a combat model adaptablefor evaluating the ... · table 1 gives the target hit recorded in exercise...

International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: [email protected]

Volume 3, Issue 11, November 2014 ISSN 2319 - 4847

Volume 3, Issue 11, November 2014 0

ABSTRACT Complexity of military combat modeling is being highlighted by a review using Lanchester equations in order to determine damage/coverage of weapon. This in turn was used as a measure of capability/implementability. Some concepts in reliability have been adopted and applied to a class of problems found in a system whose component items have chain link. The proportion of available logistics items needed to execute projects/programmeswas used,in recent application concept, to obtain the Availability Capability (AC) via reliability, and the Implementability or Delivery Capability (Damage Coverage) (DC) via mean Time To Failure (MTTF). A military formation, DC was found to be 30.9, which yielded Percentage implementability. Keywords:- Projects, Reliability, Mean Time to Failure, Implementability, Availability, Delivery, Damage, Capability, Coverage, Logistics.

1.INTRODUCTION The modeling and analysis of military combat using differential equations (DE) were rigorously, and exhaustively handled by Taylor (1973), (1974) and (1975). Some of the results obtained are being given below. 1. Lanchester Fundamental Duel (One-on-One) Deterministic Linear (Ancient) Law DE:

=-r , = b ; is the Blue strength or forcelevel. = - b, = r, is the Red strength or force level. =-r , = b ; is the Blue strength or force level. = - b, = r, is the Red strength or force level.

Where b is number of Blue units remaining at time t ( at t = 0, b = B) r = is number of Red units remaining at time t ( at t = 0, r = R) is the rate at which single Blue unit Kills Red units. is the rate at which single Red unit kills Blue units. The time independent solution of this system, Taylor (Taylor J, 1974) is given by ( B2 – b2) = (R2 – r2) If is the Blue attrition rate of single round (bullet), and is rate of fire of each weapon then the overall Blue attrition rate = , and similarly for Red = Using the Principle of War based on (encourages) “Rapid Fire or High Attrition” the optional solutions, Taylor [13] are given by a. - Blue Force wires b. - Red Force wires c. - Parity (No Victor No Vanquished). The time dependent solutions are:

a. b = B cosh

b. r = r cosh

2. Lanchester Indirect Fire (Combinatories) Deterministic Square (Modern) Warfare Law DE:

=- = is Blue Kill rate

=- , = is Red Kill rate

Where Ar, Ab = areas where Red and Blue forces are located respectively. Aer ,Aeb = areas of effectiveness of a single shot from Red and Blue respectively. fr, fb = rates of fire of Red and Blue weapons respectively.

A COMBAT MODEL ADAPTABLEFOR EVALUATING THE IMPLEMENTABILITY

OF PROJECTS AND PROGRAMMES

Navy Captain MO Oladejo

Department of Mathematics, NDA, Kaduna



Volume 3, Issue 11, November 2014 Page 11

The notion of square is derived from the dependence on the squares of the quantities (ORBAT/Logistics) or distribution of fire over the areas. The solution obtained by this square law is based on the Principle of War “Concentration of Force”. The time independent solution of this system, Taylor (1974) is given by Kb (B – b) = Kr (R – r) At the instance of supporting fire units, e.g. Artillery , the DE describing the engagements are:

= - (1 - ) - r

= - - r

= - (1 - ) - b1

= - - b1 = no of Blue, Red Infantry units remaining at time t, = no of Blue, Red Artillery units remaining at time t,

Kxy = Kill rate of side with x units when engaging the opposing force of y units. The solutions to these non deterministic square law DE, are numerous due to the range of , and various combinations of attrition rates and force levels of contending forces. This research looked at combat modeling devoid of DE approach, which has been exhaustively dealt with by JG Taylor. Output evaluations are numerous and varied depending on the target, Taylor (1973), Taylor (1974)b just like comparison of availability of brakelights, Asalor (1984), manpower planning, Bartholomew (1991), forecasting applications Da lurgio (1988), applications in probability, Feller (1957), industrial engineering applications, Haribaskaran (2005). Feasibility studies have been conducted to determine viability of projects and programmes, Theoretical Development, Oladejo and Ovuworie, (2006), Theoretical Development, Oladejo (1995), Theoretical Development and Application, Oladejo, (2008). The success or implementability of programmes and projects are being tackled using some models that have not included percentages or proportions as inputs, as is the case in the reliability model that uses hazard/failure rates, to get output as delivery capability based on the proportions of available logistics. Proportions are here being considered and used instead of reliability, reliability and life testing, Barlor and Proschan, (1975), control and simulation, Edward and Lees, |(1973). The proportion of each item is taken as its reliability. The overall reliability of the system is obtained and is called Availability Capability (AC). In this work, the computed MTTF are called and used as the Implementability of project/programmes, reliability and life testing Barlor and Proschan, (1975), energy projection, Gregoria, (1979), reliability testing, Oroge (1991). This recent application concept has been extended to determine the Delivery Capability (DC) which was used to obtain Implementability. In the illustrative example using military formation, the DC was used as the evaluated Damage Capability (DC) of the formation weapon system. This damage capability was calculated and used to determine the Implementability of the task/project.

2.METHODOLOGY Using reliability theory and Spectral analysis models were derived for forecasting damage coverage (delivery capability) and hence determine implementability of chosen project. Number Cruncher Statistical (NCS) package was used to obtain Fourier Analysis Model using derived coefficients an and bn that are significant. Thereafter, used these models to forecast output, damage coverage, and ultimately the implementability of project/programs. For every component item calculate the proportion p, and the percentage of the items available, then compute the various Availability Capability (AC) and then the Fourier Analysis and Regression models would be derived for forecasting target hit and damage outcomes. The result obtained would be used to determine the delivery capability/Implementability. Availability Capacity Series system:

AC = =

, where t, time to failure is exponentially distributed. Parallel system:

AC =

=

components have same reliability = 1- [1 – e-t]n, constant failure rates




Delivery Capability Series system: DC

where ao = 2 mean value of f() (Observed values) an = 2 mean value of f() Cos n bn = 2 mean value of f() Sin n the computed values are on Table 2. Let Probability Density Function (Pdf) of Soldiers/riffles for the Ex be SRS i.e. Discrete Uniform. The mapping involved is bijective, since the correspondences between the sets of soldiers/Riffle F are injective and surjective. Then the PDF of Fourier forecast values is also discrete uniform. Definition: The Damage Coverage Capability Implementability I = F/n, is the corresponding value obtained by calculating the discrete uniform pdf of the Fourier predicted value. The value obtained should be x 100% to get the % of forecast observation implementable. Applications 1. Shooting Range Exercise Table 1 gives the target hit recorded in Exercise Marksmanship (a soldier fires shots from a riffle at a stationary calibrated target) and the calculated damages with their corresponding Fourier series values that can be used to forecast.

Table 1. Coefficient of Derived Model of Soldier/weapon range classification (Single Firer) SN Sld/Riffle Tgthit

s X r R w Iw 0 Dw F1 I Ip

1 NDA1/R1 15 0.50 0.615 0.3075 4.61250 12 3.622649 2 NDA2/R2 4 0.133 0.160 0.02128 0.08512 24 0.066853 3 NDA3/R3 20 0.667 0.699 0.44622 8.92446 36 7.009254 4 13 0.433 0.099 0.04287 0.55727 48 0.437679 5 9 0.300 0.942 0.2826 2.5434 60 1.997582 6 11 0.367 0.827 0.30351 3.33860 72 2.62213 7 23 0.767 0.625 0.47938 11.025625 84 8.659506 8 19 0.633 0.396 0.25067 4.76269 96 3.740608 9 6 0.200 0.118 0.0236 0.1416 108 0.111212 10 NN01/R11 5 0.167 0.064 0.0107 0.0534 120 0.04194 11 NN02/R12 27 0.900 0.756 0.6804 18.3708 132 14.42839 12 8 0.267 0.394 0.1052 0.8416 144 0.660991 13 25 0.833 0.066 0.0550 1.3745 156 1.07953 14 16 0.533 0.214 0.1141 1.8250 168 1.433352 15 10 0.333 0.922 0.3070 3.0703 180 2.411408 16 NN01/R21 14 0.467 0.206 0.0962 1.3468 192 1.057774 17 17 12 0.400 0.749 0.2996 3.5952 204 2.823663 18 18 22 0.733 0.228 0.1672 3.6784 216 2.889009 19 19 19 0.633 0.261 0.1652 3.1391 226 2.465443 20 NN10/R20 3 0.1000 0.025 0.0025 0.0075 240 0.00589 21 NAF011/R21 6 0.2000 0.968 0.1930 1.1580 252 0.909491 22 NAF02/R22 7 0.233 0.265 0.0618 0.4328 264 0.33992 23 23 26 0.8670 0.096 0.0832 2.1648 276 1.70023 24 24 15 0.5000 0.267 0.1335 2.0025 288 1.57276 25 19 0.6330 0.154 0.0975 1.8522 300 1.454714




26 NAF10/R30 9 0.3000 0.557 0.1671 1.5039 312 1.18116 27 NDAn/Rn 21 0.7000 0.027 0.0189 0.3969 324 0.311725 28 17 0.5667 0.287 0.1626 2.7649 336 2.171547 29 12 0.4000 0.610 0.244 2.9280 348 2.299646 30 30 0.999 0.033 0.0330 0.9890 360 0.776759

Graph 1: Degrees against Dw (Example 1)

F1 = F(, Dw) = Y’ is forecasts obtained after deriving appropriate model (see Table 3).The choice of spectral analysis to derive the model for this research was predicated on the sinusoidal outputs, as depicted on graphs of original data. No of hits = x damage to tgtsor no of successful hit. R reliability of weapon (riffile) or accuracy of weapon.

raccuracy of Sld (wpn handler) = = , n = no of round (bullets) issued for firing. .

w =rR = damage coefficient Iw = wx = = rRx = = impact on tgt

Dw = IwP(A) is damage to tgt, P(A) is proportion of tgt covered by bullets i = (12i)o = , i = 1,2,3,…,30 (angles require in deriving Fourier Model)

I implementability = F1/n I convert SN & Soldier/Riffle to angular values i.e

Dw translates to proportion of task (project/Programme) assigned that can be achieved.

= Iw

Fig 2: Single Firer target

Result

rb = 0.1m , Ab = 0.01 m2, p(Ab) =

ri = 0.5m , Ai = 0.25 m2, p(Ai) =

r0 = 1.0m ,Ab = 0.01 m2, p(Ab) =

Prob of a pt in any circular target or of radius rtc is given by P(Atc) =




I(k) = + SS, (sum of squares) k = 1,2,……,

T = ≥ 0.5, test statistics for significance of coefficients to be accepted in the equation/model.

RSEk = for a season.

Table 2 : Fourier Analysis of Single Firer Frequency

Wavelength Period

Cosine(a's) Sine(b's) I RSE Spectrum T

0.307178 20.45455 15.20152 -1.958461 -1.591235 47.7569874 2.98481171 8.65306 -1.52406

0.4049164 15.51724 2.104604 -0.8883041 -0.304122 6.61180683

0.413237927 7.204719 -0.4652

0.5026549 12.5 12.30483 -1.828336 -1.345892 38.6567835

2.416048971 10.24067 -1.32145

0.6003932 10.46512 8.176512 -0.2259184 -1.836826 25.6872666

1.605454161 5.561211 -7.10635

0.6981317 9 2.945911 -4.26E-02 -1.110029 9.25485669

0.578428543 3.826142 -13.5716

0.7958701 7.894737 4.706373 0.2155723 -1.387418 14.7855009

0.924093808 4.889582 4.2867

0.8936086 7.03125 5.07279 1.153949 -0.890667 15.9366397

0.996039978 3.484326 0.863158

0.991347 6.338028 1.895862 0.8317432 0.3199061

5.95602498

0.372251561 1.025704 0.447556

1.089085 5.769231 0.1555459 0.2424829 -7.97E-02

0.48866204

0.030541377 1.47456 0.125953

1.186824 5.294117 2.793575 1.008405 0.3915225

8.77627884

0.548517428 3.908364 0.543946

1.284562 4.891304 5.023153 0.1769834 1.439712 15.7807033

0.986293953 6.551914 5.572805

1.382301 4.545455 8.080674 -1.068588 1.497647 25.3862014

1.586637586 11.33913 -1.4848

1.480039 4.245283 14.59759 -2.46174 -0.23337 45.85969 2.866230627 12.22855 -1.16431

1.577778 3.982301 9.859504 1.95E-02 -2.032131 30.9745339

1.935908368 6.557017 99.12105

1.675516 3.75 3.254531 0.8742769 0.7738829

10.2244113

0.639025707 3.707471 0.730919

1.773255 3.543307 4.16041 -1.268177 0.3666556

13.0703192

0.816894953 2.82311 -0.64415

1.870993 3.358209 1.485811 -0.5866731 -0.527437 4.66781257

0.291738286 1.472694 -0.49728

1.968731 3.191489 1.459578 -0.4590535 -0.632974 4.58539935 0.28658746

0.8829318 -0.6243

2.06647 3.04054 0.3062856 0.2882544 -0.212617

0.96222441

0.060139026 1.260212 0.208632

2.164208 2.903226 2.214139 -0.9629127 1.60E-02 6.95592245

0.434745153 4.276066 -0.45149

2.261947 2.777778 6.337994 8.43E-02 -1.62719 19.911406 1.244462873 5.316692 14.76196

2.359685 2.662722 4.295391 1.338243 9.14E-02 13.494368 0.843398002 2.932959 0.630228

2.457424 2.556818 1.570526 0.3266777 0.7423895

4.93395367

0.308372104 2.541772 0.943964

2.555162 2.459016 3.513019 -0.2167711 1.193541 11.0364737

0.689779607 4.950722 -3.18206

2.6529 2.368421 6.388424 -1.61436 0.2642329

20.0698293

1.254364329 4.585515 -0.777

2.750639 2.284264 2.782605 -0.5014824 -0.956081 8.74181177

0.546363236 1.646609 -1.0895

2.848377 2.205882 0.5106136 -6.81E-02 -0.457431 1.6041399

0.100258744 1.053444 -1.47156




2.946116 2.132701 1.596275 0.6815157 -0.451866 5.01484627

0.313427892 3.178491 0.459898

3.043854 2.06422 4.760706 0.2481965 1.390165 14.9562017

0.934762608 6.342934 3.76622

3.141593 2 7.925162 -1.822 9.68E-14 24.89763 1.556101875 6.342934 -0.85406

Table 3 : Forecasts by Derived Spectral Model ( = 120) Y = X Y' I 11 1.404065 5.395664 23 -0.82755 -3.18018 5 -0.10182 -0.39128 27 0.980009 3.766064 16 1.466358 5.635049 10 -1.14322 -4.39327 6 -0.83558 -3.21104 7 0.522388 2.007478 26 0.190881 0.733534 12 -1.39531 -5.36202

Test of Significance as coefficients of model which lead to acceptance or otherwise. The spectral analysis model of example 1, a single firer, is given by this formula Y’ = + cos n Because the Fourier Analysis Model does not give accurate forecasts other models must be found for the same exercise. The models considered were: a. Linear, Y11= -0.957 + 0.199X b. Logarithnmic, Y1g = - 3.72 + 2.390 In(X) c. Y1q = -0.959 + 0.258X – 0.002X2

TABLE 4 : Regression Forecasts (Using the formulae)

15 10 1.033 1.783178 1.421 16 14 1.829 2.587347 2.261 17 12 1.431 2.218927 1.849 18 22 3.421 3.667591 3.749 19 19 2.824 3.317209 3.221 20 3 -0.36 -1.09432 -0.203 21 6 0.237 0.562305 0.517




2. Brigadier EZA, Military Formation

Table 5 gives the ORBAT of a military formation (Brigade EZA). Network Pi(t=1) ℷii Pi(2) ℷ2i Pi(3) ℷ3i A 0.55 0.59784 0.55 0.29892 0.55 0.19928 B,C 0.9, 0.6 0.10536

0.51083 0.9,0.6 0.05268

0.25542 0.9,0.6 0.03512

0.17028

(D,E,F) (G,H)

(0.7,0.8,0.5), (0.4,0.7)

0.35668 0.22314 0.69315 0.091629 0.35668

(0.7,0.8,0.5), (0.4,0.7)

0.17834 0.11157 0.34658 0.45815 0.17834

(0.7,0.8,0.5) (0.4,0.7)

0.11889 0.07438 0.23105 0.30543 0.11889

I 0.3 1.20397 0.3 0.60199 0.3 0.40132 Logistics Items in this military formation A Arsernal/Armoury D Bayonetted Riffle B Ammo C Shell E RPG F GPMG G Rocket Luncher H Artillery/Bofors I Damage coverage calculation/evaluation

Fig 4 System network

S/N X YIL Yig Yiq 1 15 2.028 2.75224 2.461 2 4 -0.161 -0.40676 0.041 3 2 3.023 3.4398 3.401 4 13 1.63 2.410229 2.057 5 9 0.834 1.531367 1.201 6 11 1.232 2.01097 1.637 7 23 3.62 3.773831 3.917 8 19 2.824 3.317209 3.221 9 6 0.237 0.562305 0.517 10 5 0.038 0.126557 0.281 11 27 4.416 4.15705 4.549 12 8 0.635 1.249865 0.977 13 25 4.018 3.973113 4.241 14 16 2.227 2.906487 2.657 15 10 1.033 1.783178 1.421 16 14 1.829 2.587347 2.261 17 12 1.431 2.218927 1.849 18 22 3.421 3.667591 3.749 19 19 2.824 3.317209 3.221 20 3 -0.36 -1.09432 -0.203 21 6 0.237 0.562305 0.517

22 7 0.436 0.930725 0.749 23 26 4.217 4.066851 4.397 24 15 2.028 2.75224 2.461 25 19 2.824 3.317209 3.221 26 9 0.834 1.531367 1.201 27 21 3.222 3.556409 3.577 28 17 2.426 3.05138 2.849 29 12 1.431 2.218927 1.849 30 30 5.013 4.408862 4.981




Implementability optimal value is the overall or cummulative delivery capability implementable by the network given above. Computations using methodology were conducted for the various AC and DC. The values of p(1),ℷ1 ,p(2),ℷ2 ,p(3),ℷ3 , from the table above were used in the analysis.

3.RESULT Availability Capacity for p(1),ℷ1 :

A : AC1 = 0.55, pi(t) is proportion available at time t BC: AC2 = 1 – (1 – 0.9)(1 – 0.6) = 0.96 DEF: AC3 = 1 – (1 – 0.7)(1 – 0.8)(1 – 0.5) = 0.97 G,H: AC4 = 1 – (1 – 0.4)(1 – 0.7) = 0.72 (D,E,F),(G,H): AC5 = 1 – (1 – 0.97)(1 – 0.72) = 0.9916 I: AC6= 0.3

AC5 = AC1.AC2.AC5.AC6 = 0.15707 15.71% , expendable available logistics. Delivery Capability for p(1),ℷ1 : A: MTTFA = MTTF1 = = 1.67269, since I = -Inpit-1 is the supply/replenishment rates.

BC :MTTFB,c = MTTF2 = 9.49127 + 1.95760 – (1.62288)

= 9.82599 DEF :MTTFD,E,F = 7.68847 – (1.72467 + 1.09136) + 0.78557 = 5.65801 GH :MTTFG,H1.09136 + 2.80363 – (0.78557) = 3.10942

DEF,GH : MTTFD,E,F,G,H = MTTF3= 18.12579 + 3.05979 – (2.61787) = 18.56771,where DEF = DEF = 0.05517,andGH = GH = 0.32682 I :MTTI = MTTF4= = 0.83059 MTTFs = = 30.89698

This DC is the Damage Capability of the Military Formation. Availability Capacity for p(2),ℷ2 :

A : AC1 = 0.55, pi(t) is proportion available at time t BC: AC2 = 1 – (1 – 0.9)(1 – 0.6) = 0.96 DEF: AC3 = 1 – (1 – 0.7)(1 – 0.8)(1 – 0.5) = 0.97 G,H: AC4 = 1 – (1 – 0.4)(1 – 0.7) = 0.72 (D,E,F),(G,H): AC5 = 1 – (1 – 0.97)(1 – 0.72) = 0.9916 I : AC6 = 0.3 AC5 = AC1.AC2.AC5.AC6 = 0.15707 15.71% , expendable available logistics.

Delivery Capability for p(2),ℷ2: A: MTTFA = MTTF1 = = 3.34538, since I = -Inpit-1 is the supply/replenishment rates.

BC :MTTFB,c = MTTF2= = 18.98254 + 3.91512 – (3.24570)

= 19.65196 DEF : MTTFD,E,F = 14.57025 – 5.63204 + 1.57112 = 10.50933 GH : MTTFG,H= 2.18269 5.60727 – 1.57112 = 6.21884 DEF,GH : MTTFD,E,F,G,H = MTTF3 = 10.50933 + 6.21884 = 16.72817,where DEF = DEF = 0.0069,and GH = GH = 0.08171 I : MTTI = MTTF4 = = 1.66116 MTTFs = = 41.38667 This DC is the Damage Capability of the Military Formation. Availability Capacity for p(3),ℷ3 :

A : AC1 = 5.01811, pi(t) is proportion available at time t BC: AC2 = 28.47380 + 5.87268 – (4.86855) = 34.34648 – 4.86855 = 29.47793 DEF: AC3 = 26.18405 – 8.44840 + 2.35682 = 20.09247 G,H: AC4 = 3.27407 + 8.41114 – 2.35671 = 9.3285 (D,E,F),(G,H): AC5 = 20.09247 + 9.3285 = 29.42097 DEF = DEF = 0.0020,andGH = GH = 0.03631 I : AC6 = 2.49178




AC5 = AC1.AC2.AC5.AC6 = 0.15707 15.71% , expendable available logistics. Delivery Capability for p(3),ℷ3: A: MTTFA = MTTF1= = = 5.01811, since I = -Inpit-1 is the supply/replenishment rates.

BC :MTTFB,c = MTTF2= = 28.47380 + 5.87268 – (4.86855) = 34.34648 – 4.86855 = 29.47799

DEF : MTTFD,E,F =26.18405–(8.44840) + 2.35682= 20.09247 GH : MTTFG,H=3.27407 + 8.4114 – (2.35671) = 9.3285 DEF,GH : MTTFD,E,F,G,H = MTTF3 = 20.09247 + 9.3285 = 29.42097 ,where DEF = DEF = 0.00204,and GH = GH = 0.03631 I : MTTI = MTTF4 = = 2.49178 MTTFs = = 71.4269 This DC is the Damage Capability of the Military Formation.

Table 6: Spectral Coefficients f() = Dw yt f() Cos f()Sin f() Cos2 f()Sin2 120 24.276 y0 -12.138 21.024 -12.138 21.024 240 32.518 y1 -16.259 -28.161 -16.259 -28.161 360 56.121 y2 56.121 0 56.121 0 total 112.915 27.724 -7.137 27.724 -7.137

F2 (240, 32.518) = 56.794 F2 (360, 56.121) = 112.240 F2 (0, 0) = 112.24 Forecast F2 (480, 0) = 48.553 These Computed Values were used to obtain Coefficient of Model

Table 7 Spectral Model Goodness of Fit DC = Iw Dw = Iw F(:Dw) = F2 Dw - F2 Yp(Goodness Fit From Computer Model)

0 - - 112.240 120 30.897 24.276 48.553 24.277 Very Poor 240 41.387 32.518 56.794 24.276 Very Poor 360 71.427 56.121 112.240 56.119 Very Poor 480 - - 48.553 112.915 217.587

Table 8 =DwVs I i h p(i) Dw F2 fh ei I Ip 1 1 P(1) 24.276 120 48.553 1/3 24.277 0.2231 0.2231 2 2 P(2) 32.518 240 56.794 1/3 24.276 0.2610 0.2610 3 3 P(3) 56.121 360 112.24 1/3 56.119 0.5158 0.5158 112.915 217.587 104.672

=34.891

Table 7 and 8 show that the Spectral derived model is not suitable for forecasting data on these tables. The values of I also corroborate undependability of this model for forecasting because the values x 100% shows the level implementable which are very low. The unsuitability of Fourier model warranted derivation of alternative model. The derived alternative regression models are given below:




Table 9: Value to obtain Regression Coefficient

Table 10 : Forecast of Quadratic Model

Fig 12: Degrees vs Dw (Example 2)




4.DISCUSSION In the case of a single firer (example 1), a spectral model was derived whose pattern (graph) appears sinusoidal but does not yield acceptable results. Even the implementability values are low and fluctuate stochastically. The AC are the same for the three stages, because the respective AC at different stages are fixed, due to the assumed p(available proportion that now stands as reliability). Whereas the DC varied according to the values of t, the stages of the system. It was observed that as the stages increased decreased while the DC increased. This means that on the long run the DC (damage capability) also increased even at lower rates of logistics supply. This is so because for all values of p>0, however infinitesimal, a certain amount of damage would be recorded.

5.CONCLUSION The results of damages to target by single firer and weapons system combat, were used to obtain implementability of individual (dual) and group (indirect fire or weapons system) projects/programmes or tasks, with the aid of appropriate pdf transformations. These derived models were used to determine the implementability as shown on Tables 1 and 8.

6.FURTHER RESEARCH Further research can be carried out using various values of x,r,R, ,n p and to determine Dw, FAC and DC of systems.

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a combat model adaptablefor evaluating the ... · table 1 gives the target hit recorded in exercise...

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