Fault diagnosis in loop-connected systems

The paper considers fault diagnosis in a large system comprising a collection of small subsystems or units which can test one another for the existence of a faulty condition. If subsystem a is not faulty and tests subsystem 8, a correct indication of the status of j.3 is obtaiued; if a is faulty, the test outcome contains meaningless information. A particular form of interconnection is examined. For a system with n units %u, ,..., u,_,, for each i unit u, te& q+l,U{+2,..., I++” (modulo n arithmetic being understood), where A is a preselected integer. If t is the maximum munber of faulty units, we show that when t 2t+l;wealsoshowthatwhent>A,atlcastAfaultscanbe diagnosedifandonlyifn>s(t-.4~s)+t+A+l,wheresistheintegerwhichmexim&xthe; quadratic function Ax) = x(t Ax) of the integer variable x.