Repetitive testing of multiple products with limited capacity

Purpose – The purpose of this paper is to develop a model‐based methodology for the repetitive testing of multiple products with limited capacity, when the testing process is imperfect. Design/methodology/approach – In a repetitive testing process, items that are classified as non‐conforming may be conforming, resulting in excessive scrapping of good items. Failed items are commonly retested to reduce scrapping costs. This paper develops a stochastic optimization formulation and its solution to determine the numbers of repetitive tests for multiple products that minimize the sum of the expected scrapping costs and variable testing costs, subject to a testing equipment capacity constraint. It also develops a procedure to estimate the parameter values that are used in the optimization formulation. Findings – Computational experiments are conducted to evaluate the estimation and solution procedure and to understand the effect of testing machine capacity on the optimal total cost. These results demonstrate the viability of the proposed approach and the criticality of accurate parameter estimation. Research limitations/implications – This research shows the usefulness of the proposed optimization/statistical estimation approach to a real‐life complex inspection problem. However, the proposed model has to be modified when the characteristics of the testing equipment are changed. Practical implications – The authors capture the idiosyncrasies in semiconductor manufacturing such as the high outgoing quality level, the repetitive testing environment, the high coefficient of variation in the number of failure products, and the testing capacity constraint. Conducting extensive computational experiments, the authors demonstrate that the proposed approach is viable. Originality/value – The paper describes a complex, real‐life inspection management situation, develops a rigorous model‐based solution approach, and carefully demonstrates its viability.