Inference for dependent competing risks model under m-cycle minimum ranked set sampling

Minimum ranked set sampling offers an effective approach for collecting failure time data while optimizing testing resources. This paper examines dependent competing risks model within the context of m-cycle minimum ranked set sampling data. Assuming that component lifetimes adhere to a two-parameter generalized inverted exponential distribution, we develop dependence structures utilizing the Marshall-Olkin distribution framework. The study establishes maximum likelihood estimation and Bayesian inference procedures under both unrestricted parameters and ordered restrictions. The theoretical analysis confirms the existence and uniqueness conditions for maximum likelihood estimators, with corresponding interval estimators being subsequently derived. For Bayesian inference, we derive posterior estimates under flexible prior specifications, employing Metropolis-Hastings and importance sampling algorithms to address complex posterior calculations. Through comprehensive numerical simulations and real-world case analysis, this study systematically evaluates the comparative performance of different estimation approaches while examining how cyclic sampling strategies influence estimation precision. Finally, implementation guidelines and production-oriented conclusions are provided based on the study results.