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.
Bordes,L. and Mercier,S. (2022). Extended Geometric Processes: Semiparametric Estimation and Application to ReliabilityImperfect repair, Markov renewal equation, replacement policy. Journal of the Iranian Statistical Society, 12(1), 1-34.
MLA
Bordes,L. , and Mercier,S. . "Extended Geometric Processes: Semiparametric Estimation and Application to ReliabilityImperfect repair, Markov renewal equation, replacement policy", Journal of the Iranian Statistical Society, 12, 1, 2022, 1-34.
HARVARD
Bordes L., Mercier S. (2022). 'Extended Geometric Processes: Semiparametric Estimation and Application to ReliabilityImperfect repair, Markov renewal equation, replacement policy', Journal of the Iranian Statistical Society, 12(1), pp. 1-34.
CHICAGO
L. Bordes and S. Mercier, "Extended Geometric Processes: Semiparametric Estimation and Application to ReliabilityImperfect repair, Markov renewal equation, replacement policy," Journal of the Iranian Statistical Society, 12 1 (2022): 1-34,
VANCOUVER
Bordes L., Mercier S. Extended Geometric Processes: Semiparametric Estimation and Application to ReliabilityImperfect repair, Markov renewal equation, replacement policy. JIRSS, 2022; 12(1): 1-34.
Journal of the Iranian Statistical Society