Robot reliability through fuzzy Markov models

Abstract

In the past few years, new applications of robots have increased the importance of robotic reliability and fault tolerance. Standard approaches of reliability engineering rely on the probability model, which is often inappropriate for this task due to a lack of sucient probabilistic information during the design and prototyping phases. Fuzzy logic oers an alternative to the probability paradigm, possibility, that is much more appropriate to reliability in the robotic context. Fuzzy Markov modeling, the technique developed in this paper, is a technique for analyzing fault tolerant designs under considerable uncertainty, such as is seen in compilations of component failure rates. It is suciently detailed to provide useful information while maintaining the fuzziness (uncertainty) inherent in the situation. It works well in conjunction with fuzzy fault trees, a wellestablished fuzzy reliability tool. Perhaps most importantly, it builds directly on existing reliability techniques, making it easy to add to our reliability toolbox.

Evaluating the reliability of prototype degradable systems

“…We de®ne two more criteria, fuzzy validity and probabilistic validity, to deal with the two most common problems. For our purposes, any piecewise continuous function bounded on the [0,1] interval is a valid fuzzy membership function [13]. The requirement for probabilistic validity is that we do not ever have any possibility greater than zero of probabilities outside of the [0,1] interval.…”

“…Although space constraints limit the detail presented in this paper, a more complete discussion is available in Refs. [13,24].…”

“…For these it can be suf®cient to propagate the various corresponding a -cut end points through the fault tree as if they were crisp, and then take the resulting extremal points as the corners of the output possibility distribution [10,13,14,21]. Unfortunately, this method requires many constraints inherent in the fault tree method which are not present for Markov models, and thus violates the uncertainty criterion in all but the most trivial Markov systems.…”

“…The lower edge of the interval was the ®rst sample, the upper the last. The resulting crisp Markov models were solved using a ®nite-difference method [13], but any accurate Markov modeling method should give virtually identical results. Note that the symbolic solution to the Markov model can be especially useful in this case, as it can signi®-cantly reduce computation.…”

“…This is an important consideration, as the robot arm is inserted through a narrow riser and must be`limp' (straight) to remove from the tank. Due to the hazardousness of the tank's contents, only severely limited options are available for in-tank repair if the system fails [13].…”