Reliability and Cost Optimization of a System with k-out-of-n Configuration and Choice of Decreasing the Components Failure Rates

Mani Sharifi, Ghasem Cheragh, Kamran Dashti Maljaii, Arash Zaretalab, Mohammadreza Shahriari
2020 Scientia Iranica. International Journal of Science and Technology  
This paper presents a new redundancy allocation problem for a system with the k-out-of-n configuration at the subsystems' level with two active and cold standby redundancy strategies. The failure rate of components in each subsystem depends on the number of working components. The components are non-reparable, and the failure rate of the component can be decreased with some preventive maintenance actions. The model has two objective functions: maximizing the system's reliability and minimizing
more » ... he system's costs. The system aims to find the type and number of components in each subsystem, redundancy strategy of subsystems, as well as the decreased values of components failure rates in subsystems. Since the redundancy allocation problem belongs to NP-Hard problems, two Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Non-Dominated Ranked genetic algorithm (NRGA) metaheuristic algorithms were used to solve the presented model and to tune algorithms parameters we used response surface methodology. Besides, these algorithms were compared using five different performance metrics. Finally, the hypothesis test was used to analyze the results of the algorithms. There are many real-world manufacturing and operational systems that increase their reliability through the concepts of RAP, which can be counted, including aircraft engines, the number of pumps at a water pumping station, and so on. Considering the nature of these manufacturing and operating systems, many hypotheses and limitations have been added to the RAP to draw the problem closer to the real-world conditions. Therefore, researchers categorized this problem in different aspects, including categorization based on the functional status of the components (binary or multi-state), the type of component failure rate (constant or time-dependent), components configuration in the system (active or standby). Considering the importance of the system's reliability and system's cost in this problem, in many studies, both objectives considered as objective functions, and this problem is transformed into a two-objective problem (and even more than two). In this paper, we investigate a multi-objective RAP whose failure rates depend on the number of working elements. The subsystems are k-out-of-n, and the failure rate of components can be reduced with spending money. The objective functions of the model are maximizing system reliability and minimizing system weight. The type of each subsystem component and subsystem redundancy strategies are the system variables. Since the model is Np-Hard, we used Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Non-Dominated Ranked genetic algorithm (NRGA) algorithms for solving the presented model. This paper organized as follows: In Section 2, we present a literature review to confirm that there exist no studies that exactly meet this research conditions. In Section 3, we discussed the mathematical model and system assumptions. In Section 4, the NSGA-II and NRGA algorithms are presented. In Section 5, a numerical example is presented to compare the algorithms results. Section 6 is the managerial insights, and the final Section deals with the conclusion and further studies. Literature review In real-world problems, many parameters affect the system's reliability. One of the most important ones is the failure rate of the components. This parameter in RAP studies has two categories: constant failure rate (CFR) and time-dependent failure rate. Regarding CFR models, Misra and Sharma [3] presented a RAP model with the choice of allocating identical components to each subsystem and active redundancy strategy, then solved the presented model with zero-one programming. Ida [4] used a genetic
doi:10.24200/sci.2020.52944.2960 fatcat:qtpjcm6zjvenfi25ymdfijn33a