Abstract
Background: The main key input variables to this optimization technique for constructing incomplete block designs are using bipartite and spanning subgraphs through numerical examples of vehicle fuel consumption and emissions. The theory of graphs plays a significant role in mathematical sciences and engineering technologies. In addition, the graph models many relations and processes in physical, biological, social, and information systems.
Aims and Objectives: The construction methods using Partially Incomplete Block Designs (PBIBD) with differential equations through bipartite and spanning subgraphs that predict hot stabilized vehicle fuel consumption and emission rates for different drivers using different cars are studied in this paper. The other modelling of fuel consumption and emissions have appeared as an essential tool, which helps to develop and measure vehicle techniques and to help estimate vehicle fuel consumption and emissions. This paper aims to develop an optimization technique for the construction method for incomplete block designs LSD with PBIBD(2) through vehicle fuel consumption and emissions.
Methods: An incomplete block design can be constructed using LSD statistical analysis with bipartite and spanning subgraphs. First, the method for the construction of LSD using bipartite graphs. The second method for the construction of PBIBD(m) using spanning subgraphs. The two construction methods are through numerical examples of an oil company testing five mixings of petrol for fuel efficiency and emission according to the variability of five drivers and five models of cars.
Results: The inference of the first model of PBIBD(2) using LSD F-value of 0.08 implies the model is not significant (P-values greater than 0.05). The second model has no significant difference between petrol fuel efficiency and emissions. In the third model, there is no significant difference in fuel efficiency between different cars of petrol bunks.
Conclusion: Finally, it is concluded that the response variable is represented above the maximum quality scores from our fourth driver using a second car to the fourth petrol bunk in fuel efficiency.
