Our study aimed to compare ordered ranked set sampling with moving extremes ranked set sampling in the context of type Ⅱ censoring. We focused on deriving Bayesian estimations and predictions using the linear exponential model. This analysis included various loss functions, such as squared error, Al-Bayyati, and general entropy. To evaluate the efficiency of the estimators we produced, we assessed their mean squared error and relative absolute bias. Additionally, we provide Bayesian point and interval predictions for the ordered future lifetime, considering both squared error and general entropy loss functions. To ensure the accuracy and effectiveness of these estimation and prediction methods, we conducted numerical tests using Monte Carlo simulations. Finally, we illustrated these theoretical concepts with a practical example that utilized real-world medical data.