{"title":"应用于小样本的卷积神经网络的质量控制","authors":"Rallou A. Chatzimichail, Aristides T. Hatjimihail","doi":"10.1515/eqc-2023-0001","DOIUrl":null,"url":null,"abstract":"Abstract Artificial neural networks (NNs) have been extensively studied for their application to quality control (QC) to monitor the conformity of processes to quality specifications. However, the requirement of at least five QC measurements increases the associated costs. This study explores the potential of using NNs on samples of QC measurements of very small size. To achieve this, three one-dimensional (1-D) convolutional NNs (CNNs) were designed, trained, and tested on datasets of n -tuples of simulated, standardized, normally distributed QC measurements, where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>2</m:mn> <m:mo>≤</m:mo> <m:mi>n</m:mi> <m:mo>≤</m:mo> <m:mn>4</m:mn> </m:mrow> </m:math> {2\\leq n\\leq 4} . The performance of the designed CNNs was compared to that of statistical QC functions applied to samples of equal sizes, maintaining equal probabilities for false rejection. The results demonstrated that for n -tuples of QC measurements distributed as <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi mathvariant=\"script\">𝒩</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:msup> <m:mi>s</m:mi> <m:mn>2</m:mn> </m:msup> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> \\mathscr{N}(0,s^{2}) , where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>1.2</m:mn> <m:mo><</m:mo> <m:mi>s</m:mi> <m:mo>≤</m:mo> <m:mn>9.0</m:mn> </m:mrow> </m:math> 1.2<s\\leq 9.0 , the designed CNNs outperformed their statistical QC functions counterparts. Therefore, the use of 1-D CNNs applied to samples of two to four QC measurements can effectively enhance the detection of nonconformity of a process to quality specifications. This approach has the potential to significantly reduce the costs of QC measurements and improve the overall efficiency of the QC process.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"17 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quality Control Using Convolutional Neural Networks Applied to Samples of Very Small Size\",\"authors\":\"Rallou A. Chatzimichail, Aristides T. Hatjimihail\",\"doi\":\"10.1515/eqc-2023-0001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Artificial neural networks (NNs) have been extensively studied for their application to quality control (QC) to monitor the conformity of processes to quality specifications. However, the requirement of at least five QC measurements increases the associated costs. This study explores the potential of using NNs on samples of QC measurements of very small size. To achieve this, three one-dimensional (1-D) convolutional NNs (CNNs) were designed, trained, and tested on datasets of n -tuples of simulated, standardized, normally distributed QC measurements, where <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:mn>2</m:mn> <m:mo>≤</m:mo> <m:mi>n</m:mi> <m:mo>≤</m:mo> <m:mn>4</m:mn> </m:mrow> </m:math> {2\\\\leq n\\\\leq 4} . The performance of the designed CNNs was compared to that of statistical QC functions applied to samples of equal sizes, maintaining equal probabilities for false rejection. The results demonstrated that for n -tuples of QC measurements distributed as <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:mi mathvariant=\\\"script\\\">𝒩</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\\\"false\\\">(</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:msup> <m:mi>s</m:mi> <m:mn>2</m:mn> </m:msup> <m:mo stretchy=\\\"false\\\">)</m:mo> </m:mrow> </m:mrow> </m:math> \\\\mathscr{N}(0,s^{2}) , where <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:mn>1.2</m:mn> <m:mo><</m:mo> <m:mi>s</m:mi> <m:mo>≤</m:mo> <m:mn>9.0</m:mn> </m:mrow> </m:math> 1.2<s\\\\leq 9.0 , the designed CNNs outperformed their statistical QC functions counterparts. Therefore, the use of 1-D CNNs applied to samples of two to four QC measurements can effectively enhance the detection of nonconformity of a process to quality specifications. This approach has the potential to significantly reduce the costs of QC measurements and improve the overall efficiency of the QC process.\",\"PeriodicalId\":37499,\"journal\":{\"name\":\"Stochastics and Quality Control\",\"volume\":\"17 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Stochastics and Quality Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/eqc-2023-0001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics and Quality Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/eqc-2023-0001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Quality Control Using Convolutional Neural Networks Applied to Samples of Very Small Size
Abstract Artificial neural networks (NNs) have been extensively studied for their application to quality control (QC) to monitor the conformity of processes to quality specifications. However, the requirement of at least five QC measurements increases the associated costs. This study explores the potential of using NNs on samples of QC measurements of very small size. To achieve this, three one-dimensional (1-D) convolutional NNs (CNNs) were designed, trained, and tested on datasets of n -tuples of simulated, standardized, normally distributed QC measurements, where 2≤n≤4 {2\leq n\leq 4} . The performance of the designed CNNs was compared to that of statistical QC functions applied to samples of equal sizes, maintaining equal probabilities for false rejection. The results demonstrated that for n -tuples of QC measurements distributed as 𝒩(0,s2) \mathscr{N}(0,s^{2}) , where 1.2<s≤9.0 1.2
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