE. regression analysis for the response. Kills. produced the. following model:. r?. B. = 59. 887-1. 500X -0.100X 2 -0.700X 3 + 0.300X 4 -1.950X 5 -0.312X. 0.875X. 1. 1. X. 3. +. 1. .250X. 1. X. 4. -0.312X. 1. X 5 -0.312X X 2. 3. 1. X. 2. +. + 0.937X 2 X 4 + 0.250X 2 X 5 +. 0.250X 3 X -0.437X 3 X 5 + 0.187X 4 X 5 + 0.544X 2 -0.331X 2 2 + 0.044X 3 2 + 4. 1. 0.044X 4 2 + 0.294X 5 2. (7). where X! = #LRTs/#TOWs, X 2 = #LRTs/#MBTs, X 3 = MBT Range, X 4 = TOW 31.

(47) Range,. and. coefficients,. of. t 0025. X. 5. = LRT. max. Range.. Table 5 summarizes the estimated. standard error of estimate,. with 31 degrees of freedom. is. t-ratio,. and p-value. The table value. the same as the. approximately 2.04. Again, those factors marked at a = 0.05.. 32. "*". RED. in. Kills. model and. is. Table 3 are significant.

(48) TABLE. 5.. BLUE KILLS REGRESSION MODEL SUMMARY.. VARIABLE x x. COEFF. EST.. STD. DEV.. t-RATIO. p-VALUE. -1.5000. 0.5626. -2.67. 0.0121*. -0.1000. 0.5626. -0.18. 0.8601. x3. -0.7000. 0.5626. -1.24. 0.2228. x x5. 0.3000. 0.5626. 0.53. 0.5977. -1.9500. 0.5626. -3.47. 0.0016*. 1. 2. 4. x,. 2. 0.5443. 0.6188. 0.88. 0.3858. x. 2. -0.3306. 0.6188. -0.53. 0.5969. X3 2. 0.0443. 0.6188. 0.07. 0.9433. x x. 2. 0.0443. 0.6188. 0.07. 0.9433. 2. 0.2940. 0.6188. 0.48. 0.6376. XjX 2. -0.3125. 0.6290. -0.50. 0.6228. XjX 3. 0.8750. 0.6290. 1.39. 0.1741. xx. 1.2500. 0.6290. 1.99. 0.0558. x,x 5. -0.3125. 0.6290. -0.50. 0.6228. X X3. -0.3125. 0.6290. -0.50. 0.6228. XX 2. 4. 0.9375. 0.6290. 1.49. 0.1462. XX 2. 5. 0.2500. 0.6290. 0.40. 0.6938. XX 3. 4. 0.2500. 0.6290. 0.40. 0.6938. XX 3. 5. -0.4375. 0.6290. -0.70. 0.4919. xx. 5. 0.1875. 0.6290. 0.30. 0.7676. 59.8871. 1.2069. 54.10. 0.0001*. 2. 4. 5. x. 4. 2. 4. CONSTANT. 33.

(49) 5.. Analysis of Variance. -. Red. Kills.. For multiple regression, the analysis of variance. is. a technique that. is. used to partition the variance and to compare models that include different sets. The output provided from the SAS. of variables [Ref.8:p.48].. (AN OVA). The. analysis of variance table. experiment. TABLE. The. 6.. is. AN OVA table. corresponding to this. presented in Table 6 below.. ANALYSIS OF VARIANCE TABLE RED KILLS -. SOURCE. DF. SS. MS. F-VALUE. p-VALUE. REGRESSION. 20. 2189.69. 109.48. 3.55. 0.0008. ERROR. 31. 955.29. 30.81. TOTAL. 51. 3144.98. total variation in the data is called the "total. computed by adding the sum of squares due. sum. includes an. sum. to the regression (SSR). of squares of the residuals (SSE) [Ref.6:p.l0].. associated with the. SST. observations (N = 52). is. freedom. for the. the. The F. SSE. N-l,. where. The degrees. number. where n. is. is. N. is. of squares", SST, and. the total. The degrees number. model. and the. of freedom. of experimental. of freedom associated with the. of terms in the fitted. is. SSR. is n-l,. The degrees. (n = 21).. of. N-n = 31.. statistic is. used to test the null hypothesis (H. ). that the fitted. response surface model does not have a significant effect on the measured. 34.

(50) F. The. response.. —. a. alternate hypothesis (H a ). have a significant. is. mean square. The value. of. =. l/~/.i. = 0.05).. If. mean square. F Model. is. —. Mean Square Regression — — z Mean Square Residuals. —n. compared. then the null hypothesis (a. The F model. statistic is. of the regression and. of the residuals (as follows) [Ref.6:p. 11].. _,. P. that the fitted surface model does. on the measure response.. effect. calculated using values associated with the. the. -. F Model <. n .!. Nn. is. ,. the a level of significance.. =. —. SSRf(n-l). /C y&> v. SSEjiN-n). to the table value. F n 1Nna .. If. .. F Model >F nlN na .. ,. rejected at a reasonable level of significance. then the one. The. fails to reject. table value for. the null hypothesis at. F 2031005. RED. 1.92 for the. is. Kills.. 6.. Analysis of Variance. The The degrees value of. of freedom for the. F Model. is. Kills.. BLUE. Kills is. BLUE. is. >. The. Kills is. shown. the same as the. again compared to the table value. < F n .i,N-n. a then the one. significance.. BLUE. analysis of variance table for the. then the null hypothesis ^Modei. -. F n 1Nna .. .. RED. If. in. Table. The. Kills.. FModel >Fn 1N na .. rejected at the a level of significance (a = 0.05). fails to reject. table value for. F 2031005. 35. 7.. _. ,. If. the null hypothesis at the a level of is. 1.92 for the. BLUE. Kills..

(51) TABLE. 7.. ANALYSIS OF VARIANCE TABLE BLUE KILLS -. SOURCE. DF. SS. MS. F-VALUE. p-VALUE. REGRESSION. 20. 405.27. 20.26. 1.60. 0.1167. ERROR. 31. 392.50. 12.66. TOTAL. 51. 797.77. 7.. Analysis of Results, a.. RED The. hypothesis (H. ). Kills. regression model and the. AN OVA table. indicate that the null. that the fitted model does not have a significant effect can be. rejected (3.55 > 1.92). fitted. Model.. Therefore, the alternate hypothesis. model does have an. effect. is. accepted that the. on the response at a level of significance.. Further investigation of the regression results indicate that most of the estimated coefficients. may be. zero.. If. the values of. |t|. >. t a/2 for. estimated coefficient, then the null hypothesis that the coefficient. be rejected at a. Also, the p-values for the. level of significance.. variables are so large that. H. will. The. never be rejected.. is. each. zero can. remaining. variables not. associated with the zero coefficients (see asterisks in Table 3) and for which is. rejected are:. X (#LRT/#TOW), X (#LRT/#MBT), X (LRT max 2. 1. 5. H. range),. and the constant. This does not mean that the other variables do not influence the results, rather, there. is. not sufficient evidence to provide accurate. estimates of their effects [Ref.6:p.l2]. These three variables are. 36. all. associated.

(52) with the. LRT. (force ratio. BLUE. b.. For the. Kills. BLUE does. RED. force. BLUE. Using the. Kills. not. Model.. BLUE kills model, it was expected that the blue force would. be killed due to the attacking. and range).. significant. F Model = 1.60). Therefore, there fitted. model has no. effect. null hypothesis. cannot be. effect. (H. force. ANOVA. regression model and the. model indicate that the. have a. BLUE. outnumbering the. ). RED. and. table for the. that the fitted model. rejected. (F 2031a = 1.92. >. no evidence to reject the hypothesis that the. is. on the response at 11.67%. level of significance.. Further investigation of this regression model also indicates that most of the estimated coefficients. may be. zero.. If. the value of. |t|. >. t a/2. each. for. estimated coefficient, then the null hypothesis that the estimated coefficient is. zero can be rejected at the. is 2.01.. (a) level. Also, the p-values for the. of significance.. The. table value of. t 48. H. remaining variables are so large that. 025. will. never be rejected. The variables not associated with the zero coefficients (see asterisks in Table 5). and. for. (#LRT/#TOW), X5 (LRT max. H. which. range),. is. rejected (|t|. >. 2.01). are:. Xj. and the constant. This does not mean. that the other variables do not influence the results, rather, there. is. not. sufficient evidence to provide accurate estimates of their effects [Ref.6:p.l2].. Recall, this. model. is. based on the number of. BLUE. Kills response.. It is. desirable to keep the response as small as possible (survivability). Therefore,. 37.

(53) it is. hoped that the impact of the. The. response variable.. sign. coefficients contribute to decreasing the. of the. significant. supporting the previous statement. As a a. TOW,. the response. those factors.. LRT. is. coefficients. decreased through the negativity of the coefficient for. is. This indicates that. the. number. LRT/TOW. it is. better to replace the. the LRT.. of. BLUE. it is. better to replace the. number. Increasing the. negatively the. Also, the. kills.. number. of. BLUE. of. LRTs. Kills. TOW first. to the. magnitude of the. ratio is smaller (larger negative). This indicates that. negative,. added to the force replacing. more vulnerable weapon system) but adding more LRTs decrease the. is. than the. system. (the will. coefficient for. LRT/MBT. ratio.. TOW first and then the MBT with that replace the. TOW. increases. more than replacing the MBTs with. LRTs. C.. CONCLUSIONS. The. is. results. from the. RED. Kills. model indicate that the regression model. a fairly good predictor of the response variable.. influence the variation in the response are the. Max Range.. LRT. The key parameters. that. and the. LRT. force ratios. This agrees with what one would instinctively believe. a longer range weapon.. Since the regression equation. convex. Therefore there exist an extreme point.. is. when given. second order,. it is. The nonlinear program solver. General Algebraic Modelling System (GAMS) was used to maximize the regression equation.. The. result indicated that the. 38. model. is. maximized. at the.

(54) upper endpoints. JANUS(A). is. (all. variables set at their. were. all positive.. raising the factor level for the force ratios or the. larger than. Xv. RED. This indicates that. contribute to the destructive capability of the. Also, the significant coefficients. response (number of. level).. and that a longer range weapon system. sensitive to opening range. (in this terrain) will significantly. force.. maximum. kills).. The magnitude. This indicates that. it is. more. TOW (the weaker weapon) then the MBT.. LRT. This indicates that. range will increase the. of the coefficient for. X was 2. beneficial to first replace the. All of these results agree. with the. answers posited prior to conducting this experiment and support the hypothesis that the longer the range of a. weapon system and the number. of those systems. in the force, the larger the contribution to the destructive capability of the force.. The model. results. is. from the. not as good a. sufficient as a basis. are those expected.. X. 5. fit. BLUE. Kills. model were. also as posited.. to the variation in the response. and therefore not. from which to draw conclusions, the significant. The model. While the. coefficients. indicates that the non-zero coefficients X, and. contribute negatively to the response variation. Recalling that the desired. response for this model that as X! and decreases).. paper:. X. 5. is. as small as possible (# of Blue Kills), this indicates. increase, the response decreases (the. number. of. BLUE. kills. This coincides with what was posited at the beginning of this. that the addition of a long range. 39. weapon system. will increase the.

(55) One. survivability of the. owning. force.. model may be due. to the. random replacement. MBTs. (as. that. D.. in. Chapter. more LRTs are entered. that as force. mentioned. III).. possible reason for the of the. the. LRTs were. for. TOWs. Another possible explanation. and. for this is. into the force, the detectability of the Blue. by the Red force increases, thus exposing them if. LRTs. bad regression. to. enemy fire sooner than. not in the force.. FURTHER TESTING AND ANALYSIS. In order to determine possible reasons for the lack of the. regression to model the response, a follow-on experiment this experiment, a. more. traditional. BLUE. Kills. was conducted. For. method was chosen, and ten. additional. Janus(A) runs were made. The values for each of the variables were fixed at. what was. felt. might be the most reasonable settings. The. into the scenario (no variation in the factors).. their center point, while the. The. MBT. if. this. system was inserted. force ratios. were. set at. TOW and LRT were set at their maximum ranges.. opening range was set at. its. upper radial point. This configuration. was chosen because the P h and P k values. for the. MBT. decrease rapidly at the. maximum range and it was felt that realistically, MBT gunners do not open fire at their. maximum. range, but wait to get. Also, these are the values. and gunners get. more. efficient shots at the. where the P h and P k values begin. effective shots at long ranges.. influential values indicated in. Chapter. 40. I.. enemy.. to drop off rapidly. These are the posited. Therefore, the values of the.

(56) parameters were. shown. TABLE. in. 8.. Table. (Xj = 0,. X. 2. = 0,. X. 3. =. 1. X. ,. 4. X 5 = 2). The results. = 2,. of the runs are. 8.. RESULTS OF ADDITIONAL RUNS.. RUN. RED KILLS. BLUE KILLS. RUN. RED KILLS. BLUE KILLS. 53. 51. 55. 58. 51. 59. 54. 64. 55. 59. 56. 57. 55. 64. 56. 60. 61. 58. 56. 54. 43. 61. 76. 54. 57. 66. 53. 62. 63. 50. For these runs, as in the. first. 52 runs, the replacements were done randomly. for each run.. To study the. number. effects of range. of kills by. on both the. weapon system was. box plot graphs were developed: one plotting the. each. BLUE. number. of. RED. for. RED. Kills. and. BLUE. plotted in 500 meter range bands.. each. Kills versus. system plotting the number of. the. LRT. and the number of LRTs scored most of. apparent that the ranges. This. RED. means. killed. its kills at. BLUE. that having a. by. number. RED. system versus. Kills of that. of. systems.. 7).. RED It is. kills. LRT. 41. LRTs. at the. RED. force's. in one's force will kill. scored by. apparent that. the longer ranges (5-6 kms).. force killed the. Six. 500 meter range bands and one for. Figures 2 and 3 depict the LRT, both the. LRT. the. BLUE system (LRT, TOW, MBT). the range bands in which they were killed (Figures 2 through. the. Kills,. It is also. maximum. more enemy. at.

(57) 4. 22. t. i. i. r. i. r. 1. -i. t. 1. r. 1. _. JL. 20 18 16 14. 12. lO "T" B 6. 2. D. RANGE BANDS Ckms^. Figure. 2.. LRT. 1. 500 meter Range Bands.. Kills in. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. -. -T. ,. J. i I. T. ------. _. ::::i:: 1. i. D-. i. SO. SO-1. i. 4-1.3. i. 1. i. .3-3. »-3 3. I. .3-J. ::... i. »-3 3. i. .. 3-. -4—4. RANGE BANDS CKmsD. Figure. 3.. LRTs. Killed in 500 meter. 42. Range Bands.. i. .. 3.

(58) greater ranges but. maximum. RED. also attract. more enemy. The LRT's long range. ranges.. who then. force,. will. it. return. of. MBTs. did most of. at the. enemy's. exposes their positions to the. fire.. Figures 4 and 5 are box plots of the. number. fire. fire. kills. scored by the. MBT. and the. by range bands. These figures indicate that the. killed. its killing at. MBT. the longer ranges with the main tank round. But, at. the shorter ranges, where the alternate weapon (machine gun) might be more. weapon was,. practical, the alternate. killed. by the. possible time. RED -. the. force, again. maximum. the. in fact, used.. For the number of. enemy engages the MBTs. MBTs. at the earliest. range of their weapons.. Figures 6 and 7 depict the same information as discussed above for the. TOW. The. significant point here is that the. of kills that the impact of this. TOW scored such a small amount. weapon can hardly be evaluated. The. its. antitank weapon to engage targets at the longer ranges and. to. engage targets at the shorter ranges. With such few. force. TOWs. and the discrete values of the number of TOWs, the. number. of. TOWs. killed. Positioning of the. by the. RED. its. weapon systems. the. greatly affected the probability of the. make. is. what. initially in. force cannot be evaluated.. in the battle, at close or far ranges.. difficult to tell. machine gun. significance of the. systems being killed early on it. TOW uses. going on with the addition of the. that the weapons on both sides attempt to. 43. kill. These graphs. LRTs. except. targets at the greater ranges..

(59) ^. 7. —. 5. h. LU cr. —. o. _L. _L. J_. _L. O- .50. 5 0-11-1 .51 .5-2 2-2.52. 5-3 3-3. 53. 5-4. RANGE BANDS C^^sD. Figure. 4.. 1. MBT Kills in 500 meter Range Bands.. 1. 1. 7. B. LU. 3. ^Z 10 fc-. cn. 2 O. 9. uu. z. 1. 1. O- 3d. 1. SO-1. 1. -»-1.3. 1. I. 0-2 3. 1.3-B. I. I. H.3-3. 3-3.9. I. S.3-*. I. •^•i.S. RANGE BANDS CKms). Figure. 5.. MBTs. Killed in 500 meter. 44. Range Bands.. l.

(60) UJ Li. i-i3. 30-1. o- 90. 1. 05-3. a-» 3. a-a. 3-13. 3 3-1. RANGE BANDS CKrns^. Figure. s. —. «. —. 6.. TOW Kills in 500 meter Range Bands. —. —. i-. Q LU. —. r. -r. .30-1. 1-13. •. •. o. O- 3D. 13- 8. 8-33. B3-1. »- 3 3. J3-1. -^-13. RANGE BANDS CK^IS}. Figure. 7.. TOWs. Killed in 500 meter. 45. Range Bands.. —.

(61) The. what was. results depicted. and what the. intuitively suspected. CCD. experiment depicted: that range matters in this scenario.. The other. intuitive result. from this additional research. is. that the. more. long range weapons in a force, the larger the contribution to the destructive capability of that force.. The LRT comprised 50%. of the Blue force, while the. TOW and MBT comprised 18% and 32%, respectively. of the Blue systems to the total. LRT, TOW, MBT.. respectively, for the. dominate system,. in. Two. in the force. This does not. killing.. results agree with the. a system. likelihood of. Red. Kills. it. was 71%, 9%, and 21%,. This indicates only that the most. CCD. than any other system. that the. LRTs. will. is,. this additional. so they do. most of. experiment are that:. 1). the. experiment that range matters both to the. be fired upon and. if it is. -. killing.. are "best" overall.. and the destructive capability of the. exposed to the enemy. how good. mean. drawn from. conclusions. survivability. of. contribution by each. term of total number of systems, does most of the. There are more LRTs the. number. The. killed.. force,. and. 2). a system. This means that no matter. positioned in a tactically unsound area, the. contributing to the overall force. 46. is. small..

(62) V.. A.. CONCLUSIONS AND RECOMMENDATIONS.. CONCLUSIONS. The. results of this study demonstrated that the. effective experimental design in the analysis of. Janus(A).. CCD. is. efficient. and. advanced technologies using. Reducing the number of experimental runs while. statistical significance of. an. still. gaining the. the main and second order effects allows the analyst. to obtain the important data without a large. number. of experimental runs.. For this study and the advanced technology chosen to demonstrate using Janus(A) and the CCD, the results were encouraging. In almost every respect, the Janus(A) results were those expected for this scenario. analysis. and. ANOVA. weapon system effect of the. greatly improves the destructive capability of the force.. LRT. on the survivability of the. of the. fact,. The LRT and. MBT. survivability. and TOW.. its. BLUE. force. TOW, and maybe. the. obsolete for this scenario. available.. regression. indicated that the addition of a long range direct fire. This study showed that, in. may be. The. if. this. was not. The. as evident.. the main battle tank,. advanced technological system was. long range capability clearly dominated the effects. The. was unclear due. results indicated that the impact on the blue to the. overwhelming red force and the. fact that. the scenario was not run through the end of the battle. However, the addition 47.

(63) weapon system may decrease the number. of a long range direct fire. of blue. systems killed in this scenario.. Another result from. this study. was that using. force ratio as a factor in the. experiment allowed the analysis of an optimal force mix the analytical results of the this scenario. was found. scenario, replacing in. terms of number of. to pick out the. upper end points of the design.. at the. RED. TOWs and MBTs with LRTs gave kills.. Use. weaker system, both. survivability.. The. therefore the. TOW,. entirely in both the. From. CCD and response surface, an optimal force mix for. of the. all. for the scenario.. scenario. was. For this. the best results. of these force ratios enabled the in. model. terms of destructive capability and. ideal for a long range. armored. vehicle,. the short ranged, lightly armored system, was replaced. RED. Kills. model and the. BLUE. Kills. model.. Given the results observed by this analysis, Janus(A). may be an. appropriate simulation model to study the influence of advanced technological. weapons on. battle outcomes. It. and as a data. collector.. was easy. Using the. to use, both as. CCD. an experimental. enabled a manageable number of. experimental runs to be made during a short period of time. surface methodology. most and. was very. least effect. effective in identifying the factors. on the responses.. expected outcome of this study.. 48. tool. The. The response which had the. results supported the initially.

(64) B.. RECOMMENDATIONS. Several recommendations are presented stemming from problems and. discoveries learned by the author.. Army, more people. will learn. As Janus(A) comes. more about. it.. to. wider uses. in. the. use has not yet been. Its entire. explored. It is. recommended. Janus(A). be. that further studies of advanced technologies using. Studies. conducted.. involving. the. themselves as the isolated factors should be done.. weapon. characteristics. In particular, follow-up. studies of the propulsion system and target sensors on a long range direct fire. system are warranted.. problems with aiming. Aiming a weapon. errors.. The type and. at greater. characteristics of the propulsion of. a round to great ranges at high velocities. These problems may be analyzed. in. ranges poses possible. may. also pose physical problems.. Janus(A) early on to get an indication of. the magnitude of the effect in a force on force scenario.. This study considered only one scenario. this. weapon, the LRT,. abundant.. in a. wooded type. A follow-up study should consider. terrain,. where long ranges are not. Consideration for the type of mission given the force would also. warrant further study. This study considered the defensive mission given the. BLUE. force.. Both of these variations are of importance when considering a. weapon system the. LRT. for further. development.. If all. the world were. might be the answer, but, with various. 49. flat. and open,. terrains, various missions,.

(65) weapon systems, the. various mixes of other. recommended. that further studies of this. results. weapon. would be. different.. It is. in different scenarios be. conducted. Finally,. it is. evident that the. experimental design.. It is. CCD. is. recommended. an extremely that the. CCD. efficient. and. effective. and response surface. methodology be used more often when time and resources prevent replicated full factorial designs.. gained through a. The. fairly. benefit of the. small. number. CCD. is. the amount of information. of experimental runs.. 50.

(66) APPENDIX A: ANALYSIS FRAMEWORK. This appendix describes in general terms the Analysis Framework shown in Figure 8.. While this framework can be applied. to almost. any simulation. model, JANUS(A), was the simulation model used for this thesis.. A.. BACKGROUND. JANUS. is. an interactive, two-sided,. wargaming simulation featuring versions.. One, developed. closed, stochastic,. precise color graphics.. for. Command (TRAC). at. comes. in several. a nuclear effects modelling simulation by. initially as. the Lawrence Livermore National Laboratory, Analysis. It. ground combat,. is. called. TRADOC. JANUS(L).. White Sands Missile Range developed a version. Army combat development needs. of JANUS(L) developed for the. Army. called. JANUS(T). JANUS(A). for use in. is. a version. both combat development and. training communities. Interactive refers to the interplay. between the military analysts who. decide what to do in crucial situations during simulated combat and the system. that models that combat. Two-sided refers to the two opposing forces directed. simultaneously by two sets of players.. Closed means that the actions of the. opposing side are relatively unknown to each other.. way the system determines the. Stochastic refers to the. results of actions like direct fire engagements,. 51.

(67) Input. Process. Output Justification o(. Operational. Need & Relationship to Threat. Doctrine. Design. System Configuration Alternatives. System Performance & Capabilities. Compare and Analyze. System Trade-offs. Required Capabilities. System Characteristics &Performance Envelope Employment Concept. Figure. 8.. Analysis. Framework for the study of Advanced Technologies.. 52.

(68) i.e.,. according to the laws of probability and chance.. battle. is. on the ground maneuver and. The. but JANUS(A). artillery units,. model weather conditions, day and night. visibility,. employment and breaching, rotary and. fixed. principal focus of the is. able to. engineer support, minefield. wing. aircraft, resupply,. and a. chemical environment. The simulation uses digitized terrain developed by the. Defense Mapping Agency and displays vegetation, and urban areas. visibility. with contour. it. lines, roads, rivers,. Additionally, the terrain realistically affects. and movement.. A decision was made to use JANUS(A) as a research tool for the Operations Research Center (ORCEN) and as a teaching tool for cadets at. JANUS(A). currently used to evaluate. is. classroom environment. analytical. tool. established,. for. The. realistic. it is felt. intention. is. new. USMA.. potential technologies in a. to use. JANUS(A). as an actual. With a methodology. advanced technologies.. that the results of an analysis could be used as input into. the decision making process for further research or procurement.. B.. APPROACH. The. Analysis. Framework shown. in. Figure. 8. forms the basis. for. incorporating inputs, processes, and outputs into a detailed, step-by-step process.. The. final. characteristics. output would be a report of the required capabilities, system. and performance envelope, and the employment concept. advanced technology being studied.. 53. for the.

(69) The. initial. step in this analysis. is. to. determine the operational need, the. There may be. motivation for development of an advanced technology. doctrinal, operational, organizational, or mission. threat that requires a material response. operational advantage held by the. the threat. is. Army. An or. exploitation of a technological or. some. also valid justification of a need.. earlier) are the agencies. which may have. changes or a newly recognized. vulnerability existing within. TRADOC. this information.. and. AMC. With. (defined. this in mind,. the analysis will be guided toward satisfying the operational need rather than the success of the technology.. Along with the operational need, the analyst definitions. of. advanced technological. will. need. approaches.. have the. to. These. provide. information on the material options available to address a capability shortfall or. enhancement opportunity that supports the operational need.. These. advanced technological approaches provide the analyst with the desired technologies in terms of relationships between system performance (range, reliability,. endurance,. lethality,. survivability,. etc.),. system. physical. characteristics (weight, size, ease of maintenance, etc.), cost, schedule for availability, supportability factors,. to note that the. and technical. risk [Ref.10].. It is. important. performance data must be available for the analyst before. proceeding with this methodology.. These advanced technologies must be. engineered and tested rather than experimental. Preferred documentation will. 54.

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