Lz -transform: Definition, Main Properties and Examples

The Chapter presents the Lz-transform, a specific approach, which has been widely applied to Multi-state systems (MSS) reliability analyses. This approach allows one to algebraically find the entire MSS performance distribution through the performance distribution of its elements. In contradict to Universal Generating Function techniques, operated with steady-state performance distribution, the Lz-transform may be applied to dynamic MSS reliability analyses of a discrete-state continuous-time Markov process. In this Chapter, we present the Lz-transform definition, its main properties, some simple examples of applications and their numerical solution with MATLAB software.