Definition of mathematical models of shots distance determination using biological imitators of human tissues

Abstract

Introduction. One of the most common tasks in expert practice which is solved during investigation of almost all the facts of firearms usage is determination of shots distance. To realize this aim laboratory diagnostic methods are widely used mainly based on identifying of shot products and their effects. The traditional and most accessible way for an expert to achieve it is visual comparison of a remote track with some experimental samples of shot marks from the similar weapon model. The main advantages of the method are its simplicity and accessibility; however, it has some disadvantages that can lead to a mistake in determining specific shooting distance. Determination of shots distance based on statistical analysis of interdependence, frequency of occurrence and shot trace signs variation does not require appliance of full-scale collections, albums and descriptions of shots marks and allows to get conclusion with known probability of error. Materials & Methods. The shots were carried out from pistols "Fort-12" and "Fort-14TP" produced by the Science Industrial Association "FORT" of the Ministry of Internal Affairs of Ukraine (Vinnitsa City) with standard 9 x 18 mm caliber ammunition. Skin-muscular flaps of large white pig corpses with thickness from 1 cm to 4.5 cm were used as biological imitators of human body tissues. Series of five shots were conducted from a distance of 1 cm to 300 cm. Obtained objects were examined visually and with the complex of laboratory methods. All calculations of the research indicators were made with the help of a spreadsheet of "Microsoft EXCEL". When modeling dependencies, licensed statistical packages Statistica 10.0 Enterprise and IBM SPSS 20 were used. Based on the results of statistical processing of the experiment, using pistols "Fort-12" and "Fort-14TP", paired and multiple linear regression models were built to determine shorts distance depending on parameters of shot products distribution on the skin surface of biological human tissue imitators. A qualitative assessment of statistical data using correlation and regression analysis has been made. Results & discussion. Construction of regression models for skin damage. The obtained results of calculations of the characteristics of paired regression models of distance of shots from 3 cm to 150 cm depending on the diameter of the peripheral zone of gunpowder deposits in the “Statistica” system for "Fort-12" pistols and "Fort-14TP" pistols are shown. The indicators of multiplex and paired linear models of shots distance calculation  from the parameters have been analyzed. Confidence intervals of 95% reliability for predicted values of shots distances for pistols "Fort-12" and "Fort-14TP" have been built. The conclusions drawn, obtained shots distance models are adequate and statistically significant both in individual parameters and in general, therefore the equations obtained can be used for determination of predicted values of the shots distance for "Fort-12" and "Fort-14TP" pistols. Conclusion. Thus, based on generalization of the obtained data using correlation-regression analysis, the most significant factors that can be considered as diagnostic criteria for determining of the shot distance from pistols "Fort-12" and "Fort-14TP" have been revealed. Statistically valid linear multi-factor and pair regression models that allow to calculate shorts distance from "Fort-12" and "Fort-14ТP" pistols for skin lesion based on experimental data have been made. Using the correlation-regression analysis statistical verification of regression models based on the Student’s t-criteria and Fisher's F criteria has been made. It allowed to reveal the statistical significance of the obtained models. Close correlation link between determined parameters and shot distance allowed to establish that the models of the regression equation are adequate and can be used to predict shots distance.