OPTIMIZATION OF THE RELIABILITY POLYNOMIAL IN PRESENCE OF MEDIOCRE ELEMENTS

Some connections between extremal set theory and the optimization of t he reliability polynomial are shown. Then the concept of the reliabili ty polynomial is generalized for the case when the elements can have t hree different states: good, mediocre and bad. The state of the device can be described by a 0,1,2 sequence. Such a state is called operativ e if the device operates when its elements are in the states described by the sequence. The maximum of the generalized reliability polynomia l is studied under the condition that the set of operative states form s an antichain.