Characteristic Curves for Multiple-Inspector Sampling Plans with Inspection Errors

Classical single sampling plans (SSPs) are designed assuming that product units sampled from a lot are inspected by one inspector, in the absence or presence of inspection errors. The scenario becomes more complicated when SSPs are applied assuming that multiple inspectors operate in parallel on the same sample, as occasionally required in high-value-added or highly customized industries (e.g., aerospace, defence, luxury goods, etc.). Current literature lacks a rigorous formulation of operating characteristic (OC) curves for SSPs involving multiple inspectors, who independently perform conformity assessments on the same product units. This paper addresses this gap by extending classical OC-curve theory to scenarios involving multiple inspectors, each characterized by distinct individual error rates (i.e., probabilities of misclassifying conforming units as defective ones and vice versa). The resulting analytical models are flexible enough to incorporate alternative aggregation criteria and sequences for consolidating individual inspectors’ conformity assessments into an overall lot-disposition decision. Both hypergeometric (Type-A) and binomial (Type-B) formulations of the multiple-inspector OC curve are presented. Results show that in the absence of inspection errors, the multiple-inspector OC curve converges to the classical single-inspector curve. Moreover, aggregation criteria may significantly influence the OC-curve shape: a majority aggregation criterion yields robust OC curves, even under moderate to high error rates, whereas an unanimity criterion produces excessively severe OC curves, unless inspection errors are very low. Overall, the proposed analytical framework enables a realistic design of SSPs, particularly beneficial for sectors demanding highly reliable inspections.