redundancy allocation problem

One of the common approaches for improving the reliability of a specific system is to use parallel redundant components in subsystems. This approach, which is known as the redundancy allocation problem (RAP), includes the simultaneous selection of the component type and its level for each subsystem in order to maximize the system reliability.Traditionally, there are two redundancy strategies, namely active and standby, for the redundant components. Recently, a new powerful strategy called mixed strategy has been developed. It has been proved that the mixed strategy has a better performance when compared to both previous strategies. The main issue in utilizing the mixed strategy is its complicated formulation and sophisticated calculations, leading to a time-consuming procedure for solving the problems. Hence, in this paper, a new formulation based on the recursive approach is introduced to ease the calculation of the mixed strategy. In the new formulation, the complex double integral calculations are removed and the calculation times is reduced. The proposed recursive formulation provides a general statement for the mixed strategy formula which is not changed by altering the number of components in each subsystem. This flexibility and stability in the formula can be very important, especially for large scale cases. In order to evaluate the new approach and to compare its performances with the previous formulation, a benchmark problem with 14 subsystems is considered and the results of the two formulation are compared with each other.

System reliability optimization is one of practical issue in design and engineering. Adding parallel redundant component is a common approach in order to improve the reliability of a specific system. This approach that is known as redundancy allocation problem (RAP), includes discrete component choices with known characteristics such as reliability, cost, weight in order to maximize system reliability. In RAPs, redundancy strategy plays a significant role in increasing reliability of a system or subsystem. Generally, there are three types of redundancy strategies, namely, active, standby and mixed. The latter is a new strategy which is a combination of the two former and have had some noticeable results. This paper presents a new redundancy strategy for system reliability optimization which is called Sync-Mixed. The proposed strategy is a general form of a recently introduced strategy called "Mixed Strategy" that effort to decrease number of switching system usages. In order to evaluate the efficiency of the Sync-Mixed strategy with regarding complexity of formulas for new strategy, a single specific subsystem with five components will be used and reliability of the subsystem will be computed by considering all three previous strategies and the new one. In previous studies, some well-known benchmark problems, including series system, series-parallel system, parallel-series system, and complex system, have been taken into account. The performances of all strategies are compared byconsidering different values of switching and components reliabilities. In RAP, it is assumed that the switch reliability and components reliability are predetermined parameters. However, in this study different combinations of components reliability and switching system reliability are taken into consideration. The main objective is to evaluate the performance of the new strategy compared to traditional strategies in different situations. Obviously, the subsystem reliability has a direct relationship with the components reliability, switch reliability and type of redundancy strategy. This study is an attempt to shed light on the sensitivity of subsystem reliability as a result of switch and component reliability changes in all redundancy strategies.

Nowadays, with technological advances and the need for high reliable systems, extensive research has been done in the eld of reliability optimization. Redundancy allocation problem (RAP) is one of the main issues that has been raised in relation to this subject. Many studies have been carried out in this area and many solutions such as redundancy allocations and component failure rate reduction have been brought up to increase the system reliability. In this paper we considered a seriesparallel system with k-out-of-n subsystems and developed a RAP with components failure rate that depend on the number of working components. In this type of failure rate, when a component fails, the remained components work with more pressure and failure rate of these components increases. The system redundancy strategies are considered as cold standby or active for the subsystems. This model has two objective functions (1) maximizing system reliability and (2) minimizing the system cost. The goals of this model are to select the redundancy strategy between active and cold standby and to determine component type and number of allocated redundant components to each subsystem. As RAP belongs to NP-hard problems, so it is very dicult to optimally solve such a problem by using traditional optimization tools. Therefore for solving the model, two eective meta-heuristic algorithms named Non-dominated Sorting Genetic Algorithm (NSGAII) and Non-dominated Ranked Genetic Algorithm (NRGA) are presented. We use design of experiment (DOE) for parameter tuning of this algorithms response surface methodology (RSM) is applied for determining the optimum amount of parameters. Then to illustrate the eectiveness of algorithms, a numerical example is presented and algorithms are compared using ve dierent performance metrics. In order to determine whether there is a signicant dierence between the performance of algorithms, a single factor ANOVA in signicant level ( = 0:05) is performed. Finally performance of the algorithms is analyzed and the results are reported.