Stochastic analysis of robot-safety systems.

Abstract

Robot population is increasing at an incredible pace. Over the last fifteen years, robot population grew from 30,000 in 1983, to the forecasted 820,000 by the end of 1998. Their infancy period has come to an end and they are not just being used in the automotive industry or required to perform simple tasks. They are now being employed in various sectors of industry and handle much more complex operations. Increased robot system complexity and their critical applications utilization have led to various reliability and safety problems. In 1982, the Machine Tool Trade Associations guidelines stated that a working robot can be a potential hazard to personnel under certain circumstances. The need for robot system safety was highlighted by a 10-million dollar lawsuit awarded to the family of a worker killed by an industrial robot in 1983. This study presents a detailed introductory aspect of robot safety, an identification of the most appropriate robot systems reliability and safety assessment techniques, and probabilistic modelling of robot-safety systems. The domain of the probabilistic models include: a stochastic analysis of a system containing one robot with n-redundant safety units, a stochastic analysis of a system composed of n-redundant robots with one safety unit, and an availability analysis of robot systems susceptible to common-cause failure. The primal intent of the analyses is to develop generalized and numerical expressions relating to the performance indices for robot systems operating with or without the safety unit. Generalized models are introduced and generalized expressions including reliability, time-dependent availability, steady-state availability, and mean time to failure (MTTF) are developed. In order to assess performance indices, some special cases of the generalized models are presented resulting in the formation of numerical values. Robot system performance indices are determined by means of the Markovian and non-Markovian methods. The method of supplementary variables and the device of stages are used to deal with the non-Markovian models. Various failed system repair time distributions (i.e., exponential, gamma, Weibull, Rayleigh, and log-normal distributions) have been considered to obtain generalized steady state availability expressions. Markov method is utilized in models where failure and repair rates are assumed constant. With the aid of Laplace transforms, a system of first-order differential equations are solved and generalized reliability and MTTF expressions are developed.