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An Elementary Proof of the "No Internal Zeros" Property of System Signatures

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F.J. Samaniego at University of California, Davis
F.J. Samaniego
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RG -- Elementary proof of NIZ property of system signatur
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... Using this observation, the second inequality follows from the assumption that − (1−u) (u) (u) is increasing and positive in u ∈ (v, 1). Equations (9) and (10) give simple sufficient conditions on the signature vector for two systems to be ordered according to hazard rate and reverse hazard rate orderings. This problem has also been studied by Navarro • If r = 4 and k = 2, then ...
... In Tables 1 and 2 Ross et al. (1980) proved that the number N of failed components at the time a system fails has the discrete increasing failure rate on average property. As elaborated in Navarro and Samaniego (2017), this fact implies that the signature of a system of arbitrary order n cannot have internal zeros; that is, there exist no integers i ∈ {1, . . . , n − 2} and j ∈ {2, . . . ...
... , p j , 0, 0, . . . , 0) for some j < n satisfies the condition (9), and that every signature vector of the type (0, 0, . . . , 0, p j , p j+1 , . . . ...
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