Although there is extensive literature on the application of artificial neural networks (NNs) in quality control (QC), to monitor the conformity of a process to quality specifications, at least five QC measurements are required, increasing the related cost. To explore the application of neural networks to samples of QC measurements of very small size, four one-dimensional (1-D) convolutional neural networks (CNNs) were designed, trained, and tested with datasets of $ n $-tuples of simulated standardized normally distributed QC measurements, for $ 1 \leq n \leq 4$. The designed neural networks were compared to statistical QC functions with equal probabilities for false rejection, applied to samples of the same size. When the $ n $-tuples included at least two QC measurements distributed as $ \mathcal{N}(μ, σ^2) $, where $ 0.2 < |μ| \leq 6.0 $, and $ 1.0 < σ\leq 7.0 $, the designed neural networks outperformed the respective statistical QC functions. Therefore, 1-D CNNs applied to samples of 2-4 quality control measurements can be used to increase the probability of detection of the nonconformity of a process to the quality specifications, with lower cost.