Coherent systems with multistate components

The basic rules of the Boolean algebra with restrictions on variables are briefly recalled. This special type of Boolean algebra allows one to handle fault trees of systems made of multistate (two or more than two states) components.Coherent systems are defined in the case of multistate components. This definition is consistent with that originally suggested by Barlow in the case of binary (two states) components. The basic properties of coherence are described and discussed. Coherent Boolean functions are also defined. It is shown that these functions are irredundant, that is they have only one base which is at the same time complete and irredundant. However, irredundant functions are not necessarily coherent.Finally a simplified algorithm for the calculation of the base of a coherent function is described. In the case that the function is not coherent, the algorithm can be used to reduce the size of the normal disjunctive form of the function. This in turn eases the application of the Nelson algorithm to calculate the complete base of the function. The simplified algorithm has been built in the computer program MUSTAFA-1. In a sample case the use of this algorithm caused a reduction of the CPU time by a factor of about 20.