Application of Extended Universal Generating Function Technique to Dynamic Reliability Analysis of a Multi-state System

Abstract

The paper presents an overview of applications of a new special technique to reliability assessment for complex multi-state system. The system and its components can have different performance levels ranging from perfect functioning to complete failure. Straightforward Markov method applied to solve the problem will require building of the system model with great number of states and solving a corresponding system of differential equations. Lz-transform method, which is used for reliability assessment, drastically simplified the solution. Instead of straightforward finding of the resulting output stochastic process for entire Multi-state system (MSS) the method proposed finding Lz-transform of this output process, which is essentially simpler because of using Ushakov's Universal Generating Operator. Some reliability indices such as availability, expected performance, etc. may be found from the expression of this Lz-transform. In order to find other indices such as reliability function, mean time to failure etc. inverse LZ-transform is using that completely reveals underlying output process. This special technique is called as Extended Universal Generating Function Technique. The technique was already applied to multi-state system reliability analysis in some research works. The paper presents an overview of this accumulated experience.