FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1996, VOLUME 2, NUMBER 4, PAGES 1101-1105

On bounds for the pointwise availability of a repairable component

I. N. Kovalenko

Abstract

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An alternating renewal process is considered with d.f. $A(t)$ and $B(t)$ of its up-phases and down-phases, respectively. It is assumed that an up-phase starts at the point $t\; =\; 0$. Let $P(t)$ denote the up-state probability at time $t$. Assume that $A(+0)\; =\; 0$, the mean duration of an up-phase equals 1 whereas that for a down-phase equals $$r. Introduce the function $$D(t) by the relation

Let then $B(t)\; =\; B$_r(t), $$r → 0. It is proved that under a mild assumption for any non-exponential distribution $A(t)$ the equality

cannot hold for every positive $$d and $T$.

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