scholarly journals Asymptotic Normality of Linear Combinations of Functions of Order Statistics

1969 ◽  
Vol 40 (6) ◽  
pp. 2041-2050 ◽  
Author(s):  
Galen R. Shorack
Keyword(s):  
Asymptotic Normality ◽  
Order Statistics ◽  
Linear Combinations

The asymptotic time to failure of a bundle of fibers with random slacks

1981 ◽  
Vol 13 (03) ◽  
pp. 548-566 ◽  
Author(s):  
L. Tierney
Keyword(s):  
Asymptotic Normality ◽  
Order Statistics ◽  
Load Sharing ◽  
Time To Failure ◽  
Linear Combinations ◽  
Stochastic Nature ◽  
Mean And Variance ◽  
Asymptotic Time ◽  
Normally Distributed

Consider a bundle that has been constructed by placing n fibers in parallel between two clamps. The simplest assumption on fiber load sharing is that all non-failed fibers share the load applied to the bundle equally. Phoenix (1978b) shows that, as n tends to ∞, the time to failure of such a bundle is asymptotically normally distributed under certain assumptions on the stochastic nature of the fibers. In this paper we show that this asymptotic normality is preserved but with changed mean and variance if random slacks are introduced, as caused by random variations in the lengths of the fibers. A theorem on random linear combinations of order statistics, which is given in the appendix, is used to prove the result.

The asymptotic time to failure of a bundle of fibers with random slacks

1981 ◽  
Vol 13 (3) ◽  
pp. 548-566 ◽  
Author(s):  
L. Tierney
Keyword(s):  
Asymptotic Normality ◽  
Order Statistics ◽  
Load Sharing ◽  
Time To Failure ◽  
Linear Combinations ◽  
Stochastic Nature ◽  
Mean And Variance ◽  
Asymptotic Time ◽  
Normally Distributed

Consider a bundle that has been constructed by placing n fibers in parallel between two clamps. The simplest assumption on fiber load sharing is that all non-failed fibers share the load applied to the bundle equally. Phoenix (1978b) shows that, as n tends to ∞, the time to failure of such a bundle is asymptotically normally distributed under certain assumptions on the stochastic nature of the fibers. In this paper we show that this asymptotic normality is preserved but with changed mean and variance if random slacks are introduced, as caused by random variations in the lengths of the fibers. A theorem on random linear combinations of order statistics, which is given in the appendix, is used to prove the result.

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