The present manuscript optimized the First and Second Law performance of the triple effect vapour absorption refrigeration systems (TE-VARS) using statistical techniques like Taguchi, Taguchi-based GRA, and RSM-based GRA methods, which provide the most accurate and optimized results. Liquified pertrolium gas (LPG) and Compressed natural gas (CNG) are considered as the source of energy to operate TE-VARS, as the system requires significantly higher generator temperature. Also, volume flow rate of these gases along with the annual operating cost to drive the system have been presented. A thermodynamic model was first formulated using EES software for the computation of the coefficient of performance (COP) and exergetic efficiency (ECOP). The most influential parameters like temperature in the main generator, concentration and pressure at different components are studied and determined using ANOVA and Taguchi methods. The optimum parameters were determined based on the mean effect plot of S/N ratios for COP and ECOP. It has been found that the maximum COP and ECOP were calculated to be 1.915 and 0.15, respectively under the Taguchi method. Furthermore, Taguchi-GRA was used for the simultaneous optimization of the operating parameters and performance of the system. It is observed that the absorber temperature is the most influential parameter for affecting COP and ECOP. Moreover, a RSM-based GRA method was also applied and developed regression models that yield most optimum COP and ECOP as 1.963 and 0.1606, respectively. Comparison shows that the RSM-based GRA method provide the most optimum conditions, which is one of the key finding of the present study. Also, rate of exergy destruction at each component of TE-VARS has been plotted under optimized operating conditions. The optimum volume flow rate for LPG and CNG comes out to be 0.057 and 0.177 m3/s, while the minimum operating cost (yearly) are 299.827$ and 183.293$, respectively.

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