An optimal inspection and diagnosis policy for a multi-mode system

This paper considers a multi-mode system that is inspected periodically, and the period of inspection is a random variable. The system has three modes: normal (N), abnormal (A) and failure (F), where F is a self-announcing mode whereas, N and A are non-self-announcing and operating modes. When the system is operating, it is inspected once every random time T to make sure whether it is in N or A until it attains F, or until it is detected to be in A. Each inspection consists in measuring a value taken by a diagnostic parameter. The diagnostic parameter, which is a random variable, has a close relation with the operating modes. If it is found to have exceeded a certain critical value, a preventive maintenance (or repair) is performed. By using the supplementary variable technique, the reliability indices and an optimal inspection and diagnosis policy for the system are obtained.