Diagnosability in stochastic Petri Net based DES models

Failure Detection and Diagnosis (FDD) has become an important part for most modern day complex systems. Discrete Event System (DES) paradigm has been applied for FDD of a wide range of applications because of modeling simplicity and computational efficiency due to abstraction. Several variants of DES frameworks namely, FSMs, process algebra, Petri Nets (PN) etc. have been used for FDD based on the type of system being considered. In most of the works on FDD of DES models, the conclusion was binary i.e., diagnosable or non-diagnosable. Thorsley et al. investigated diagnosability of stochastic DES, where failure is determined when it is found that probability of the system traversing though failure states is higher than a threshold (which may be dynamic). Thorsley's work was based on FSM based DES models, which are suitable for centralized systems. In this paper we will concentrate on PN based DES framework which is mainly applicable for decentralized systems. FDD algorithms for PN based DES work successfully for systems where binary decisions regarding diagnosability suffice. However, there exist many decentralized systems where incorporation of stochastic information in the models and diagnosability decisions by comparison with a threshold are more practical. In this paper we propose a new FDD mechanism for Stochastic PN based DES models. The scheme is illustrated on a simple chemical reaction chamber.