In recent years, several novel modeling applications have been able to better fit complex datasets, and they can provide insights that would not be possible with traditional distributions. A new model developed by mixing the exponential and gamma models, called the Garima model, is discussed in this article. This model exhibits a better behavior fit than exponential and Lindley, among others. When the reliability practitioner wishes to score a specific number of failed units, a generalized progressive-hybrid-censored Type-II technique has been proposed to reduce both the length and expense of a life test. Given the availability of the presented data, the difficulty of estimating the scale parameter and various reliability time aspects of the Garima model is investigated using likelihood and Bayes inferential approaches. In addition, when the Garima parameter is assumed to have gamma density prior, the Markovian-Chain via Monte-Carlo sampler from a symmetric loss is performed to obtain the symmetric Bayes’ infer. Besides the asymptotic confidence intervals, the highest intervals for all unknown subjects are also developed. Simulation comparisons are also carried out, and useful recommendations are provided. A real data application is examined based on genuine datasets from the physical sector to see how the examined approaches may be implemented in real-life situations.