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In this paper we will introduce a new method to compute the reliability importance of components for different reliability models which has independent identical units relative to minimal cut and minimal path sets. We will compare the results of this method with the method known as Birnbaum's measure, which is used in calculating the reliability importance of units for different systems, in order to demonstrate the accuracy of the new proposed method's outcomes. [ABSTRACT FROM AUTHOR]

The study is about how to use makov chain to find the reliability,availability of repairable system Evaluating time dependent probabilities method,we generalized state probabilities and reliability models for maintained-systems by Markov models. Such systems are composed of (n) identical independent (i.i.d) units with constant failure and repair rates, represented by λ, μ respectively. So, this study will about two axes: Firstly, some definitions that related to reliability and markov model. Secondly, use stochastic transitional probability matrix to find the reliabity of two,three reliable components by evaluating time dependent probabilities and find the General forms for Laplace transforms and General form of inverse Laplace transforms. [ABSTRACT FROM AUTHOR]

The purpose of this research is to learn how to use the Makov Chain to determine the repairability and availability of systems that can be repaired. We used Markov models to generalize state probability and reliability models for maintained-systems after evaluating the limiting state probabilities technique. These systems are made up of (n) identical independent (i.i.d) equipment with a high rate of failure and repair, which are denoted by and respectively. As a result, our research will focus on two axes: firstly, some definitions that related to reliability and markov model. Secondly, by limiting state probabilities and finding the general form, use a Matrix of stochastic transitional probability to find the reliabity of two, three, and four reliable components. [ABSTRACT FROM AUTHOR]

In this research, we will study two main topics that are closely related to the process of increasing the reliability of complex systems, and these two topics are importance and redundancy, and studying the relationship between them will help in understanding the mechanism of increase that can be obtained by a complex system. [ABSTRACT FROM AUTHOR]

In this paper, we will study the reliability of the mixed system and how to increase its reliability using the redundancy technique. We will present this technique in two ways, the first way using the reduction method on the system and the other way without it, and then we will compare the results between the two methods to determine the best way. [ABSTRACT FROM AUTHOR]

The current research addresses the reliability allocation to increase the reliability of mixed systems. This issue requires us to perform a reduction process for the mixed system. We will perform a reduction for the given system using the method of reducing the elements of the system to a series system. We will then use the minimum effort method to distribute the assumed increase in the system's reliability in a fair way to all components of the system. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce two allocation methods in order to increase the reliability of mixed systems. A comparison between these two methods has been made to prove which is the best method to allocate higher to all units of the mixed system. [ABSTRACT FROM AUTHOR]

In this article, the reliability of a complex network has been calculated as a complex system using limited paths. The reliability of this system has been assigned to explore alternate ways assignment of reliability values on reducing the total expense of the process. Among the initial findings were: 1. To quantify Comprehensive device costs, three cost functions were used: The paradigm of exponential behavior, the exponential behavior model and finally, there's the logarithm model. 2. Solving the challenges of maximizing the dynamic system's reliability, the reliability of each part of the system was determined using the ant colony optimization (ACO) algorithm. [ABSTRACT FROM AUTHOR]

In the current work, the systems that are subjected to maintenance are examined using Markov models. Markov models help explain the actions of the systems at work. Furthermore, it has a realistic estimate of when the system will malfunction or when the system will be maintained if it deteriorates during the working cycle. This expectation aids the continuity of the system. In the long term, this would increase the system's reliability. [ABSTRACT FROM AUTHOR]

This paper use two contemporary optimization algorithms inspired by nature to optimize the reliability of complex networks. The first one is the Bat (BA) algorithm that simulates the behavior of bats to echo-locate prey and barriers while the second simulates the command hierarchy and style of hunting mode of gray wolves which is called Grey wolf optimization (GWO) algorithm. To find out the best reliability with the lowest cost, we used five different cost functions whose are logarithm, exponential, exponential with feasibility factor, power and tan functions with these two algorithms, and we got different results. A comparison was made between the results of two algorithms, in addition to discussing the results obtained using five cost functions with two algorithms. [ABSTRACT FROM AUTHOR]

This paper focuses on the reliability of calculating the reduction in oxygen supply ROSS spacecraft computed as a complex system using probability theory. The genetic algorithm (GA) was employed to tackle the problem of reliability assignment and optimization, as well as the capacity to handle complex problems that are common in engineering systems. Having a high cost of execution usually requires a larger number of duplicates. We applied the particle swarm optimization (PSO) algorithm in addition to GA. This technique is based on the behavior of accumulating organisms. This study will perform a comparison of two algorithms to examine the robustness of the algorithm that helps to calculating the fitness of a given system. [ABSTRACT FROM AUTHOR]

In this paper the inclusion and exclusion approach was used to calculate the reliability expression for the Advanced Research Projects Agency Network (ARPANET). The policy entails the use of either a path group or a segment set. Additionally, the paper deals with a computationally efficient and easy-to-concept method for obtaining minimum path sets using the powers of a network connection matrix. The method is simple and computationally efficient, and it can be used on graphs with finite non-zero failure probabilities in both nodes and branches. The method makes use of Boolean algebra and graph theory principles. The method is demonstrated with an example. [ABSTRACT FROM AUTHOR]

In our research, we will present three reduction strategies for calculating the reliability of complex networks. In the first method we systematically update every parallel path via an equal single path, and ultimately lessen the given system to one together with most effective series detail, which is called reduction to series elements. The second is the decomposition method which is an application of the law of total probability that includes choosing a key component and then calculating the reliability of the network when the key failed once and the second time the key succeeded. These two probabilities are then blended to obtain the reliability of the system. And the third method is the delta-star transformation. All of these methods convert a complex network into simple network. [ABSTRACT FROM AUTHOR]