By Yu Hayakawa, Telba Zalkind Irony, Min Xie
ISBN-10: 9810248652
ISBN-13: 9789810248659
This quantity is a set of articles on reliability structures and Bayesian reliability research. Written via respected researchers, the articles are self-contained and are associated with literature studies and new examine principles. The booklet is devoted to Emeritus Professor Richard E. Barlow, who's renowned for his pioneering study on reliability thought and Bayesian reliability research
Read or Download System and Bayesian Reliability: Essays in Honor of Professor Richard E. Barlow PDF
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Additional info for System and Bayesian Reliability: Essays in Honor of Professor Richard E. Barlow
Sample text
Corollary 14: If M is a F reliability model and b g- M, then for all z,yG{0,l}*, xbygM. The following results pinpoint the relations among the F models, the G models and the regular models. Corollary 15: If M is a G or F reliability model, then M is regular. Lemma 16: / / M is both a F model and a G model, then M is either § or {0,1}*. Proof: Consider the empty string e. If e € M, then M = {0,1}* because M is a G model. If e £ M, then e <£ M and M = 0,1* because M i s a F model. Therefore M must be either (j> or {0,1}*.
Stopping with X(Q) gives H = v(i,d). For any positive integer N, here is another stopping rule: stop as soon as S(n) > an + d or when n = N.
Further consequences are given in the Esary, Proschan, and Walkup paper. We first consider two simple examples where we can obtain upper and lower bounds on the system reliability using just the marginal component reliabilities. 24 J. N. Hagstrom and S. M. Ross Example 4: Let the components of a series system be indexed i = 1 . . n. Let the random variable Xi = 1 if component i is working; Xi = 0 otherwise. The system is working if Yl"=1 Xi ~ 1. The reliability of the system is E(J3" = 1 Xi). If the random variables Xi are associated, E n n *=1 i=l dI^)>ii(E^)- Also, we have n E(nXi)System and Bayesian Reliability: Essays in Honor of Professor Richard E. Barlow by Yu Hayakawa, Telba Zalkind Irony, Min Xie
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