Failure detection with likelihood ratio tests and uncertain probabilities: An info-gap application

• The likelihood ratio test (LRT) has attractive failure-detection properties.
• Knowledge of future failures and probability distributions is limited and uncertain.
• Info-gap theory is used to robustify the LRT against uncertainty.
• An info-gap analog of the probabilistic detection-error trade off curve is developed.
• Illustrated with an industrial application.

The likelihood ratio test (LRT) has attractive failure-detection properties. However, evaluating the likelihood ratio and implementing the LRT require knowledge of the underlying probability distributions. Data or knowledge, especially about future failures, is often quite limited. In this paper we employ the info-gap robustness function in specifying the parameters of the LRT when the probability distributions are imperfectly known. We develop an info-gap analog of the probabilistic detection-error trade off curve, and demonstrate the results by application to pressure measurements on an industrial production device.