A new framework of complex system reliability with imperfect maintenance policy

Abstract

The interactions and dependencies between software and hardware are often neglected in modeling system reliability in the past few decades due to the mathematical complexity. However, many system failures occurred from the interactions or simultaneous occurrences of software and hardware. This paper first proposes a new diagram of categorizing system-level failures and further incorporates such a diagram into the development of complex system reliability framework. System-level failures result from software subsystem, hardware subsystem, and the interactions of software and hardware subsystems. The focus of this study is on the investigation of the interactions failures generated from the interactions of software and hardware subsystems. In addition to the considerations of total hardware failures, software-induced hardware failures, and hardware-induced software failures introduced by Zhu and Pham (Mathematics 7(11):1049, 2019), we further introduce the partial hardware failures that can be respectively induced by hardware and software to explicitly demonstrate the dependencies and interactions between software and hardware. Hence, a new complex system reliability framework is developed based on such system-level failure categorization with the Markov process. Furthermore, the numerical examples are studied to illustrate the impacts on system reliability with the changes of state transition parameters that modeling the interactions of software and hardware subsystems. Finally, we have studied two maintenance policies of the proposed complex system reliability model.