Probabilistic diagnostics with P-graphs

This paper presents a novel approach for solving the probabilistic diagnosis problem in multiprocessor systems. The main idea of the algorithm is based on the reformulation of the diagnostic procedure as a P-graph model. The same, well-elaborated mathematical paradigm - originally used to model material flow - can be applied in our approach to model information flow. This idea is illustrated by deriving a maximum likelihood diagnostic decision procedure. The diagnostic accuracy of the solution is considered on the basis of simulation measurements, and a method of constructing a general framework for different aspects of a complex problem is demonstrated with the use of P-graph models

Gradient based system-level diagnosis

Traditional approaches in system-level diagnosis in multiprocessor systems are usually based on the oversimplified PMC test invalidation model, however Blount introduced a more general model containing conditional probabilities as parameters for different test invalidation situations. He suggested a lookup table based approach, but no algorithmic solution has been elaborated until our P-graph based solution introduced in previous publications. In this approach the diagnostic process is formulated as an optimization problem and the optimal solution is determined. Although the average behavior of the algorithm is quite good, the worst case complexity is exponential. In this paper we introduce a novel group of fast diagnostic algorithms that we named gradient based algorithms. This approach only approximates the optimal maximum likelihood or maximum a posteriori solution, but it has a polynomial complexity of the magnitude of O\left (N \cdot NbCount + N^2\right ), where N is the size of the system and NbCount is number of neighbors of a single unit. The idea of the base algorithm is that it takes an initial fault pattern and iterates till the likelihood of the actual fault pattern can be increased with a single state-change in the pattern. Improvements of this base algorithm, complexity analysis and simulation results are also presented. The main, although not exclusive application field of the algorithms is wafer-scale diagnosis, since the accuracy and the performance is still good even if relative large number of faults are present