Title: Estimation of Component Reliability in Coherent Systems,
Abstract: The first step in statistical reliability studies of coherent systems is the
estimation of the reliability of each system component. For the cases of
parallel and series systems the literature is abundant. It seems that the
present paper is the first that presents the general case of component
inferences in coherent systems. The failure time model considered here is the
three-parameter Weibull distribution. Furthermore, neither independence nor
identically distributed failure times are required restrictions. The proposed
model is general in the sense that it can be used for any coherent system, from
the simplest to the more complex structures. It can be considered for all kinds
of censored data; including interval-censored data. An important property
obtained for the Weibull model is the fact that the posterior distributions are
proper, even for non-informative priors. Using several simulations, the
excellent performance of the model is illustrated. As a real example, boys
first use of marijuana is considered to show the efficiency of the solution
even when censored data occurs.