Reliability of systems with fuzzy-failure criterion

In many situations, such as robot path planning and automated manufacturing systems, the output for a given input cannot be simply classified as being either correct (no failure) or incorrect (failure). Instead of an ad hoc binary classification of the correctness of the output, it is more intuitive to use a fuzzy set based classification scheme. One approach is to let the value of the fuzzy set membership function denote the degree of acceptability (i.e., correctness) of the output. In this paper, we investigate several such fuzzy-failure criteria and their effects on system reliability in embedded computer systems. We first model the fuzzy output level of a response to a sensor event as a random variable in the range of [0,1] with 0 indicating that the output is completely acceptable and 1 indicating that the output is completely unacceptable. Then we derive analytical expressions for the reliability of systems for various fuzzy-failure criteria and compare their numerical solutions. We conclude that the reliability of such systems depends significantly on the fuzzy-failure criterion defined by the system designer