Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 25, No 4, (1999), 311p-320p
We introduce a robot-safety device system attended by two
different repairmen. The twin system is characterized by the natural feature
of cold standby and by an admissible “risky” state. In order to analyse the
random behaviour of the entire system (robot, safety device, repair facility)
we employ a stochastic process endowed with probability measures satisfying
general Hokstad-type differential equations. The solution procedure is
based on the theory of sectionally holomorphic functions, characterized by
a Cauchy-type integral defined as a Cauchy principal value in double sense.
An application of the Sokhotski-Plemelj formulae determines the long-run
availability of the robot-safety device. Finally, we consider the particular
but important case of deterministic repair.