In Gåsemyr and Natvig (2001) partial monitoring of components with applications to preventive system maintenance was considered for a binary monotone system of binary components. The purpose of the present paper is to extend this to a multistate monotone system of multistate components, where the states more realistically represent successive levels of performance ranging from the perfect functioning level down to the complete failure level. We start out close to the spirit of Arjas (1989) by using a marked point process with complete monitoring of all components, and hence of the system, as the basic reference framework. We then consider a marked point process linked to partial monitoring of some components, for instance in certain time intervals. Incorporation of information from the observed system history process is then treated. Mainly, we assume that the inspection strategy is determined by the observed component history process only, with a possible exception of a full or partial autopsy after an observed change of state of the system. Furthermore, we consider how to arrive at the posterior distribution for the relevant parameter vector by a standard simulation procedure, the data augmentation method. The idea is to extend the observed data to the complete component history process. The theory is applied to an electrical power generation system for two nearby oilrigs with some standby components, as considered in Natvig et al. (1986).