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Several mathematical models have been developed in the past to consider reliability when designing energy systems. However, these models focus on the system reliability which only considers the operability of the system. Hence, a reliability indicator called supply reliability is introduced to explicitly assess an energy system's reliability meeting the desired energy demand. Besides, previous models can only allocate equipment with identical sizes and equipment reliability. This could overdesign systems and ignore the possibility of allocating a combination of different equipment sizes and reliability. This paper presents a combinatory matrix methodology for allocating equipment with different sizes and reliabilities to improve supply reliability of an energy system design. This combinatory matrix method is a novel feature that allows decision-makers to efficiently evaluate various configurations of equipment based on size and reliability. A case study consisting of a power distribution network is first presented and solved as a pedagogical example to illustrate the methodology and features of the proposed approach. Then, a large-scale power system case study in Malaysia combining existing conventional power equipment and a palm-based bioelectricity supply chain is solved. Based on the optimized results, the redundancy allocated increased the energy generated from the bioelectricity supply chain by 74.14% and cost by 82.96% to achieve the desired energy demand at high supply reliability. This allows decision-makers to determine the cost associated with improving supply reliability for an energy system. [ABSTRACT FROM AUTHOR]