By Jack C. Richards
A accomplished direction in listening abilities.
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Extra info for Basic Tactics for Listening, 1st Edition
Xn Þ; the corresponding system will also be denoted by ðu; f Þ: Denote by sðu; f Þ the probability-signature of ðu; f Þ: For our aims, the following definition is useful. Let ðu0 ; f 0 Þ and ðu00 ; f 00 Þ be two systems where u0 ; u00 : f0; 1gn ! f0; 1g are coherent structure functions and f 0 ; f 00 joint probability densities over Rnþ : Definition 2 We say that ðu0 ; f 0 Þ and ðu00 ; f 00 Þ are reliability-equivalent, and write ðu0 ; f 0 Þ¼ ~ R ðu00 ; f 00 Þ; if and only if we have that sðu0 ; f 0 Þ ¼ sðu00 ; f 00 Þ; and Pu0 ;f 0 ðTk:n [ tjEk Þ ¼ Pu00 ;f 00 ðTk:n [ tjEk Þ for all k such that sk ðu0 ; f 0 Þ [ 0 and sk ðu00 ; f 00 Þ [ 0: Remark 2 In view of Eq.
If system reliability is a function R ¼ Wðp1 ; p2 ; . ; pk Þ of component reliability pj , then BIM of component j is defined as BIMj ¼ oWðp1 ; . ; pk Þ ¼ Wðp1 ; . ; pjÀ1 ; 1; pjþ1 ; . ; pk Þ opj À Wðp1 ; . ; pjÀ1 ; 0; pjþ1 ; . ; pk Þ: ð2:1Þ 2 Using D-Spectra in Network Monte Carlo Fig. 1 Network with two terminals 25 1 s 2 t 3 4 BIM has a transparent probabilistic meaning: it is the gain in system reliability received from replacing a down component j by an absolutely reliable one. BIMj gives the approximation to the system reliability increment dR resulted from component j reliability increment by dpj .
Acknowledgments Our sincere thanks go to the Editors of this volume for extending an invitation to prepare this article. We also appreciate their patience and support during the course of this work. We are especially grateful to Professor Gertbakh for several helpful suggestions during the preparation of this paper. S. Army Research Office under grant W911NF-08-1-0077 (to FJS) are all gratefully acknowledged. 1 Signature Representation and Preservation Results for Engineered Systems 21 References Agrawal A, Barlow RE (1984) A survey of network reliability and domination theory.