ON a Model of Optimal Trouble Diagnosis and Inspection Policies

This paper deals with a 2-unit system with a multivariate diagnostic parameter, which is a random vector. One of the units has two modes (normal and failure) and the other has three modes (normal, abnormal and failure). When the system is working, it is inspected once every time u to make sure whether the 3-mode unit is normal or abnormal until the system fails, or until the result of the inspection shows that the unit is abnormal. The inspection is based on the multivariate diagnostic parameter and can bring about wrong conclusions. The optimal critical value of the parameter and the optimal inspection cycle of the system are obtained by using probability analysis, the supplementary variable technique and an optimization method