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<p>Statistical quality control methods are essential for maintaining consistent production standards in manufacturing processes. The classical methods follow a global normality assumption for the data; however, this assumption does not hold for all processes, leading to incorrect decisions and wasted resources. In the context of multivariate data, the primary concern is to determine the multivariate distribution while preserving the dependencies between variables. To achieve this, we utilize a copula function to ensure dependence in the resulting distribution. Motivated by the small unwanted shift detections, we develop a multivariate control chart that leverages the maximum entropy principle alongside the copula function. We first derive the joint distribution of a manufacturing process dataset. Then, we establish a control limit using maximum copula entropy, creating a novel and robust control chart. Furthermore, we present two practical examples, a simple two-dimension and complex four-dimension, that utilize the non-parametric (distribution-free) chart in conjunction with the Hotelling <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13571_2025_374_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(T^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>T</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> statistics.</p>

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Non-Parametric Multivariate Control Chart Using Copula Entropy

  • 期刊论文

  • 发表日期：

    2025年8月9日

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  • Seyedeh Azadeh Fallah Mortezanejad,
  • Ruochen Wang,
  • Gholamreza Mohtashami Borzadaran,
  • Kim Phuc Tran

摘要

Statistical quality control methods are essential for maintaining consistent production standards in manufacturing processes. The classical methods follow a global normality assumption for the data; however, this assumption does not hold for all processes, leading to incorrect decisions and wasted resources. In the context of multivariate data, the primary concern is to determine the multivariate distribution while preserving the dependencies between variables. To achieve this, we utilize a copula function to ensure dependence in the resulting distribution. Motivated by the small unwanted shift detections, we develop a multivariate control chart that leverages the maximum entropy principle alongside the copula function. We first derive the joint distribution of a manufacturing process dataset. Then, we establish a control limit using maximum copula entropy, creating a novel and robust control chart. Furthermore, we present two practical examples, a simple two-dimension and complex four-dimension, that utilize the non-parametric (distribution-free) chart in conjunction with the Hotelling \(T^2\) T 2 statistics.