ABSTRACT
The statistical inference regarding the parameters involved will provide the proper modelling mechanism for descriptive as well as for predictive and preventive purposes, especially when the phenomenon, if it occurs, is associated with financial or natural disasters. This chapter presents some preliminaries regarding Semi-Markov (SM) processes and multi-state systems for a family of distributions closed under extrema. It provides the likelihood function and the associated maximum likelihood estimators of the parameters under investigation obtained under the general setting of censoring at the beginning and/or at the end. The chapter proposes the corresponding estimators of reliability indicators. SM processes are typical tools for the modelling of technical systems. Such classes of stochastic processes generalize typical Markov jump processes by allowing general distributions for sojourn times. The chapter aims to devote to the construction of estimators for a variety of reliability indicators in the case of several censored paths at the beginning and/or at the end.
