Bounding the Risk Probability
Abstract
For some safety–critical applications, it is important to calculate the probability that a discrete time autoregressive (AR) process leaves a given interval at least once during a certain period of time. For example, such AR process can be interpreted as a temporally correlated safety indicator and the interval as a target zone of the process. It is assumed that the safety of the system under surveillance is compromised if the above-mentioned probability becomes too important. This problem has been previously studied in the case of known distributions of the innovation process. Let us assume now that the distributions of the innovation and initial state are unknown but some special bounds for the cumulative distribution functions and/or for the probability density functions are available. Numerical methods to calculate the bounds for the above-mentioned probability are considered in the paper.