Fuzzy Apportionment of System Reliability

The concept of reliability apportionment is general and has even been applied to the allocation of man-machine reliability. Typically, however, the process of optimally apportioning individual component reliability to meet some desired system reliability level subject, perhaps, to constraints on cost, volume, weight, etc. has always been imprecise and vague at best. In real problems, the resource constraints are no more sacred than the objective system reliability; they are frequently flexible. In view of the inherent vagueness of the reliability objective as well as constraints in a typical ill-structured reliability apportionment problem, this paper formulates the nonlinear optimization problem in the fuzzy-set theoretic perspective. To illustrate the philosophy, a simple reliability apportionment example with a budgetary constraint for a 2-component series structure is analyzed. Then the concept is generalized into a more realistic problem with multiple components and constraints. This tutorial paper is an easy introduction for the newcomer to fuzzy-system theory.