A Cost-Minimization Model for Multicharacteristic Component Inspection

Abstract

In this paper a mathematical model is developed for determining the optimal number of inspections for multicharacteristic components where failure can be catastrophic. The model optimizes the expected total cost per accepted component resulting from (1) type I errors, (2) type II errors, (3) cost of added inspection, and (4) ordering of quality characteristics for inspection. The model considers components with several characteristics to be inspected. Failure to meet the quality requirements of any one characteristic results in the rejection of the component. Taking into consideration all three costs referred to above, a mathematical expression for expected total cost per accepted component is obtained. Also, an expression is developed for finding the optimal sequence of characteristic inspection. Finally, a computational procedure is outlined to determine the optimal sequence of characteristic inspection and the optimal number of inspections using the two expressions stated above.