A Joint Optimization of RAM Design and PM Intervals Problem for a Multi-Unit System

Nowadays, large-scale systems perform various missions with multiple functions during life cycles for satisfying the customer’s various needs. Therefore, we should develop the robust and attractive systems and be accurately evaluated prior to development of the system. System availability is often considered to represent the performance of the repairable systems and can be increased through improving system reliability and system maintainability. Usually, system reliability is increased through increasing component reliability (component reliability) or allocating redundancy to the units in the system (redundancy allocation). System maintainability can be improved through performing the maintenance at the module level because of less maintenance times. However, we cannot improve system reliability and system maintainability infinitely because of the limitation of technical and budget. As such, system RAM design is an optimization problem, and in this respect there have been many studies in RAM design to date. Yun et al. [1] wanted to design optimal values of MTBF (Mean time between failures) and MTTR (Mean time to repair) of the components in a multi-unit system. Later, Yun et al. [2] considered more complex reliability structure as stand-by and k-out-of-n structures in a searching system. In recent RAM design literatures, the redundancy allocation has been often studied, as it is difficult to increase the components reliability. Yun and Kim [3] dealt with a multi-level redundancy allocation problem and considered that only one level (system, module or component) can be selected for redundancy. Later, Yun et al. [4] considered that all available levels can be selected simultaneously. Kumar et al. [5] proposed a new genotype method for representing a hierarchical system. Also, He et al. [6] proposed a two-dimensional encoding method to fix the length of a chromosome for representing a hierarchical system. Although highly reliable systems are developed in the system design and development phase, system reliability may be decreased with usage in the operational phase. Therefore, we need to maintain a high degree of system reliability and thus, the systems are commonly maintained periodically and preventively throughout the operational phase. However, frequent PM (Preventive maintenance) incurs high maintenance costs. Therefore, optimal PM policies should be established to provide optimal system reliability and satisfy the required system performance with low maintenance costs. Cepin [7] proposed a simulated annealing algorithm in order to determine an optimal maintenance schedule for a nuclear power plant. Zequeira et al. [8] studied an imperfect PM policy with repairable and non-repairable failure modes and Duarate et al. [9] considered a multi-unit system with linearly increasing hazard rates and constant repair rates. Also, Zhu et al. [10] determined an optimal preventive maintenance threshold and PM intervals of the units that maximize the availability subject to a repair cost constraint. Yun et al. [11] proposed a heuristic method to determine optimal a PM scheduling problem for a rolling stock with cyclic operation. Usually, there is dependency between the components in a multi-unit system and Nicolai and Dekker [12] explained three different types of dependency: economic dependency, structural dependency and stochastic dependency. Laggoune et al. [13] considered a partial periodic renewal policy with minimal repair at failures for a multi-component system. They proposed a multi-grouping maintenance approach in order to coordinate the optimal replacements of the components in the system. To date, many researchers have considered RAM design and PM interval optimization problems separately. However, an efficient and effective PM policy can increase system reliability while reducing development costs which might otherwise be required to increase the component reliability. Therefore, we consider a join optimization problem for a multi-unit system by incorporating system reliability and system maintainability into design considerations, and determining PM intervals of components in the system.