Skip to main content Accessibility help
×
Home

ON MEASURE OF SYSTEM INTERVAL AVAILABILITY

Published online by Cambridge University Press:  01 July 1999


Jie Mi
Affiliation:
Department of Statistics, Florida International University, University Park, Miami, Florida 33199

Abstract

Let [script S] be a system that can be in one of two states, up or down. We can interpret the up state as the working state and the down state as the nonworking state for system [script S]. Assume the system [script S] is up at time t = 0. Denote the elapsed time from zero until [script S] enters down state by U1, and the elapsed time from then until [script S] is up again by D1. The interval [0,U1 + D1) is called cycle 1, and, at that point, cycle 2 starts and the sequence is repeated so on and so forth. In general, the up time and down time in the jth cycle are denoted by Uj and Dj, respectively, for j ≥ 1. We can introduce a binary process {X(t), t ≥ 0} to describe the state of [script S] at time t using X(t) = 1(0) to indicate [script S] is up (down). Many problems require finding the probability that [script S] is up at time t, that is, P(X(t) = 1). However, an even more interesting question to answer is what the probability is that [script S] is in the up state in an interval of length w starting at time t, that is, P(X(s) = 1, tst + w). Due to the complexity of this problem, no explicit expressions are available for most systems even in the case where (Uj, Dj), j ≥ 1 are i.i.d. Fortunately, in practice engineers are more interested in the long-run properties of the above two probabilities.


Type
Research Article
Copyright
© 1999 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below.

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 54 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 3rd December 2020. This data will be updated every 24 hours.

Hostname: page-component-79f79cbf67-jgbff Total loading time: 0.225 Render date: 2020-12-03T05:17:17.539Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags last update: Thu Dec 03 2020 05:06:19 GMT+0000 (Coordinated Universal Time) Feature Flags: { "metrics": true, "metricsAbstractViews": false, "peerReview": true, "crossMark": true, "comments": true, "relatedCommentaries": true, "subject": true, "clr": false, "languageSwitch": true }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

ON MEASURE OF SYSTEM INTERVAL AVAILABILITY
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

ON MEASURE OF SYSTEM INTERVAL AVAILABILITY
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

ON MEASURE OF SYSTEM INTERVAL AVAILABILITY
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *