CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt170",{id:"formSmash:upper:j_idt170",widgetVar:"widget_formSmash_upper_j_idt170",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt178_j_idt181",{id:"formSmash:upper:j_idt178:j_idt181",widgetVar:"widget_formSmash_upper_j_idt178_j_idt181",target:"formSmash:upper:j_idt178:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Properties and tests for some classes of life distributionsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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1980 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Umeå: Umeå universitet , 1980. , p. 16
##### Keywords [en]

Life distribution, survival function, exponential distribution, IFR, IFRA, NBUE, DMRL, HNBUE, shock model, total time on test transform, testing of exponentiality
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-78990OAI: oai:DiVA.org:umu-78990DiVA, id: diva2:638387
##### Public defence

1980-10-17, Samhällsvetarhuset, hörsal D, Umeå universitet, Umeå, 09:15
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt825",{id:"formSmash:j_idt825",widgetVar:"widget_formSmash_j_idt825",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt837",{id:"formSmash:j_idt837",widgetVar:"widget_formSmash_j_idt837",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt852",{id:"formSmash:j_idt852",widgetVar:"widget_formSmash_j_idt852",multiple:true});
##### Projects

digitalisering@umu
##### Note

##### List of papers

A life distribution and its survival function F = 1 - F with finitemean y = /q F(x)dx are said to be HNBUE (HNWUE) if F(x)dx < (>)U exp(-t/y) for t > 0. The major part of this thesis deals with the classof HNBUE (HNWUE) life distributions. We give different characterizationsof the HNBUE (HNWUE) property and present bounds on the moments and on thesurvival function F when this is HNBUE (HNWUE). We examine whether theHNBUE (HNWUE) property is preserved under some reliability operations andstudy some test statistics for testing exponentiality against the HNBUE(HNWUE) property.The HNBUE (HNWUE) property is studied in connection with shock models.Suppose that a device is subjected to shocks governed by a counting processN = {N(t): t > 0}. The probability that the device survives beyond t isthen00H(t) = S P(N(t)=k)P, ,k=0where P^ is the probability of surviving k shocks. We prove that His HNBUE (HNWUE) under different conditions on N and * ^orinstance we study the situation when the interarrivai times between shocksare independent and HNBUE (HNWUE).We also study the Pure Birth Shock Model, introduced by A-Hameed andProschan (1975), and prove that H is IFRA and DMRL under conditions whichdiffer from those used by A-Hameed and Proschan.Further we discuss relationships between the total time on test transformHp^(t) = /q ^F(s)ds , where F \t) = inf { x: F(x) > t}, and differentclasses of life distributions based on notions of aging. Guided by propertiesof we suggest test statistics for testing exponentiality agains t IFR,IFRA, NBUE, DMRL and heavy-tailedness. Different properties of these statisticsare studied.Finally, we discuss some bivariate extensions of the univariate properties NBU, NBUE, DMRL and HNBUE and study some of these in connection with bivariate shock models.

There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.

Available from: 2013-07-30 Created: 2013-07-30 Last updated: 2018-03-15Bibliographically approved1. Some properties of the HNBUE and HNWUE classes of life distributions$(function(){PrimeFaces.cw("OverlayPanel","overlay638402",{id:"formSmash:j_idt1002:0:j_idt1010",widgetVar:"overlay638402",target:"formSmash:j_idt1002:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. HNBUE survival under some shock models$(function(){PrimeFaces.cw("OverlayPanel","overlay638388",{id:"formSmash:j_idt1002:1:j_idt1010",widgetVar:"overlay638388",target:"formSmash:j_idt1002:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. IFRA or DMRL survival under the pure birth shock process$(function(){PrimeFaces.cw("OverlayPanel","overlay638389",{id:"formSmash:j_idt1002:2:j_idt1010",widgetVar:"overlay638389",target:"formSmash:j_idt1002:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Some tests against aging based on the total time on test transform$(function(){PrimeFaces.cw("OverlayPanel","overlay638395",{id:"formSmash:j_idt1002:3:j_idt1010",widgetVar:"overlay638395",target:"formSmash:j_idt1002:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Testing exponentiality against HNBUE$(function(){PrimeFaces.cw("OverlayPanel","overlay638412",{id:"formSmash:j_idt1002:4:j_idt1010",widgetVar:"overlay638412",target:"formSmash:j_idt1002:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. On some classes of bivariate life distributions$(function(){PrimeFaces.cw("OverlayPanel","overlay638423",{id:"formSmash:j_idt1002:5:j_idt1010",widgetVar:"overlay638423",target:"formSmash:j_idt1002:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1878",{id:"formSmash:j_idt1878",widgetVar:"widget_formSmash_j_idt1878",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1931",{id:"formSmash:lower:j_idt1931",widgetVar:"widget_formSmash_lower_j_idt1931",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1932_j_idt1934",{id:"formSmash:lower:j_idt1932:j_idt1934",widgetVar:"widget_formSmash_lower_j_idt1932_j_idt1934",target:"formSmash:lower:j_idt1932:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});