To collect failure data while saving time and money, ranked set sampling (RSS) offers an effective and adaptable method. The inference of a competing risk model is suggested in this work using the widely used RSS known as minimum ranked set sampling with unequal sample configuration. Classical and Bayesian estimations are examined, respectively, where the lifetimes of competing risks have generalized lifetime distribution and the related failure causes are partially observable. The existence and uniqueness of maximum likelihood estimators (MLEs) are established, and approximate confidence intervals (ACIs) are also computed. Bayesian estimators and credible ranges for the highest posterior density (HPDs) are discussed under general flexible priors. Maximum likelihood and Bayesian estimations are also discussed when there is an extra order restriction available. In the end, two real-world data and in-depth simulation studies are provided as examples.