# Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach
## 2 Literature Review  
The GPP is a relatively new method of solving nonlinear programming problems. It is used to minimize functions in the form of posynomials subject to constraints of the same type. Practical algorithms have been developed for solving geometric programming problems [1; 2; 3]. [PERSON] [5] proposed the posynomial GPP subject to fuzzy relation inequalities. In 2018, [PERSON] and [PERSON] [6] also studied a class of posynomial GPPs that considers the evaluation of a posynomial GPP subject to fuzzy relational equations with max-min composition. [PERSON] and [PERSON] [7] also addressed the interval-based solution approach for solving transportation problems under varying input parameters. [PERSON] et al. [8] discussed the multiobjective GPP with the aid of fuzzy geometry. [PERSON] et al. [9] presented the reliability optimization problem under an intuitionistic environment. [PERSON] and [PERSON] [10] investigated the modified GPP and applied it to many engineering problems. [PERSON] and [PERSON] [11] developed a new multiobjective GPP model and used it to solve the transportation problem. Recently, a interesting study on GPP was presented by [12; 13; 14; 15]. [PERSON] et al. [16] developed a new optimization technique for GPP. [PERSON] and [PERSON] [17] also solved the reliability of a system using the GPP approach.  
However, the geometric programming research approach in the field of reliability optimization is being performed in the context of mathematical modeling and real-life applications. Some recent work is also available on the system reliability, ensuring a significant contribution to the literature. [PERSON] et al. [18] presented a hybrid optimizer model for system reliability. [PERSON] and [PERSON] [19] developed a stochastic model for multi-microgrid constrained reliability system and applied it to clean energy management. [PERSON] and [PERSON] [20] proposed an integrated system reliability model for the inbuilt component under uncertainty. [PERSON] and [PERSON] [21] developed a novel computational strategy for redundant components in the system reliability optimization. [PERSON] et al. [22] discussed the interval parameters by the sequential moving asymptote method for the system reliability based on the integrated co-efficient approach. [PERSON] et al. [23] presented a research work by integrating the second-degree difficulty in carbon ejection controlled, reliable, innovative production management and implemented it on a computational dataset. [PERSON] et al. [24] used the modeling texture of the GPP in the levelized cost of energy-oriented modular string inverter design and discussed it in the field of PV generation systems. [PERSON] et al. [25] also introduced a novel method for energy-efficient ultrareliability using the outage probability bound and the GPP technique. [PERSON] et al. [26] designed multi-objective single-phase differential buck inverters by considering an active power decoupling and applied it to power generation. [PERSON] and [PERSON] [27] suggested the geometric programming approach for optimizing multi-VM migration by allocating transfer and compression.  
All the studies are confined to either fuzzy- or stochastic-based approaches, but it may possible that input parameters may vary within some specified intervals bounded by upper and lower bounds. In this situation, the fuzzy and stochastic approaches may not be applied successfully. Thus, to overcome this issue, we developed a bounded solution method comprising the two-level GPP, and the values of the objective function are obtained directly. Hence, the present study lays down a new direction for obtaining the optimal solution under the varying parameters. The proposed method is applied to system reliability optimization problems and yields a result without affecting the system reliability under variations.