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Ismihan Bayramoglu - One of the best experts on this subject based on the ideXlab platform.

  • the mean residual life Function of a k out of n structure at the system level
    IEEE Transactions on Reliability, 2006
    Co-Authors: Majid Asadi, Ismihan Bayramoglu
    Abstract:

    In the study of the reliability of technical systems, k-out-of-n systems play an important role. In the present paper, we consider a k-out-of-n system consisting of n identical components with independent lifetimes having a Common Distribution Function F. Under the condition that, at time t, all the components of the system are working, we propose a new definition for the mean residual life (MRL) Function of the system, and obtain several properties of that system.

Majid Asadi - One of the best experts on this subject based on the ideXlab platform.

  • the mean residual life Function of a k out of n structure at the system level
    IEEE Transactions on Reliability, 2006
    Co-Authors: Majid Asadi, Ismihan Bayramoglu
    Abstract:

    In the study of the reliability of technical systems, k-out-of-n systems play an important role. In the present paper, we consider a k-out-of-n system consisting of n identical components with independent lifetimes having a Common Distribution Function F. Under the condition that, at time t, all the components of the system are working, we propose a new definition for the mean residual life (MRL) Function of the system, and obtain several properties of that system.

Tomasz Rychlik - One of the best experts on this subject based on the ideXlab platform.

  • Optimal bounds on expectations of order statistics and spacings from nonparametric families of Distributions generated by convex transform order
    Metrika, 2015
    Co-Authors: Agnieszka Goroncy, Tomasz Rychlik
    Abstract:

    Assume that $$X_1,\ldots , X_n$$ X 1 , … , X n are i.i.d. random variables with a Common Distribution Function $$F$$ F which precedes a fixed Distribution Function $$W$$ W in the convex transform order. In particular, if $$W$$ W is either uniform or exponential Distribution Function, then $$F$$ F has increasing density and failure rate, respectively. We present sharp upper bounds on the expectations of single order statistics and spacings based on $$X_1,\ldots , X_n$$ X 1 , … , X n , expressed in terms of the population mean and standard deviation, for the family of all parent Distributions preceding $$W$$ W in the convex transform order. We also characterize the Distributions which attain the bounds, and specify the general results for the Distributions with increasing density Function.

  • bounds for the mean residual life Function of a k out of n system
    Metrika, 2011
    Co-Authors: Mohammad Z Raqab, Tomasz Rychlik
    Abstract:

    In the reliability studies, k-out-of-n systems play an important role. In this paper, we consider sharp bounds for the mean residual life Function of a k-out-of-n system consisting of n identical components with independent lifetimes having a Common Distribution Function F, measured in location and scale units of the residual life random variable Xt = (X−t|X > t). We characterize the probability Distributions for which the bounds are attained. We also evaluate the so obtained bounds numerically for various choices of k and n.

Waikit Lam - One of the best experts on this subject based on the ideXlab platform.

  • universality of the time constant for 2d critical first passage percolation
    arXiv: Probability, 2019
    Co-Authors: Michael Damron, Jack Hanson, Waikit Lam
    Abstract:

    We consider first-passage percolation (FPP) on the triangular lattice with vertex weights $(t_v)$ whose Common Distribution Function $F$ satisfies $F(0)=1/2$. This is known as the critical case of FPP because large (critical) zero-weight clusters allow travel between distant points in time which is sublinear in the distance. Denoting by $T(0,\partial B(n))$ the first-passage time from $0$ to $\{x : \|x\|_\infty = n\}$, we show existence of the "time constant'' and find its exact value to be \[ \lim_{n \to \infty} \frac{T(0,\partial B(n))}{\log n} = \frac{I}{2\sqrt{3}\pi} \text{ almost surely}, \] where $I = \inf\{x > 0 : F(x) > 1/2\}$ and $F$ is any critical Distribution for $t_v$. This result shows that the time constant is universal and depends only on the value of $I$. Furthermore, we find the exact value of the limiting normalized variance, which is also only a Function of $I$, under the optimal moment condition on $F$. The proof method also shows an analogous universality on other two-dimensional lattices, assuming the time constant exists.

Lam Wai-kit - One of the best experts on this subject based on the ideXlab platform.

  • Universality of the time constant for $2D$ critical first-passage percolation
    2019
    Co-Authors: Damron Michael, Hanson Jack, Lam Wai-kit
    Abstract:

    We consider first-passage percolation (FPP) on the triangular lattice with vertex weights $(t_v)$ whose Common Distribution Function $F$ satisfies $F(0)=1/2$. This is known as the critical case of FPP because large (critical) zero-weight clusters allow travel between distant points in time which is sublinear in the distance. Denoting by $T(0,\partial B(n))$ the first-passage time from $0$ to $\{x : \|x\|_\infty = n\}$, we show existence of the "time constant'' and find its exact value to be \[ \lim_{n \to \infty} \frac{T(0,\partial B(n))}{\log n} = \frac{I}{2\sqrt{3}\pi} \text{ almost surely}, \] where $I = \inf\{x > 0 : F(x) > 1/2\}$ and $F$ is any critical Distribution for $t_v$. This result shows that the time constant is universal and depends only on the value of $I$. Furthermore, we find the exact value of the limiting normalized variance, which is also only a Function of $I$, under the optimal moment condition on $F$. The proof method also shows an analogous universality on other two-dimensional lattices, assuming the time constant exists.Comment: 29 pages, 3 figure