Employing an improved adaptive Type-II progressively censored sample, this paper provides various point and interval estimations when the parent distribution of the population to be studied is the inverted Lomax distribution. The estimations include both the model parameters and two reliability metrics, namely, the reliability and failure rate functions. Both maximum likelihood and maximum product of spacing are studied from the conventional estimation standpoint. Along with the point estimations utilizing the two traditional approaches, the approximate confidence intervals based on both are also examined. The Bayesian point estimations with the squared error loss function and credible intervals for various parameters are investigated. Depending on the source of observed data, Bayesian estimations are obtained using two different types of posterior distributions. Numerous censoring designs are looked at in the simulation study to compare the accuracy of classical and Bayesian estimations. Using both conventional methodologies, several optimality metrics are suggested to identify the best removal design. One chemical and a pair of engineering actual data sets are examined to support the significance of the indicated methodologies. The analysis showed that the Bayesian estimation, using the likelihood function, is preferable when compared to other classical and Bayesian methods.