Reliability Evaluation of Augmented Cubes on Degree

The [Formula: see text]-dimensional augmented cube [Formula: see text], proposed by Choudum and Sunitha in 2002, is one of the most famous interconnection networks of the distributed parallel system. Reliability evaluation of underlying topological structures is vital for fault tolerance analysis of this system. As one of the most extensively studied parameters, the [Formula: see text]-conditional edge-connectivity of a connected graph [Formula: see text], [Formula: see text], is defined as the minimum number of the cardinality of the edge-cut of [Formula: see text], if exists, whose removal disconnects this graph and keeps each component of [Formula: see text] having minimum degree at least [Formula: see text]. Let [Formula: see text], [Formula: see text] and [Formula: see text] be three integers, where [Formula: see text], if [Formula: see text] and [Formula: see text], if [Formula: see text]. In this paper, we determine the exact value of the [Formula: see text]-conditional edge-connectivity of [Formula: see text], [Formula: see text] for each positive integer [Formula: see text] and [Formula: see text], and give an affirmative answer to Shinde and Borse’s corresponding conjecture on this topic in [On edge-fault tolerance in augmented cubes, J. Interconnection Netw. 20(4) (2020), DOI:10.1142/S0219265920500139].

Reliability Evaluation of CNC Machine Tools Considering Competing Failures of Fault Failure Data and Machining Accuracy Degradation Data

Traditional reliability evaluation of CNC machine tools usually considers a single failure mode of fault failure or degradation failure, or considers fault failure and degradation failure to be independent of each other. However, in the actual working conditions, fault failure and degradation failure are mutually affected, and the reliability evaluation of the competing failure models of CNC machine tools by considering the two failure modes comprehensively can get more accurate evaluation results. Therefore, this paper proposes a reliability evaluation method for CNC machine tools considering fault failure data competing with machining accuracy degradation data. A fault failure model of CNC machine tools is established based on a non-homogeneous Poisson process. The fault failure model is updated according to the different effects of each maintenance result of the failure on machining accuracy. By integrating multiple geometric errors of CNC machine tools through multi-body system theory, the amount of machining accuracy degradation is extracted. A machining accuracy degradation failure model is established using the Wiener process. Considering the correlation between fault failure and degradation failure, a competing failure model based on the Coupla function is developed for evaluating the reliability of CNC machine tools. Finally, the effectiveness of the proposed method is verified by example analysis.