Mathematical Model for Determining the Number of Re-inspections Considering Inspection Effectiveness

Zahmatkesh Saredorahi, Faeze; Fallah Nezhad, Mohammad Saber

doi:10.22034/IJRRS.2026.9.1.7

Mathematical Model for Determining the Number of Re-inspections Considering Inspection Effectiveness

Document Type : Original Research Article

Authors

Faeze Zahmatkesh Saredorahi

Mohammad Saber Fallah Nezhad

Department of Industrial Engineering, Yazd University, Yazd, Iran

10.22034/IJRRS.2026.9.1.7

Abstract

This paper addresses the critical challenge of determining the optimal number of re-inspections in industrial applications to detect non-apparent failures. These failures, often subtle or latent, can have significant consequences if they reach the end-user. We develop a comprehensive mathematical model aimed at minimizing the total expected cost associated with defect detection. This model intricately considers the probability of detecting defective items at each inspection stage, acknowledging the inherent imperfections and potential for false positives and false negatives in any inspection process. The core of our approach lies in balancing the direct cost of inspecting with the indirect but potentially substantial risk and cost of releasing undetected nonconforming items into the market or the next stage of production. Through a detailed mathematical formulation, we derive an optimal re-inspection policy. An illustrative example is provided to demonstrate the practical applicability of our model, followed by a thorough sensitivity analysis to assess the impact of key process parameters on the derived inspection policy. This work contributes to improving quality control by providing a data-driven framework for optimizing inspection resources.

Keywords

Inspection effectiveness

Inspection policy

Optimization

Re-inspection

Subjects

Risk

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