On Birnbaum importance assessment for aging multi-state system under minimal repair by using the L_z-transform method

This paper considers a reliability importance evaluation for components in an aging multi-state system. 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 importance assessment. In order to challenge the problem, this paper proposes a new method that is based on an L_Z-transform of the discrete-state continuous-time Markov process and on Ushakov's Universal Generating Operator. The paper shows that the proposed method can drastically reduce a computational burden. In order to illustrate the method, a solution of a real world problem is presented as a numerical example. - Highlights: • Aging multi-state system under minimal repair is studied. • A new method for Birnbaum importance assessment is developed. • The method is based on the L_Z-transform. • The proposed method provides a drastic reduction of computation burden. • Numerical example is presented in order to illustrate the method