news Using the general theory some multivariate NBU conditions are introduced and studied. In this paper, we develop a general multivariate new better than used (MNBU) distribution based on a multivariate common shock model. Proofs of some related well-known implications are simplified.

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Cited by:All material on this site has been provided by the respective publishers and authors. A property of new better than used in expectation (NBUE) and new worse than used in expectation (NWUE) is derived as an application to the variability ordering of fuzzy random variables.

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In this paper we provide new results about stochastic comparisons of the excess lifetime at different times of a renewal process when the interarrival times belong to several ageing classes. Learn more about Institutional subscriptions
A stochastic process , such that P{Z(0) = 0} = 1, is said to be new better than used (NBU) if, for every x, the first-passage time Tx = inf {t: Z(t) x} satisfies P{TX s + t} for everys . In the M/G/1+Gw queue customers have deadlines for their waiting times, and they leave the system immediately if their services do not start before the expiration of their deadlines. Two models, depending on whether the size of the nth shock is correlated with the length of the interval since the last shock or with the length of the succeeding interval until the next shock, are considered. The concept of generalized variability orderings of nonnegative fuzzy random variables representing lifetime of components is introduced.

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1007/s00184-020-00773-3Instant access to the full article PDF. Received: 03 October 2019Published: 30 April 2020Issue Date: January 2021DOI: https://doi. Examples of such processes include processes with shocks and recovery, processes with random repair-times, various Gaver–Miller processes and some strong Markov processes. In particular, we show that if the service time distribution is new better than used in expectation, then the loss probability in the M/G/1+Gs queue is greater than that in the M/G/1+Gw queue. org/data/inforea. The NBU property of processes and random variables can be used to obtain bounds on various probabilistic quantities of interest; this is illustrated numerically.

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Learn more. The properties on the dependence order and the multivariate ageing are also studied. It is shown that various waiting times for clusters of events and for short and wide gaps in some renewal processes are NBU random variables. Please log in to your accountA general theory of multivariate new better than used NBU distributions is developed.

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repec. Some of the results apply as well to multivariate increasing hazard rate average IHRA and exponential distributions. 5555/2839357. html . To manage your alert preferences, click on the button below. A key tool is a non-standard hierarchical class of stochastic orderings between discrete random variables valued in {0, 1,· ··, n}.

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In this paper we define and analyze a class of cumulative shock models associated with a bivariate sequence {Xn
, Yn
}∞
n
=0 of correlated random variables.

In this paper, we study the new better than used in expectation (NBUE) and new worse than used in expectation (NWUE) properties of Markov renewal click here now The results included equivalent conditions which justify the generalized variability orderings. The {Xn
} denote the sizes of the shocks and the {Yn
} denote the times between successive shocks. This allows to link your profile to this item.

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2019R1A2B5B02069500). You can help correct errors and omissions.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. org/10. Applications in reliability theory, queueing, dams, inventory and electrical activity of neurons are indicated.

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Learn more about Institutional subscriptionsThe authors thank the reviewers for helpful comments and valuable suggestions, which have improved the presentation of this paper considerably.

The paper is first concerned with a comparison of the partial sums associated with two sequences of n exchangeable Bernoulli random variables. .

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