### A limit formula for regular iteration groups. (Summary).

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The author considers a population Π of devices which can fail due to one of the modes of failure Ui, i=1,2,...,k. Assume that each device e in Π has a life which will terminate at time T(e) due to mode Uj. When a device is drawn at random from Π, the pair [T(e),j] is a two-dimensional random variable with probability distribution P(T,j) which determines the marginal survival function R(t)=P{T>t}, called the "reliability function before improvement". The author discusses possible improvement of...

Let $\left(\xb7\right)$, n ∈ N, be a sequence of homogeneous semi-Markov processes (HSMP) on a countable set K, all with the same initial p.d. concentrated on a non-empty proper subset J. The subrenewal kernels which are restrictions of the corresponding renewal kernels $$ on K×K to J×J are assumed to be suitably convergent to a renewal kernel P (on J×J). The HSMP on J corresponding to P is assumed to be strongly recurrent. Let [${\pi}_{j}$; j ∈ J] be the stationary p.d. of the embedded Markov chain. In terms of the averaged...

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