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This chapter describes some of the procedures for evaluating the reliability of a system rather than a single component. The example of the tank farm in the seismically active region shows how this is carried out in practice. Similar efforts have been undertaken for evaluating the safety of dams. Several points will have become obvious to the reader but should be emphasized in any case. First, all the tools and insights of the preceding chapters must be brought to bear on such an analysis, including logic trees, expert elicitation, detailed reliability assessment, and simulation. Second, some components of the system are inevitably better understood than others, and judgment must be applied to include them in the analysis. Third, the major limitation on such studies is not a limitation in reliability theory or methodology or restrictions in computer facilities but the investment of time and effort required for interaction between personnel who understand the system to be studied and those experienced in reliability studies. Finally, effective use of reliability analysis of a system requires commitment by management, as typi ed in the TONEN case just described. Without such commitment, the reliability analysis is a sterile exercise. Of course, the same comment applies to the use of the observational method. It is to be hoped that the future will see broader use of both reliability and observational approaches to deal with complicated geotechnical systems and the two approaches will be combined more closely than in the past.

This observation implies that an AC vector can be used directly for classi cation. However, depending on the sampling frequency of the ECGs, the dimensionality of an AC window can be considerably high, and dimensionality reduction is required. Discrete Cosine Transform for Dimensionality Reduction. The discrete cosine transform (DCT) is applied to the normalized autocorrelation coef cients for dimensionality reduction. This methodology is referred to as AC/DCT. The DCT frequency coef cients are estimated as

CFSTOREDPROC does not enable you to cache a result set produced by a stored procedure. But you can cache it if you call your stored procedure by using a special syntax within CFQUERY, as shown in Listing 9-13.

<cfquery name= CacheFor12Hours datasource= CFMXBible cachedwithin= #CreateTimeSpan(0,12,0,0)# > {CALL sp_GetCompanies( GA )} </cfquery> <cfoutput query= CacheFor12Hours > #CompanyName#, #ZipCode#<br> </cfoutput>

Y [u] = G[u]

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Note This technique works only for stored procedures returning a single result set. If your stored procedure returns more than one result set, you must forego query caching and call your stored procedure by using CFSTOREDPROC.

Summary

(16.2)

Probability theory is a branch of algebra with its own axioms and notation. While one can construct an algebra with almost any set of self-consistent axioms, some are more useful than others, and the particular axioms and theorems of probability theory have proven very useful over the years. The notation is sometimes opaque to the casual user; in this appendix we set out the forms most widely used in civil engineering applications. The rst notation is the expression for the probability of A, where A could be an event, a condition, a state of nature, or almost anything else. We write that the probability of A is P [A]. Obviously, we can replace A with any appropriate expression or phrase such as X x or soil lique es. All the theorems of probability theory can be derived from three axioms: 1. P [A] 0. (That is, a probability must be equal to or greater than zero.) 2. P [A] = 1 means that A is certain. 3. P [A B] = P [A] + P [B] if A and B are mutually exclusive. The notation stand for the union of A and B or that A or B or both occur. The Venn diagram, illustrated in Figure A.1, is a great help in visualizing probability concepts. The rectangular box represents the universe, that is all possible events. The circle labeled A represents event A, and that labeled B represents event B. For axiom 3 these events are mutually exclusive, so their circles do not intersect. Venn diagrams will be used below to elucidate more complicated situations.

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