Asymptotic Performance of a System Subject to Cannibalization

Warren M Hirsch

The book Asymptotic Performance of a System Subject to Cannibalization was written by author Warren M Hirsch Here you can read free online of Asymptotic Performance of a System Subject to Cannibalization book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Asymptotic Performance of a System Subject to Cannibalization a good or bad book?

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> kx}, defined for k > and the admissible values of l, j by the equations Y, j(k) = ( 1, If X. . > kx, ij - , otherwise.
Plainly, for each Index k the random variables (Y.. (k)). _, ^ are Independent, and "^ ~ ' ' " -a. Kx 1, with probability e, . , n (1) Y. . (k) = -, 1, 1 j = l Then S. (k) denotes the number of operational parts of type 1 at time kx, given that the size of the system Is n. Setting and -a. Kx p, (k) = e ^ q^(k) = 1 - p^(k), It follows from (1) and (2) and the Independence of (...Y, . (k)). _, ^ that , n (3) -nx m/, X n-m P{S.^(k) = m} = (;;)p'!;(k)qp'(k), m = 0, 1, ... , n By definition, the system performance level at time kx Is given by the random variable $ (k) = mln S. (k) l^ln^''^^» (Y2i(k), Y22(k), ... , Y2„(k)), •••> (Y^;L^^^>^r2^^^*"-'^rn^^^^ are independent. Hence, the expected performance level at time kT can be determined from the tall distribution by the well-known formula, n-1 m) E[* (k)] = I P{* (k) > X} " x=o " n-1 = I P{S^^(k) > X, S2^(k) > X, ...

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