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：尽管人工神经网络在质量控制中的应用已有大量文献，但为了监控过程是否符合质量规范，至少需要五次质量控制测量，这增加了相关成本。为探索神经网络在极小规模质量控制测量样本中的应用，本文设计、训练并测试了四种一维卷积神经网络，这些网络使用模拟标准化正态分布质量控制测量的$n$元组数据集进行训练，其中$1 \leq n \leq 4$。将设计的神经网络与具有相同虚警概率的统计质量控制函数进行对比，并应用于相同样本量的样本。当$n$元组包含至少两个服从$\mathcal{N}(\mu, \sigma^2)$分布的质量控制测量，且参数满足$0.2 < |\mu| \leq 6.0$、$1.0 < \sigma \leq 7.0$时，设计的神经网络性能优于相应的统计质量控制函数。因此，将一维卷积神经网络应用于2-4个质量控制测量样本，可在降低成本的同时提高对过程不符合质量规范的检测概率。