Fault diagnosis is constantly crucial to maintain a high level of multiprocessor systems’ reliability. In multiprocessor systems, global fault diagnosis has been extensively investigated under both deterministic and probabilistic models, while local fault diagnosis has only been committed to the deterministic models, such as PMC model and MM$^*$model. This work focuses on a probabilistic approach for local diagnosis at a node within the mixed structure under the PMC diagnostic model so that the state of this node can be identified correctly by utilizing maximum a posteriori probability. This work is devoted to the quantitative metric on global reliability of multiprocessor systems in terms of local fault probability of node under microscale. The proposed strategy effectively reduces diagnostic delays and enhances system response in practical applications and thus improves the efficiency and accuracy of fault detection. In addition, the probabilistic approach reduces the effect of uncertainty on the fault diagnosis, which in turn improves the reliability and safety of the system. In this work, we first perform a more precise syndrome analysis for this mixed structure under the PMC model by virtue of local testing results, and suggest a modified local diagnosis algorithm calledMLDA. Subsequently, we implement the maximum a posteriori probabilistic local diagnosis algorithm calledMAPPLDAfor the mixed structure under the probabilistic PMC diagnostic model. Finally, numerical simulation results confirm the effectiveness of the syndrome analysis approach and the maximum a posteriori probability approach for the mixed structure when the node failure probability is very small.

The$(f_{1},f_{2})$-bounded symmetric comparison ($(f_{1}, f_{2})$-BSC) model, proposed by Fuhrman and Nussbaumer in 1996, is a hybrid of the symmetric comparison model and asymmetric one, which assumes that at most$f_{1}$processors fail while the upper threshold of faulty processors producing identical outcomes is$f_{2}$. Based on the$(f_{1},f_{2})$-BSC model, a novel model, abbreviated as the$f$-BSC model, is proposed by dropping the restriction on$f_{1}$but highlighting the hypothesis on maximum number of faulty processors producing identical outcomes is$f$. As a generalization of this model, a variant of MM$^*$model abbreviated as the$f$-BMM$^*$model is proposed by adding an upper threshold$f$to the number of faulty processors producing identical comparison outcomes, which are executed by a faulty comparator on two faulty neighbouring processors. Under this restriction, fewer possible syndromes are generated and therefore faulty processors can be diagnosed faster and more accurately. Subsequently, we present diverse characterizations regarding system-level diagnosis under the two new models. Moreover, we further establish the metric correlation between$g$-good-neighbor ($g$-GN) diagnosability under$f$-BMM$^*$model and$R^{g}$-connectivity of general networks. Finally, the$g$-GN diagnosabilities under$f$-BMM$^*$model are characterized among five preeminent interconnection networks.