Stochastic behaviour of a robot-safety device system

Innovations in the field of microelectronics and micromechanics have enhanced the involvement of ‘smart’ robots in various technical applications. Unfortunately, no robot is completely reliable. Therefore, up-to-date robots are often connected with a (repairable) safety device. Such a device prevents possible damage, caused by a robot failure, in the robot's neighbouring environment. However, the random behaviour of the entire system (robot, safety device, repair facility) could jeopardize some prescribed safety requirements. Therefore, an appropriate statistical analysis is quite indispensable to support the system designer in problems of risk acceptance and safety assessments. We introduce a robot-safety device system attended by two statistically different repairmen. Our system is characterized by the natural assumption of cold standby and by an admissible ‘risky’ state. In order to describe the random behaviour of the system, we introduce a stochastic process endowed with probability kernels satisfying Kolmogorov-type equations. The solution procedure is based on advanced methods of renewal theory. Next, we derive the invariant measure of the T-system and the long-run availability of the robot. Finally, we consider the particular but important case of fast repair.