Journal of Quality Engineering and Management

Abstract The reliability assessment of multi-state systems is often investigated by assuming the independence of the components. It is very useful to consider the interactions between components to evaluate the reliability of such systems. The traditional block diagrams do not evaluate the reliability of a repairable multi-state system. The use of simple stochastic process methods is very difficult due to the high dimension of the problem (the very large number of system states) for engineering applications. To the best of our knowledge, the universal generating function has not been used for systems with dependent components. In this paper, using stochastic processes and a universal generating function method, multi-system systems are analyzed in a situation in which the performance distributions of some components depend on the state of others.

Abstract This paper examines the issue of reliability and multi-objective redundancy allocation for series-parallel multi-state systems. Therefore, a suitable mathematical model is proposed in order to maximize the accessibility of the system and minimize the relevant design costs by considering the budget constraints and the physical weight of the system. In order to estimate the accessibility of a multi-state system, the general generator function method has been used, which is an efficient method for calculating the reliability and accessibility of multi-state systems. After solving the mathematical model by the Epsilon constraint method, in order to simultaneously optimize the two objective functions and generate partial solutions of the mathematical model of the problem on a larger scale, the second version of the genetic metaheuristic algorithm with unfavorable sorting has been developed. Finally, to evaluate the performance of the proposed solution algorithm, a number of sample problems in different dimensions have been generated and solved. The results of the meta-heuristic algorithm are compared with the results obtained from solving the mathematical model by the Epsilon constraint method by t-test, which indicates the efficiency of the proposed solution algorithm.

Abstract The growing need for systems with high availability/reliability has led to numerous studies in recent years on reliability optimization (availability, if the system is repairable). The use of different redundancy policies and adding extra components are generally considered effective ways to increase system availability. When the system is multi-state, due to the computational complexity involved, the methods used to calculate system availability play a crucial role in providing an acceptable solution. This paper aims to minimize costs for multi-state systems under the constraint that system availability must exceed an acceptable threshold. The redundancy allocation problem is modeled as heterogeneous, meaning that components in such a system can differ from one another. Both components and the system can have multiple states. To compute system availability, the Universal Generating Function (UGF) algorithm is employed, and to optimize the system structure, the Genetic Algorithm (GA) is used.