Replacement strategy for non self announcing failure equipment

This paper addresses the problem of generating optimal inspection strategies for randomly failing systems whose state can be determined only by physical inspection. The equipment is replaced either upon detection of failure during one inspection, or at the first inspection time in which the probability of failure occurrence exceeds a fixed given threshold, whichever occurs first. The costs incurred for such a strategy include the inspection cost, the cost associated to the elapsed time between failure and its detection, preventive replacement cost and the cost of a replacement due to failure. An optimal inspection strategy is defined as the inspection sequence which minimizes the total average cost per time unit over a replacement cycle. A mathematical model which generates this optimal checking sequence, is presented. For a given equipment life time distribution function, a test case is analyzed to illustrate the proposed approach