Event space method

Fault Trees and Reliability Block Diagrams are both methods of showing probability combinations. There have been a number of solution techniques developed to solve probability combinations. These include Cut Sets, Tie sets. Event Space, Decomposition Method, Gate Solution Method, and many others. In this appendix three examples will be shown - the Event Space method and the Cut Set method, and the Gate Solution Method. Details and full development of the methods can be found in (Ref. 1) Chapter 5. 

One technique that provides a comprehensive overview of a probability combination model is the event space method. The authors have used this technique especially when a detailed knowledge of probability combinations is needed to optimize a design. The method is called systematic and comprehensive. 

To solve the fault tree or the reliability block diagram via the event space method one creates a list of all combinations of successful and failed components. For each line in the list, the probability is listed and the system operation (success or failure) is listed. By convention, this is done by quantity of failed units. 

Solution Using the event space method a table is created showing all combinations of successful and failed components starting with all components successful. This is shown in Table C-1. 

Using the event space method as shown in Figure C-5, the entire picture is laid out for easy checking. 

Figure C-5. Event Space Method for Fire Sensor System...

Fluence-Based and Microdosimetric Event-Based Methods for Radiation Protection in Space (2001)... 

The brute force method depends on a systematic variation of all involved coefficients over a reasonable parameter space. The combination yielding the lowest goodness-of-fit measure is picked as the center for a further round with a finer raster of coefficient variation. This sequence of events is repeated until further refinement will only infinitesimally improve the goodness-of-fit measure. This approach can be very time-consuming and produce reams of paper, but if carefully implemented, the global minimum will not be missed, cf. Figures 3.4 and 4.4. 

Thus, the turbulent-reacting-flow problem can be completely closed by assuming independence between Y and 2, and assuming simple forms for their marginal PDFs. In contrast to the conditional-moment closures discussed in Section 5.8, the presumed PDF method does account for the effect of fluctuations in the reaction-progress variable. However, the independence assumption results in conditional fluctuations that depend on f only through Tmax(f ) The conditional fluctuations thus contain no information about local events in mixture-fraction space (such as ignition or extinction) that are caused by the mixture-fraction dependence of the chemical source term. 

Transition state theory (TST) (4) is a well-known method used to calculate the kinetics of infrequent events. The rate constant of the process of interest may be factored into two terms, a TST rate constant based on a knowledge of an equilibrium phase space distribution of the system, and a dynamical correction factor (close to unity) used to correct for errors in the TST rate constant. The correction factor can be evaluated from dynamical information obtained over a short time scale. 

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