Reliability of an m-out of-n system when component failure induces higher failure rates in survivors

Scheuer, Ernest M.

doi:10.1109/24.3717

Cited by 86 publications

(44 citation statements)

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“…Observe that X i ∼ E(α i ), where α i = (n − i + 1)λ i−1 , and the reliability of the system is R(t) = P(T > t). Using Theorem 3.1, Scheuer (1988) …”

Section: Sums Of Compound Negative Binomial and Gamma Random Variablesmentioning

confidence: 99%

On the Sums of Compound Negative Binomial and Gamma Random Variables

Vellaisamy

Upadhye

2009

Journal of Applied Probability

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We study the convolution of compound negative binomial distributions with arbitrary parameters. The exact expression and also a random parameter representation are obtained. These results generalize some recent results in the literature. An application of these results to insurance mathematics is discussed. The sums of certain dependent compound Poisson variables are also studied. Using the connection between negative binomial and gamma distributions, we obtain a simple random parameter representation for the convolution of independent and weighted gamma variables with arbitrary parameters. Applications to the reliability of m-out-of-n:G systems and to the shortest path problem in graph theory are also discussed.

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“…Observe that X i ∼ E(α i ), where α i = (n − i + 1)λ i−1 , and the reliability of the system is R(t) = P(T > t). Using Theorem 3.1, Scheuer (1988) …”

Section: Sums Of Compound Negative Binomial and Gamma Random Variablesmentioning

confidence: 99%

On the Sums of Compound Negative Binomial and Gamma Random Variables

Vellaisamy

Upadhye

2009

Journal of Applied Probability

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“…In the case of identical eigenvalues, the pdf is that of a scaled -distribution (i.e., an Erlang distribution): (4) where is the Heaviside step function. In the case of distinct eigenvalues, the pdf of is well-known in the field of renewal theory [25] and was derived for communications purposes in [23]: (5) In the third case, with repeated eigenvalues that satisfy (3), the pdf was derived in [25] and [26]: (6) where (7) with from the set of all partitions of (with ) defined as (8) One remark is that the pdf in (6) actually becomes that in (4) if and that in (5) if . Since the expressions with identical and distinct eigenvalues are simpler and very useful in practice, we will distinguish between all three cases throughout the paper.…”

Section: (3)mentioning

confidence: 99%

“…While the former two cases are clearly structured and commonly treated in literature, the third case needs further specification [25]. Let the distinct values among the eigenvalues be ( ), with the strictly positive multiplicities ( ).…”

Section: Analysis Of Zero-mean Complex Gaussian Vectors With Normmentioning

confidence: 99%

Exploiting Quantized Channel Norm Feedback Through Conditional Statistics in Arbitrarily Correlated MIMO Systems

Björnson

Hammarwall

Ottersten

2009

IEEE Trans. Signal Process.

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Abstract-In the design of narrowband multi-antenna systems, a limiting factor is the amount of channel state information (CSI) available at the transmitter. This is especially evident in multi-user systems, where the spatial user separability determines the multiplexing gain, but it is also important for transmission-rate adaptation in single-user systems. To limit the feedback load, the unknown and multi-dimensional channel needs to be represented by a limited number of bits. When combined with long-term channel statistics, the norm of the channel matrix has been shown to provide substantial CSI that permits efficient user selection, linear precoder design, and rate adaptation. Herein, we consider quantized feedback of the squared Frobenius norm in a Rayleigh fading environment with arbitrary spatial correlation. The conditional channel statistics are characterized and their moments are derived for both identical, distinct, and sets of repeated eigenvalues. These results are applied for minimum mean square error (MMSE) estimation of signal and interference powers in single-and multi-user systems, for the purpose of reliable rate adaptation and resource allocation. The problem of efficient feedback quantization is discussed and an entropy-maximizing framework is developed where the post-user-selection distribution can be taken into account in the design of the quantization levels. The analytic results of this paper are directly applicable in many widely used communication techniques, such as space-time block codes, linear precoding, space division multiple access (SDMA), and scheduling.

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“…By using the pdf and the cumulative distribution function (cdf ) of the sum of independent and nonidentical Erlang random variables in [18],P e3,1 can be easily calculated.…”

Section: Rot For Lc Decodingmentioning

confidence: 99%

Relay on-off threshold for NDF protocol with distributed orthogonal space-time block codes

Jin

et al. 2012

J Wireless Com Network

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In this article, a relay on-off threshold (ROT) based on symbol error rate is derived for the cooperative communication networks with multiple antennas, where the non-orthogonal decode-and-forward (NDF) protocol with source antenna switching and linear combining decoding are used as the relaying protocol and decoding scheme, respectively. The optimal ROT for the cases using distributed orthogonal space-time block codes is derived for high signal to noise ratio (SNR) region and also a suboptimal ROT is provided for low SNR region. Finally, the diversity order of the NDF protocol using the relay on-off scheme with the proposed ROT is derived and its performance is verified through numerical analysis.

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Reliability of an m-out of-n system when component failure induces higher failure rates in survivors

Cited by 86 publications

References 0 publications

On the Sums of Compound Negative Binomial and Gamma Random Variables

On the Sums of Compound Negative Binomial and Gamma Random Variables

Exploiting Quantized Channel Norm Feedback Through Conditional Statistics in Arbitrarily Correlated MIMO Systems

Relay on-off threshold for NDF protocol with distributed orthogonal space-time block codes

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