Known Stochastic Coupling

KSC increases the failure rates of components from causes such as earthquake, fiic. flooding, tornado, erroneous maintenance or inis-sp ecifying the operating cnvironmcni. [ nvironmental qualification (EQ) of equipment, specified by Regulatory Guide 1.97, as.surcs ihc operation of instruments in an accident environment. Similar qualification is required for a tiesi uu-basis earthquake. 

The environmental effects on the failure rate may be modeled using Arrhenius or pow ei laws. In some cases it may be necessary to model the failure rate using the technique of overlapping -.iress/ strength distributions (Haugen, 1972). 

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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). 

Furthermore, synchronization of contraction is facilitated by gap junctional communication as well as synchronization of electrical activation. The electrical coupling between cardiomyocytes mitigates differences in the membrane potential between these cells, for example in the course of an action potential if both cells repolarize at different timepoints. This results in smaller differences in the repolarization times thereby causing a reduction in the dispersion of the action potential duration. Since increased dispersion is known to make the heart more prone to reentrant arrhythmia, sufficient gap junctional communication can be considered as an endogenous arrhythmia-preventing mechanism. For a detailed discussion of the role of gap junctional communication in the biophysics of cardiac activation as related to anisotropy, nonuniformity and stochastic phenomena, see chapter 1 for a discussion of their role in arrhythmia, see chapter 6, and for a possible pharmacological intervention at the gap junctions for suppression of arrhythmia, refer to chapter 7. 

The starting point is the well-known generalized Langevin equation (GLE) as adopted for stochastic motions involving coupling to a solvent coordinate. We employ the notation of Hynes [63] which is consistent with the discussion of solvation in Section II. 

Along with the isomerism of linear copolymers due to various distributions of different monomeric units in their chains, other kinds of isomerisms are known. They can appear even in homopolymer molecules, provided several fashions exist for a monomer to enter in the polymer chain in the course of the synthesis. So, asymmetric monomeric units can be coupled in macromolecules according to "head-to-tail" or "head-to-head"—"tail-to-tail" type of arrangement. Apart from such a constitutional isomerism, stereoisomerism can be also inherent to some of the polymers. Isomers can sometimes substantially vary in performance properties that should be taken into account when choosing the kinetic model. The principal types of such an account are analogous to those considered in the foregoing. The only distinction consists in more extended definition of possible states of a stochastic process of conventional movement along a polymer chain. 

Complex pharmacokinetic/pharmacodynamic (PK/PD) simulations are usually developed in a modular manner. Each component or subsystem of the overall simulation is developed one-by-one and then each component is linked to run in a continuous manner (see Figure 33.2). Simulation of clinical trials consists of a covariate model and input-output model coupled to a trial execution model (10). The covariate model defines patient-specific characteristics (e.g., age, weight, clearance, volume of distribution). The input-output model consists of all those elements that link the known inputs into the system (e.g., dose, dosing regimen, PK model, PK/PD model, covariate-PK/PD relationships, disease progression) to the outputs of the system (e.g., exposure, PD response, outcome, or survival). In a stochastic simulation, random error is introduced into the appropriate subsystems. For example, between-subject variability may be introduced among the PK parameters, like clearance. The outputs of the system are driven by the inputs... 

We will be mainly concerned with external noise, where the stochastic character of the system is due to random time variations in the coupling of the system to its environment. The stochastic properties of the external noise are known in this case. 

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