On sensitivity analysis of aging multi-state system by using LZ-transform

The paper considers a sensitivity evaluation for an aging multi-state system (MSS) under minimal repair. Investigation of an impact of changing different failure/repair rates of different elements in MSS is important for practical reliability engineering. In practical reliability engineering a "curse of dimensionality" (the large number of states that should be analyzed for a multi-state system model) is a main obstacle for sensitivity assessment. Straightforward Markov Method applied to solve this problem requires building a model with numerous numbers of states and solving a corresponding system of differential equations. In order to solve this problem, the paper proposes to use a new method based on an LZ-transform of the discrete-state continuous-time Markov process, and on Ushakov's Universal Generating Operator. New sensitivity measures useful for aging MSS reliability analysis were introduced. It was shown that the proposed method drastically reduces a computational burden. A numerical example is presented in order to illustrate the approach.