In-Service Inspections of Multiple Systems Under Availability Requirement

System failures are usually observed during regular maintenance or inspection and this is especially the case for systems in standby or storage, which is common for safety critical systems. A periodic inspection policy is usually adopted. During the inspection, a lot of information is gained about the status of the system. Such information should be used in deciding upon the time for the next inspection. Hence sequential inspection is more appropriate, especially when the aging property of the system is unknown, and has to be estimated with the information from inspection. In this paper, a model is developed and sequential inspection strategies are studied in this situation. The focus is on the case when there are multiple systems inspected at the same, but discrete times. We also do not assume a known distribution of the system lifetime, and the estimation of that is incorporated into the analysis and decision-making. An availability criterion is considered and numerical example is provided to illustrate the procedure.