The available method based on statistical principles for aggregating hesitant fuzzy linguistic term set (HFLTS) possibility distribution is the N-two-stage algorithmic aggregation paradigm driven by the K-means clustering (N2S-KMC). Nonetheless, the N2S-KMC method is subject to two significant limitations. (i) The grouping technique is capable of effectively partitioning decision-making information into N groups. However, it does not determine the appropriate placement of members within each group, as the number of computations is dependent on the number of elements present in each group, rather than the elements themselves. (ii) The initial clustering centers of K-means clustering are chosen without adhering to the distribution law within the aggregated hesitant 2-tuple linguistic terms set (H2TLTS) possibility distribution. This may result in a reduction in the clustering performance. In order to address the aforementioned limitations, we suggest two enhancement techniques for the former. Firstly, we propose the utilization of the minimum average difference (MAD) method to ascertain the number of groups. This approach aims to reduce the time required for the initial stage of aggregation following grouping. Secondly, we recommend the implementation of the maximize compactness degree of inter-group grouping (MCDIGG) method. This method enables the identification of group members, resulting in a more concentrated distribution of data subsequent to grouping. The present study suggests the utilization of MAD and MCDIGG techniques as a substitute for the grouping approach in the N2S-KMC model. This leads to the development of a new algorithm, IN2S-DO-KMC, wherein the data is partitioned into K subsets in a descending order to determine the initial center for KMC. Furthermore, with respect to the issue present in the subsequent phase, we propose the utilization of the density canopy (DC) algorithm to perform pre-clustering of the data and produce the initial clustering center and the quantity of clusters for the K-means algorithm. Subsequently, a refined version of the N2S-KMC model, denoted as IN2S-DC-KMC, has been suggested. Ultimately, an empirical study is conducted to assess the validity and practicability of the proposed framework for evaluating failure modes in medical devices. The outcomes are evaluated with regards to the efficacy of the algorithm, the numerical dispersion, and the pragmatic ramifications.