Multi-state Systems in Nature and in Engineering

All systems are designed to perform their intended tasks in a given environment. Some systems can perform their tasks with various distinctive levels of efficiency usually referred to as

performance rates

. A system that can have a finite number of performance rates is called a multi-state system (MSS). Usually a MSS is composed of elements that in their turn can be multi-state. Actually, a binary system is the simplest case of a MSS having two distinctive states (perfect functioning and complete failure).

The basic concepts of MSS reliability were primarily introduced in the mid of the 1970's by Murchland (1975), El-Neveihi

et al.

(1978), Barlow and Wu (1978), and Ross (1979). Natvig (1982), Block and Savits (1982), and Hudson and Kapur (1982) extended the results obtained in these works. Since that time MSS reliability began intensive development. Essential achievements that were attained up to the mid 1980's were reflected in Natvig (1985) and in El-Neveihi and Prochan (1984) where can be found the state of the art in the field of MSS reliability at this stage. Readers that are interested in the history of ideas in MSS reliability theory at next stages can find the corresponding overview in Lisnianski and Levitin (2003) and Natvig (2007).