This paper is concerned with the joint prior distribution of the dependent reliabilities of the components of a binary system. When this distribution is MTP2 (Multivariate Totally Positive of Order 2), it is shown in general that this actually makes the machninery of Natvig and Eide available to arrive at the posterior distribution of the system's reliability, based on data both at the component and system level. As an illustration in a common environmental stress case, the joint prior distribution of the reliabilities is shown to have the MTP2 property. We also show, similarly to Gåsemyr and Natvig, for the case of independent components given component reliabilities how this joint prior distribution may be based on the combination of expert opinions. A specific system is finally treated numerically.
