Survival distributions in crossing fields containing clusters of mines with possible detection and uncertain activation or kill

Abstract

Case Western Reserve U~i v c r s i~~Cle vela rid. Ohio ABSTRACTThe present paper presents an algorithm for the exact determination of survival distributions in crossing mine fields. The model under consideration considers clusters of mines, scattered at random in the field around specified aim points. The scatter distributions of the various clusters are assumed to be known. The encounter process allows for a possible detection and destruction o f the mines, for inactivation of the mines and for the possibility that an activated mine will not destroy the object. Recursive formulae for the determination of the survival prob~bililies of each object (tank) in a column of crossing at the same path are given. The distrihution of the number of survivors out o f ti objects i n a column is also determined. Numerical examples are given. ~N T R O D U~T I O NIn the present paper we develop methods for the exact numerical determination of the survival probabilities of objects (targets) crossing a field containing randomly scattered mines. The model under consideration refers to cases in which the absorption points are randomly scattered over the field in one or several clusters. Each cluster is characterized by some bivariate distribution of the mines around a center (aimpoint). More specifically we consider clusters which are distributed either as bivariate normal or uniformly over rectangular domains. The objects cross the field in columns along predetermined breaching paths. The movement of the objects through the field is in a continuous manner (like that of vehicular or tank targets). The mines may be detected by the objects and destroyed. On the other hand, if a mine is not detected it may or may not be activated. If it is not activated in a specific encounter it may be activated in following encounters. Defective mines (duds) which can never be activated play no significant role in the determination of the survival probabilities. We have to know the proportion of defective mines (duds) only in order to determine correctly the distributions of the anticipated number of active mines in the various possible crossing paths.The specific details of the probabilistic model, as related to the structure of the field, is described in Section 2.There are several papers in the available literature fl,2,3,41 which study similar models. In most of these papers the results are based on computer simulation. Both the location of