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Experiments with Bullet Proof Panels and Various Bullet Typ Experiments with Bullet Proof Panels and Various Bullet Typ

Experiments with Bullet Proof Panels and Various Bullet Typ - PowerPoint Presentation

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Uploaded On 2015-11-01

Experiments with Bullet Proof Panels and Various Bullet Typ - PPT Presentation

RA Prosser SH Cohen and RA Segars 2000 Heat as a Factor of Cloth Ballistic Panels by 022 Caliber Projectiles Textile Research Journal Vol 70 pp 709723 Data Description Response V50 The velocity at which approximately half of a set of projectiles penetrate a fabric pa ID: 179580

type bullet model equal bullet type equal model slopes models sharp layers intercepts dummy fsp variables panel lines note

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Slide1

Experiments with Bullet Proof Panels and Various Bullet Types

R.A. Prosser, S.H. Cohen, and R.A.

Segars

(2000). "Heat as a Factor of Cloth Ballistic Panels by 0.22 Caliber Projectiles," Textile Research Journal, Vol. 70: pp. 709-723.Slide2

Data Description

Response: V50 – The velocity at which approximately half of a set of projectiles penetrate a fabric panel (m/sec)

Predictors:

Number of layers in the panel (2,6,13,19,25,30,35,40)

Bullet Type (Rounded, Sharp, FSP)

Transformation of Response: Y

*

= (V50/100)

2

Two Models:

Model 1: 3 Dummy Variables for Bullet Type, No Intercept

Model 2: 2 Dummy Variables for Bullet Type, InterceptSlide3

Data/Models (t=3, bullet type,

n

i

=9 layers per bullet type)Slide4

Model 1 – Individual Intercepts/SlopesSlide5

Model 2 – Dummy Coding (Sharp (j=2), FSP (j=3))Slide6

Model 1 – Matrix FormulationSlide7

Model 2 – Matrix FormulationSlide8

Equations Relating Y to #Layers by Bullet Type

Note: Both models give the same lines (ignore rounding for Sharp). Same lines would be obtained if Baseline Category had been Sharp or FSP.Slide9

Tests of Hypotheses

Equal Slopes: Allowing for Differences in Bullet Type Intercepts, is the “Layer Effect” the same for each Bullet Type?

Equal Intercepts (Only Makes sense if all slopes are equal): Controlling for # of Layers, are the Bullet Type Effects all Equal?

Equal Variances: Do the error terms of the t = 3 regressions have the same variance?Slide10

Testing Equality of Slopes

Complete Models (Both 1 and 2)

Reduced Models (Both 1 and 2)

Model 2

Model 2

Conclude Slopes are not all equalSlide11
Slide12

Testing Equality of Intercepts – Assuming Equal Slopes

Note: Does not apply to this problem, just providing formulas.Slide13

Bartlett’s Test of Equal Variances

MSE