Mathematical optimization models for multicharacteristic repeat inspections

This paper develops three mathematical optimization models for the repeat inspections of critical components. A component is critical if its failure will result in a huge cost or hazardous situations. Such a component could be a component in an aircraft or a gas ignition system. Critical components have many characteristics and a failure of one of these characteristics will result in system failure. The first model presented is a cost-minimizing model. The model optimizes the cost due to false acceptance, false rejection, and cost of inspection. This model determines the number of times a component should be inspected in order to minimize the total expected cost of inspection. The second model focuses on minimizing the probability of accepting a defective component. The third model is the satisfying model. In this model, an upper limit is specified for the total expected cost and the probability of accepting a defective component. Then a satisfying solution is determined. Application of each of the models is cited in the paper.