Estimation and Reliability for a Special Type of Semi-Markov Process

Abstract

This work deals with multi-state systems modelled by means of semi-Markov processes. The sojourn times are seen to be independent not identically distributed random variables and assumed to belong to one of two different general classes of distributions so that the first class is closed under maxima and the second one is closed under minima. We obtain maximum likelihood estimators of the parameters of interest under several estimation schemes and investigate their asymptotic properties. Plug-in type estimators are furnished for various quantities related to the system under study.

Statistical Inference for Multi State Systems under the Generalized Modified Weibull Class

“…where h(t) = dH(t) dt the pdf associated with H(•). Recall that the baseline distribution of the ( 6) is the MWP distribution given in (5) with parameters a, λ and β, γ ≥ 0 which is denoted by MWP(a, β, γ, λ) and it is obtained if in (6) we take H(t) = 1 − e −at γ e βt .…”