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On optimal replacement policy

Raimi Ajibola Kasumu, Antonín Lešanovský (1983)

Aplikace matematiky

A system with a single activated unit which can be in k + 1 states is considered. Inspections of the system are carried out at discrete time instants. The process of deterioration of the unit is supposed to be Markovian. The unit by its operation brings an income which is monotonically dependent on its state. A replacement of the unit is associated with certain costs. The paper gives an effective algorithm for finding the replacement strategy maximizing the average income of the system per unit time....

On reliability analysis of consecutive k -out-of- n systems with arbitrarily dependent components

Ebrahim Salehi (2016)

Applications of Mathematics

In this paper, we consider the linear and circular consecutive k -out-of- n systems consisting of arbitrarily dependent components. Under the condition that at least n - r + 1 components ( r n ) of the system are working at time t , we study the reliability properties of the residual lifetime of such systems. Also, we present some stochastic ordering properties of residual lifetime of consecutive k -out-of- n systems. In the following, we investigate the inactivity time of the component with lifetime T r : n at the system...

On the number of word occurrences in a semi-Markov sequence of letters

Margarita Karaliopoulou (2009)

ESAIM: Probability and Statistics

Let a finite alphabet Ω. We consider a sequence of letters from Ω generated by a discrete time semi-Markov process { Z γ ; γ } . We derive the probability of a word occurrence in the sequence. We also obtain results for the mean and variance of the number of overlapping occurrences of a word in a finite discrete time semi-Markov sequence of letters under certain conditions.

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