In this paper, the problem of estimation when X and Y are two independent upper record values from gamma Lindley distribution is considered. Maximum likelihood and the Bayesian estimator methods were used to set the best-estimated reliability function. The importance of this research is because this model, when applied, can obtain reliability values that depend on upper record values, which is an interesting problem in many real-life applications. Also, based on WHO data on the COVID-19 pandemic, a stress-strength model was applied based on the upper recorded values for Mont-Carlo simulation data.