Stochastic comparisons and ageing properties of an extended gamma process

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TitreStochastic comparisons and ageing properties of an extended gamma process
Type de publicationJournal Article
Year of Publication2021
AuteursMasry ZAl, Mercier S, Verdier G
JournalJOURNAL OF APPLIED PROBABILITY
Volume58
PaginationPII S0021900220000741
Date PublishedMAR
Type of ArticleArticle
ISSN0021-9002
Mots-clésageing properties, cumulative deterioration, extended gamma process, Reliability theory, standard gamma process, stochastic order
Résumé

Extended gamma processes have been seen as a flexible extension of standard gamma processes in the recent reliability literature, for the purpose of cumulative deterioration modeling. The probabilistic properties of the standard gamma process have been well explored since the 1970s, whereas those of its extension remain largely unexplored. In particular, stochastic comparisons between degradation levels modeled by standard gamma processes and ageing properties for the corresponding level-crossing times are now well understood. The aim of this paper is to explore similar properties for extended gamma processes and see which ones can be broadened to this new context. As a by-product, new stochastic comparisons for convolutions of gamma random variables are also obtained.

DOI10.1017/jpr.2020.74