A multivariate CUSUM control chart for monitoring Gumbel's bivariate exponential data. (10th August 2020)

• Record Type: Journal Article
• Authors: Xie, FuPeng; Sun, JinSheng; Castagliola, Philippe; Hu, XueLong; Tang, Anan
• Is Part Of: Quality and reliability engineering international. Volume 37:Number 1(2021)
• Page Start: 10
• Page End: 33
• Publication Date: 2020-08-10
• Subjects: control charts -- process monitoring and control -- statistical quality control; Reliability (Engineering) -- Periodicals; Quality control -- Periodicals; High technology -- Periodicals; 620.00452
• DOI: 10.1002/qre.2717
• Languages: English
• ISSNs: 0748-8017

Abstract

Abstract: Exponentially distributed data are commonly encountered in high‐quality processes. Control charts dedicated to the univariate exponential distribution have been extensively studied by many researchers. In this paper, we investigate a multivariate cumulative sum (MCUSUM) control chart for monitoring Gumbel's bivariate exponential (GBE) data. Some tables are provided to determine the optimal design parameters of the proposed MCUSUM GBE chart. Furthermore, both zero‐state and steady‐state properties of the proposed MCUSUM GBE chart for the raw and the transformed GBE data are compared with the multivariate exponentially weighted moving average (MEWMA) chart and the paired individual cumulative sum (CUSUM) chart. The results show that the proposed MCUSUM GBE chart outperforms the other two types of control charts for most shift domains. In addition, an extension to Gumbel's multivariate exponential (GME) distribution is also investigated. Finally, an illustrative example is provided in order to explain how the proposed MCUSUM GBE chart can be implemented in practice.