Formal semantics of models for computational engineering: a case study on dynamic fault trees

Abstract

Computational modeling tools are critical to engineering. In the absence of a suficiently complete, mathematically precise, abstract specification of the semantics of the modeling framework supported by such a tool, rigorous validation of the framework and of models built using it is impossible; there is no sound basis for program implementation, verification or documentation; the scientific foundation of the framework remains weak; and significant conceptual errors in framework definition and implementation are likely. Yet such specifications are rarely defined. We present an approach based on the use of formal specification and denotational semantics techniques from software engineering and programming language design. To illustrate the approach, we present elements of a formal semantics for a dynamic fault tree framework that promises to aid reliability analysis. No such specification of the meaning of dynamic fault trees has been defined previously. The approach revealed important shortcomings in the previous, informal definitions of the framework, and thus led to significant improvements, suggesting that formally specihing framework semantics is critical to effective framework design.

Explicit Modelling and Treatment of Repair in Prediction of Dependability

“…The Failure Automaton (FA) defines the effect of all possible failure and repair events [20]. To define the FA, first it is necessary to model the system failure logic using a dependability model.…”

“…That is, stochastic events are replaced with timed activities (lines 11-14); immediate events are replaced with instantaneous activities (lines 15-21); if the instantaneous event's name matches with any of the input propagated events name (line 19), create the corresponding place in the component to propagate the effect of its marking change inwards, i.e., event propagation (lines 20,21). If the event is a conditional event, create the corresponding logic in SAN using IGs and places that model the events implicated in the transition events.…”

SFRs-based numerical simulation for the reliability of highly-coupled DFTS

“…To characterize sequence-and function-dependent failure behaviors existing in many real-life systems, Dugan et al [5,6] introduced several new dynamic gates, such as Sequence Enforcing (SEQ) gate, Priority AND (PAND) gate, Function Dependent (FDEP) gate, Cold Spare (CSP) gate, Warm Spare (WSP) gate, and Hot Spare (HSP) gate. Such dynamic gates are integrated into static fault trees to form DFTs.…”

The How and Why of Interactive Markov Chains

“…If one assumes that failure occurences follow exponential laws, which is a standard and sometimes justified assumption, it seems natural to expect that the resulting model is a CTMC. Actually, the first complete formalisation attempted [21] aimed at providing a CTMC semantics, but revealed a number of ambiguities in the DFT framework. Most notably, in some instances of DFTs non-determinism arises.…”