IFRA or DMRL survival under the pure birth shock process
1980 (English)Report (Other academic)
Suppose that a device is subjected to shocks and that P^, k • 0, 1, 2,00denotes the probability of surviving k shocks. Then H(t) = E P(N(t) = k)P,k=0is the probability that the device will survive beyond t, where N = (N(t): t > 0} is the counting process which governs the arrival of shocks. A-Hameed and Proschan (1975) considered the survival function H(t) under what they called the Pure Birth Shock Model. In this paper we shall prove that H(t) is IFRA and DMRL under conditions which differ from those used by A-Hameed and Proschan (1975).
Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1980. , 9 p.
, Statistical research report, ISSN 0348-0399 ; 1980:4
Shock model, birth process, survival function, variation diminishing property, total positivity, IFRA, DFRA, DMRL, IMRL
IdentifiersURN: urn:nbn:se:umu:diva-78992OAI: oai:DiVA.org:umu-78992DiVA: diva2:638389
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.2013-07-302013-07-302013-07-30Bibliographically approved