On the first time a separately maintained parallel system has been down for a fixed time

Sheldon M. Ross and Jack Schechtman

Naval Research Logistics Quarterly, 1979, vol. 26, issue 2, 285-290

Abstract: Consider a system consisting of n separately maintained independent components where the components alternate between intervals in which they are “up” and in which they are “down”. When the ith component goes up [down] then, independent of the past, it remains up [down] for a random length of time, having distribution Fi[Gi], and then goes down [up]. We say that component i is failed at time t if it has been “down” at all time points s ϵ[t‐A.t]: otherwise it is said to be working. Thus, a component is failed if it is down and has been down for the previous A time units. Assuming that all components initially start “up,” let T denote the first time they are all failed, at which point we say the system is failed. We obtain the moment‐generating function of T when n = l, for general F and G, thus generalizing previous results which assumed that at least one of these distributions be exponential. In addition, we present a condition under which T is an NBU (new better than used) random variable. Finally we assume that all the up and down distributions Fi and Gi i = l,….n, are exponential, and we obtain an exact expression for E(T) for general n; in addition we obtain bounds for all higher moments of T by showing that T is NBU.

Date: 1979
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/nav.3800260208

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:26:y:1979:i:2:p:285-290

Access Statistics for this article

More articles in Naval Research Logistics Quarterly from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().