Acceptance sampling with multiple inspectors: Critical aspects in aggregating individual assessments

In productions characterized by small scale, high customization and high added value—for example, in sectors like nuclear energy, aerospace, and haute couture—it is imperative to strive for zero risk of delivering defective products to customers. In order to achieve this, the production conformity verification can be redundant and involve multiple inspectors. In addition, since inspections are often performed manually by human inspectors, whose assessments may be somewhat subjective, a precise definition of inspection procedures and thorough training of inspectors are essential to achieve consistent results. Unfortunately, combining the assessments by multiple inspectors with the traditional acceptance-sampling schemes used for conformity verification (e.g., single, double, sequential sampling plans) is not straightforward, as these schemes generally assume that inspections are unique, nonredundant, and carried out by a single inspector. This article focuses on the aggregation of multiple-inspector conformity assessments within traditional acceptance-sampling schemes, to reach a final lot-disposition decision (typically pass/fail of the whole lot). Various aggregation approaches can be applied, often markedly different from one another; the analysis of these approaches constitutes an innovative aspect of this study. With the help of a plurality of realistic examples in the haute-couture sector, the article highlights how, starting from individual conformity assessments by each inspector, different global decision-making scenarios can be generated, often contradictory, potentially resulting in a state of total undecidability regarding the acceptance of a supply. This may happen especially in situations characterized by a certain degree of disagreement between inspectors. Finally, it is proposed to use of an inspection-agreement indicator (i.e., Gwet’s kappa) aimed at highlighting potentially controversial situations and triggering appropriate actions to make inspectors’ assessments more robust and consistent.