%0 Journal Article
%A Bordes, Laurent
%A Mercier, Sophie
%T Extended Geometric Processes: Semiparametric Estimation and Application to ReliabilityImperfect repair, Markov renewal equation, replacement policy
%J Journal of the Iranian Statistical Society
%V 12
%N 1
%U http://jirss.irstat.ir/article-1-208-en.html
%R
%D 2013
%K Imperfect repair, Markov renewal equation, replacement policy,
%X Lam (2007) introduces a generalization of renewal processes named Geometric processes, where inter-arrival times are independent and identically distributed up to a multiplicative scale parameter, in a geometric fashion. We here envision a more general scaling, not necessar- ily geometric. The corresponding counting process is named Extended Geometric Process (EGP). Semiparametric estimates are provided and studied for an EGP, which includes consistency results and convergence rates. In a reliability context, arrivals of an EGP may stand for suc- cessive failure times of a system submitted to imperfect repairs. In this context, we study: 1) the mean number of failures on some finite hori- zon time 2) a replacement policy assessed through a cost function on an infinite horizon time.
%> http://jirss.irstat.ir/article-1-208-en.pdf
%P 1-34
%& 1
%!
%9
%L A-10-1-90
%+
%G eng
%@ 1726-4057
%[ 2013