Known Deterministic Coupling

CCF means different things to different people. Smith and Watson (1980) define CCF as the inability of multiple components to perform when needed to cause the loss of one or moi e systems. Virolainen (1984) criticizes some CCF analyses for including design errors and poor quality as CCF and points out that the phenomenological methods do not address physical and statistical dependencies. Here, CCF is classed as known deterministic coupling (KDC), known stochastic coupling (KSC), and unknown stochastic coupling (USC). 

KDC has a cause and effect relationship between as the primary cause leading to secondary failures. Besides its drastic operational effects on redundant systems, the numerical etlects that reduce sy.stem reliability are pronounced Equation 2.4-5 shows that the probability ut failing a redundant. system composed of n components is the component probability raised to the n-th power. If a common clement couples the subsystems. Equation 2.4-5 is not correct and the failure rate is the failure rate of the common element. KDC is very serious because the time from primary failure to secondary failures may be too short to mitigate. The PSA Procedures Guide (NUREG,/CR-2.3(X)) cl.issities this type as Type 2.  

KSC results from an environmental change that affects the probability of failure of the affected components. An obvious example is an increased failure rate due to a change in conditions such as fire, stresses from an earthquake, or improper maintenance practices affecting several components. NUREG/CR-2300 classifies this type of common cause as Type 1.  

USC may be modeled as a power-series expansion of non-CCF component failure nates. No a priori physical information is introduced, so the methods are ultimately dependent on the accuracy of data to support such an expansion. A fundamental problem with this method is that if the system failure rate were known such as is required for the fitting process then it would not be neces.sary to construct a model. In practice information on common cause coupling in systems cannot be determined directly. NUREG/CR-2300 calls this Type 3 CCF. 

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In many cases ordinary differential equations (ODEs) provide adequate models of chemical reactors. When partial differential equations become necessary, their discretization will again lead to large systems of ODEs. Numerical methods for the location, continuation and stability analysis of periodic and quasi-periodic trajectories of systems of coupled nonlinear ODEs (both autonomous and nonautonomous) are extensively used in this work. We are not concerned with the numerical description of deterministic chaotic trajectories where they occur, we have merely inferred them from bifurcation sequences known to lead to deterministic chaos. Extensive literature, as well as a wide choice of algorithms, is available for the numerical analysis of periodic trajectories (Keller, 1976,1977 Curry, 1979 Doedel, 1981 Seydel, 1981 Schwartz, 1983 Kubicek and Hlavacek, 1983 Aluko and Chang, 1984). 

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