Target Detection in a Known Number of Intervals Based on Cooperative Search Technique

Finding hidden/lost targets in a broad region costs strenuous effort and takes a long time. From a practical view, it is convenient to analyze the available data to exclude some parts of the search region. This paper discusses the coordinated search technique of a one-dimensional problem with a search region consisting of several mutual intervals. In other words, if the lost target has a probability of existing in a bounded interval, then the successive bounded interval has a far-fetched probability. Moreover, the search domain is swept by two searchers moving in opposite directions, leading to three categories of target distribution truncations: commensurate, uneven, and symmetric. The truncated probability distributions are defined and applied based on the proposed classification to calculate the expected value of the elapsed time to find the hidden object. Furthermore, the optimization of the associated expected time values of various cases is investigated based on Newton's method. Several examples are presented to discuss the behavior of various distributions under each case of truncation. Also, the associated expected time values are calculated as their minimum values.Comment: 32 pages, 11 figure

Cooperative search model to detect a lost target based on its probabilistic distribution in a bounded zone

This study uses two unit-speed searchers to solve the challenge of finding a randomly located target in a bounded region, such as searching for bodies found under the rubble resulting from the erosion of residential units due to horrific natural disasters. The search procedure begins at(0,0). The region is subdivided into a limited even number of cells. The target’s position has a symmetric probability distribution. It is preferable to search in an optimal method in order to reduce the predicted time for discovering the target. An algorithm is used to generate the optimal search strategy. We discuss an example when the target has a symmetric truncated normal distribution. We provide an illustrated case to demonstrate this technique’s applicability.</p

Cooperative search model for finding a brownian target on the real line

In this paper, we study the cooperation between two searchers start the searching process from the origin to meet a Brownian moving target on a real line. We find the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite. This is the first model which calculates the approximate value for the expected value of the first meeting time. An illustrative example has been given to demonstrate the applicability of this model

Internal truncated distributions: applications to Wiener process range distribution when deleting a minimum stochastic volatility interval from its domain

In this paper, we apply a new definition of truncated distribution “Internal Truncated Distribution” on the Wiener process range distribution to delete a few stochastic volatility intervals from its domain. A comprehensive treatment of the statistical properties of this distribution is presented. The usefulness of the proposed distribution is illustrated with the help of a real data set

A probabilistic early fault detection model for a feedback machining system with multiple types of spares

Abstract This paper studies corrective and preventive maintenance to provide a quality control policy. The corrective maintenance, depending on the time, of a feedback machining system model with a finite source and standbys is presented. Moreover, the system has a known number of servers to repair the damaged units, and it contains an inspector to ensure the maintenance quality of the repaired units. The exact value of the probability of n units in the system will be obtained by using an efficient algorithm that depends on the Laplace transformation. To promote the concept of preventive maintenance, we use this probability to get the probability of early fault detection as a function of time and in the steady state. The applicability of this model is discussed for different system capacities