Constract A New Ballistic Missile model by Line Graph and Measuring its Reliability

Abstract

This study presented a mathematical approach for analysing the reliability of a ballistic missile system using the Line Graph technique from graph theory. The missile structure was modelled by representing the relationships between its main components such as the missile body, propulsion system, fuel system, payload, control unit, guidance system, and fins. The reduction method was applied to simplify the complex network of components and identify the critical paths within the system.

  Several reliability measures were employed to evaluate the system performance, including system reliability, Mean Time to Failure (MTTF), hazard rate, Shannon entropy, and extropy.  These measures provide a theoretical framework for understanding system behaviour and uncertainty in failure processes. The use of line graphs also helped visualize the structural relationships between components and analyze reliability behavior over time.                                                                                                                   Overall, the proposed model demonstrates how graph theory and reliability techniques can be combined to study complex engineering systems and support the improvement of system design and performance under operational condition