On Birnbaum importance assessment for aging multi-state system under minimal repair by using the Lz-transform method. (October 2015) - Lisnianski, Anatoly; Frenkel, Ilia; Khvatskin, Lev
Abstract: 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.