منابع مشابه
Superposition of renewal processes for modelling imperfect maintenance
In problems of maintenance optimization, it is convenient to assume that repairs are equivalent to replacements and that systems or objects are therefore brought back into an as-good-as-new state after each repair. Standard results in renewal theory may then be applied for determining optimal maintenance policies. In practice, there are many situations in which this assumption can not be made. ...
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Suppose all events occurring in an unknown number (ν) of iid renewal processes, with a common renewal distribution F , are observed for a fixed time τ , where both ν and F are unknown. The individual processes are not known apriori, but for each event, the process that generated it is identified. For example, in software reliability application, the errors (or bugs) in a piece of software are n...
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Superposition is a mapping on point configurations that sends the n-tuple (x1, . . . , xn) ∈ X into the n-point configuration {x1, . . . , xn} ⊂ X , counted with multiplicity. It is an additive set operation such the superposition of a k-point configuration in X is a kn-point configuration in X . A Poisson superposition process is the superposition in X of a Poisson process in the space of fini...
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The characteristic independence property of Poisson point processes gives an intuitive way to explain why a sequence of point processes becoming less and less repulsive can converge to a Poisson point process. The aim of this paper is to show this convergence for sequences built by superposing repulsive point processes. We use Papangelou intensities and Stein’s method to prove this result with ...
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The main contribution in this paper is the introduction of a methodology for approximately characterizing the superposition process of N 2 arbitrary (and possibly heterogeneous) discrete-time Markov Renewal Processes (MRP). In this model, the superposition process is characterized by a MRP with a state space that grows exponentially with N. We consider an on/oo traac source model, where the dis...
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ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 1991
ISSN: 0001-8678,1475-6064
DOI: 10.1017/s000186780002334x