<p>In modeling competing risk data, one of the main goals is to identify the significant covariates that influence the hazard function. However, it is often not possible to include all relevant covariates in the analysis, which introduces heterogeneity into the population. To tackle the issue of unobserved heterogeneity, frailty models can be an effective solution. Additionally, there may be a subset of individuals in the population who are non-susceptible to the event of interest. This situation can be modeled using frailty models that incorporate a compound distribution as the frailty distribution. This paper aims to advance the frailty model framework by incorporating non-susceptibility in the context of competing risks. This paper broadly explores the compound power series family of frailty models, highlighting the compound Poisson and compound negative binomial distributions as specific types of frailty distributions. The likelihood function is developed using hybrid censoring schemes, and the inferential problem is addressed with a computational Bayesian approach, specifically employing MCMC methods. Finally, we will demonstrate the application of the proposed models by analyzing two real-world datasets.</p>