A quantum-inspired model for statistical analysis of repairable systems

Abstract

Extensive number of models have been proposed in literature to describe the failure-repair-failure process, with the aim of obtaining a better fit of failure data in a specific application area. This paper implements an alternative approach to model the repairable systems with the application of quantum mechanics theory. With the Hilbert structure describing the system state, a non-Hermitian time-dependent Schrodinger equation is utilized to describe the intrinsic failure process. Then a repair operator is introduced to represent the degree of repair by changing the time-dependent probability amplitudes of the system state. By this means, we developed two quantum repair models for the cases of different state restoration degree. To demonstrate the validity of the proposed models for both single and multiple systems, three real-world data sets are employed and the results show that the proposed model has better fitting performance compared with the most commonly used classical repair models. Quantum mechanism indicates its validity and practical appeal of application in industry and reliability modelling.