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}(\mu, \sigma^2) $, where $ 0.2 < |\mu| \leq 6.0 $, and $ 1.0 < \sigma \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.

翻译：尽管关于人工神经网络在质量控制中应用的文献已相当丰富，但将监控过程符合质量规范所需的质控测量数据至少需要五个样本点，这增加了相关成本。为探索神经网络在极小样本质控测量中的应用，本研究设计了四个一维卷积神经网络，使用模拟标准化正态分布质控测量值的$n$元组数据集（$1 \leq n \leq 4$）进行训练与测试。将所设计的神经网络与同等虚发概率的统计质控函数进行对比，两者均应用于相同样本量。当$n$元组包含至少两个服从$\mathcal{N}(\mu, \sigma^2)$分布的质控测量值，且满足$0.2 < |\mu| \leq 6.0$、$1.0 < \sigma \leq 7.0$时，所设计的神经网络性能优于对应的统计质控函数。因此，将一维卷积神经网络应用于2-4个质控测量值的样本，可在降低检测成本的同时，提高识别过程不符合质量规范的概率。