Polynomial Representation of Markov Process and its Application for Dynamic Availability Analysis of Artillery Rocket Systems  
Author A. Lisnianski


Co-Author(s) E. Levit


Abstract In the paper polynomial representation of Markov process is suggested for dynamic availability analysis of high responsible large-scale multi-state systems. Such systems are widely used either in civil industry (for example, for exploration and measurement different parameters in aggressive environments), or for military purposes. In the paper considered a rocket launching system. The system developed to meet the battlefield challenges of special forces operating in remote, high-risk missions that are beyond the range of traditional artillery fire support, and consequently do not have significant or sufficient fire assistance. The typical system, which is considered in the paper, consists of n launching vehicle platforms and, on each platform, installed m artillery rockets. Each rocket and platform are presented as three-state components – completely available state, minor repair state and replacement state. So, the entire system is interpreted as Multi-state System. In general case the system may consists of n platforms, where each one has m rockets. Finally, n and m may be enough big even for a few artillery battalions. In such cases, entire system is large-scale and for its commander is very important at each time instant to know its real availability and performance that substantially depend on recent initial conditions of the system. It was shown that there is a great difference between steady-state availability and performance and instantaneous (short-term) availability and performance indices that significantly depend on initial states of all rockets and platforms. For high responsible system this difference is very important. A main obstacle in the problem solution is its large dimensionality. In order to overcome this difficult, polynomial representation of Markov process (LZ-transform) was used. This method has low computational complexity, facilitating Multi-state Systems reliability and availability analysis. Numerical example with two battalions of rockets launching rockets systems is presented to illustrate the proposed method.


Keywords rocket launching system, large-scale multi-state system, availability, polynomial representation of Markov process, LZ-transform
    Article #:  RQD28-385

Proceedings of 28th ISSAT International Conference on Reliability & Quality in Design
August 3-5, 2023