A novel inverted generalized gamma (IGG) distribution, proposed for data modelling with an upside-down bathtub hazard rate, is considered. In many real-world practical situations, when a researcher wants to conduct a comparative study of the life testing of items based on cost and duration of testing, censoring strategies are frequently used. From this point of view, in the presence of censored data compiled from the most well-known progressively Type-II censoring technique, this study examines different parameters of the IGG distribution. From a classical point of view, the likelihood and product of spacing estimation methods are considered. Observed Fisher information and the delta method are used to obtain the approximate confidence intervals for any unknown parametric function of the suggested model. In the Bayesian paradigm, the same traditional inferential approaches are used to estimate all unknown subjects. Markov-Chain with Monte-Carlo steps are considered to approximate all Bayes’ findings. Extensive numerical comparisons are presented to examine the performance of the proposed methodologies using various criteria of accuracy. Further, using several optimality criteria, the optimum progressive censoring design is suggested. To highlight how the proposed estimators can be used in practice and to verify the flexibility of the proposed model, we analyze the failure times of twenty mechanical components of a diesel engine.