aspg-1-3396-1792176615 20261016185015 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group American Journal of Business and Operations Research AJBOR 2770-0216 2692-2967 2025 12 2 Muddassar Sarfraz School of Management, Zhejiang Shuren University, PR China The suggested models for the spread of technical breakthroughs make use of a phase structure to illustrate the steps involved in becoming familiar with the problem and making a choice. For it to portray genuine adopting conduct, a time-lag factor is included into the dispersion process. Depicts a two-step dissemination process by taking into account the reliance of adopting on the informed group of potential purchasers. Assuming that a prospective customer first becomes intrigued by an upcoming the item's availability and then accepts the novel idea at an ulterior point, a method of analysis for sales functions that incorporates time delay is proposed. The efficient propagation method for invention is shown using the various lag factors. Applying nonlinear regression modelling to worldwide shipping data of Acer PCs and Samsung smartphones experimentally validates the suggested models for mathematics. Several comparison models are used to evaluate the predicting abilities of the suggested models. By integrating a distributed time delay function into the implementation manage, a theoretical intergenerational diffusion model is created. To measure how long it takes for innovation to be eventually accepted, the distributed time lag function that follows the Erlang distributions is used. This framework incorporates switch and substituting, two forms of pragmatist shift behaviour. Using real shipping data of LCD (Liquid Crystal Display) computer monitors from consecutive generations, the predicted effectiveness of the suggested methods is examined and contrasted with well-established research. Here is the total accuracy of the approaches that have been proposed: When contrasted with more conventional models, MGDM 1 achieves a 99.33% accuracy rate, MGDM 2 a 99.81% rate, and MGDM 3 a 99.91% accuracy rate. 2025 10 20 3396 https://creativecommons.org/licenses/by/4.0/ 10.54216/AJBOR.120202 https://americaspg.com/journal/1/article/3396 https://americaspg.com/storage/articles/manuscripts/01M07T9QC56917HQXQ6JK2Q1N5.pdf