The reliability of a warm standby series-parallel system without adequate samples is studied based on the uncertainty theory. It is assumed that the lifetimes of system elements follow independent uncertainty distributions with uncertain parameters. Three different switch models, including absolutely reliable mode, discrete mode and continuous mode, are developed for the warm standby series-parallel system. Besides, the cold standby series-parallel system is discussed as a special case. The reliability function and mean time to failure of each developed model are analyzed. A numerical example for the system with different switches is implemented to illustrate the application and efficiency of the proposed models.

The main goal in this paper is to propose an optimization model for determining the structure of a series-parallel system. Regarding the previous studies in series-parallel systems, the main contribution of this study is to expand the redundancy allocation parallel to systems that have repairable components. The considered optimization model has two maximizing the system mean time to first failure and minimizing the total cost of the system. The main constraints of the model are: maximum number of the components in the system, maximum and minimum number of components in each subsystem and total weight of the system. After establishing the optimization model, a multi objective approach of Imperialist Competitive Algorithm is proposed to solve the model.

A Bi-objective redundancy allocation problem in series-parallel systems with repairable components is addressed in this paper. A new method is proposed for this problem. In the repairable systems with multiple components the concept of availability is used instead of reliability concept and the stability of the system is important. Stability of the system can be defined as availability before the first corruption of the system. There are two main strategies to increase system reliability. The first strategy, raising the reliability of system components and another one is to add the surplus components in parallel. Due to economic and technological limitations, the best and most practical way to increase system reliability is second strategy as we considered in this research. In this paper, non-exponential distribution is considered for failure rate and repair time of components. The first objective aims to maximize the availability of the complex system. Simultaneous with the availability of the system, the total operating cost related to components is the second objective of interest to be minimized. The target of this optimization problem is to allocate adaptable redundant components to increase the system`s availability considering all limitations like system`s volume and budget. Due to the complexity of the problem is that because of steady distribution, the series-parallel system, for each subsystem with parallel components the scale of availability is separately calculated by simulation approach and the result used as an archive in the solution method. In order to solve this multi objective problem, the authors used an evolutionary algorithm named the simulated annealing based multi objective genetic algorithm (SAMOGA) for solving the mentioned problem. In order to evaluate the efficiency and performance of the suggested algorithm, the experimental results obtained on designed instances are compared statistically with Non-dominated Sorting Genetic Algorithm (NSGA-II) and multi objective particle swarm optimization (MOPSO) according to the multi objective comparison measures. The results confirm that the implemented simulated annealing based multi objective genetic algorithm is better than other solution algorithms.

In this paper‎, ‎we consider the estimation of the stress-strength reliability of a coherent system‎. ‎The distributions of stress and strength random variables are the members of a general class of distributions‎. ‎For a series-parallel system‎, ‎the reliability of the stress-strength model is estimated using the maximum likelihood estimation‎, ‎asymptotic confidence interval‎, ‎uniformly minimum variance unbiased estimation‎, ‎and Bayes estimation‎. ‎Also‎, ‎simulation studies are performed‎, ‎and two real data sets are analyzed.

A CSS1†is a system with the continues-state components. When a component has the ability to obtain all the situations from completely working to completely failed, it named continues-state component. In the real world, performance rate of elements are continuous and decrease by time. Continuity of components causes infinite working states and grows up the system states. In this paper we propose a new method for series-parallel continues-state RAP2‡using UGF3§for multi-state systems. In this method at first we consider a binary CFR4**system. Using Weibull distribution function for the performance rate of working state, this system upgraded to a CSC. Then the UGF for a series-parallel system has been studied and a numerical example presented to illustrate the reliability and availability computation.

In this paper, we study different methods of solving joint redundancy-availability optimization for series-parallel systems with multi-state components. We analyzed various effective factors on system availability in order to determine the optimum number and version of components in each sub-system and consider the effects of improving failure rates of each component in each sub-system and improving reliability of each sub-system. The target is to determine optimum values of all variables for improving the availability level and decreasing the total cost of the system. At first, the exact values of variables are determined using a mathematical model; then, the results of SA-Parallel, VDO-Parallel and genetic algorithms are compared with the exact solution.

Computer network topologies are complex systems made up of large subsystems that are arranged in series-parallel configurations. The current paper dealt with the mathematical modeling of some reliability metrics used in determining the strength, reliability, and performance of a computer distributed system stationed in two locations A and B, all of which were configured as a series-parallel system. The system is made up of six series-parallel subsystems distributed between locations A and B. In location A, there are three subsystems: four clients running in parallel as subsystem 1, six directory servers running in parallel as subsystem 2, and two replica servers running in parallel as subsystem 3, while in location B, there are two replica servers running in parallel as subsystem 4, six directory servers running in parallel as subsystem 5, and four clients running in parallel as subsystem 6. Using the Markovian process, the goal is to build mathematical models of reliability, dependability, availability, and maintainability in order to assess the system's performance, strength, and effectiveness. The ordinary differential difference equations for each subsystem are obtained from the schematic diagrams and solved iteratively. In this work, the Ramd analysis is used to quantify the performance of a system in terms of reliability, maintainability, availability, and dependability. It is tabulated the impact of subsystem repair and failure rates on reliability, maintainability, availability, and dependability. Inspecting the network's essential subsystems and their maintenance priorities improves the system's stability, maintainability, availability, and dependability while also lowering maintenance costs.

This paper addresses the mixed integer reliability redundancy allocation problems to determine simultaneous allocation of optimal reliability and redundancy level of components based on three objective goals. System engineering principles suggest that the best design is the design that maximizes the system operational effectiveness and at the same time minimizes the total cost of ownership (TCO). To evaluate the performance of the TCO allocation numerical experiments were conducted and compared with previous for the series system, the series-parallel system, the complex (bridge) system and the over speed protection system. From the results of the numerical investigation, reliability redundancy allocation based on minimum TCO will lead to a more reliable, economical design for the manufacturer as well as user compared with the initial cost optimum design and conventional reliability optimum design

Reliability is one of the most important issues in the engineering design process. When we use a system, we often want to determine the reliability of this system. Clearly, higher reliability systems are more valuable. On the other hand, the reliability of each system depends on the structure and reliability of its components. Therefore, to increase the reliability of the system, the reliability of its components can be improved. In addition, to increase the reliability of the components of a system, it is necessary to consider its costs. This study, by considering a series-parallel system, determines the amount of increase required for the reliability of system components so that the reliability of the whole system is maximized and the cost of this increase does not exceed a predetermined value. The following is a numerical example for reviewing the results. Finally, a summary of the results of the article is given.

In today’s world of technology, it is impossible to see where computer system does not play an important role. The application of distributed systems is gradually becoming broad and diverse, and as a result of this, reliability prediction is a key concern. This paper, considered a distributed system with five standby subsystems A (the clients), B (two load balancers), C (two distributed database servers), D (two mirrored distributed database serves) and E (centralized database server) is considered arranged as series-parallel system. Exponential failure and repair are susceptible for all the components of this system. Each component’s failure rates are constant and considered to obey an exponential distribution, and they are repaired using general repair or copula repair. The system is evaluated using first-order partial differential equations and the supplementary variable technique, Gumbel-Hougaard family of Copula, to find expressions for reliability metrics of system strength such as availability, reliability, MTTF, sensitivity, and profit function. These reliability metrics have been validated for different parametric values and the results are presented in tables and figures.