The article deals with reliability assessment methods for systems with three-state elements. It is shown that further development of conventional logic-and-probabilistic methods (LPM) eliminates the LPM deficiencies such as analysis of only two element states and assumption of their independency. Two models of element failure impact on the system reliability are shown which demonstrate the principles of reliability assessment using the ARBITER software which incorporates capabilities of algebra of disjoint event groups and is based on the general logic-and-probabilistic method (GLPM). Description of logic and probabilistic function transformations for disjoint events is shown in the annexes.