A Shewhart chart with alternated charting statistic to control multivariate Poisson processes

• Published in: Computers & industrial engineering 2020-07, Vol.145, p.106523, Article 106523
• Main Authors: Campos Leoni, Roberto, Fernando Branco Costa, Antonio
• Format: Article
• Language: English
• Subjects: ACS Poisson chart; Alternated charting statistic; Multivariate Poisson processes; Shewhart c chart
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/j.cie.2020.106523

•We propose the use of a Shewhart c chart with alternating charting statistic.•The ACS Poisson chart works with only one discrete quality characteristic per time.•The ACS Poisson chart outperforms all its competitors.•The ACS Poisson chart is operationally simpler than its competitors. In this article, a Shewhart c chart with alternating charting statistic (ACS Poisson chart) is proposed to control multivariate Poisson processes. Considering the bivariate case, where we have the occurrence of X and Y defects; if the current sample point is cx (cy), the number of X (Y) defects, then the next sample point will be cy (cx), the number of Y (X) defects. The ACS Poisson chart outperforms all its competitors, that is, the joint cx and cy Poisson charts and the bivariate Poisson charts with the following monitoring statistics: X + Y, X-Y, and the maximum between X and Y. At each sampling point, the ACS Poisson chart controls the occurrences of only one type of non-conformity, because of that its unit of inspection might be twice larger. The ACS Poisson chart requires larger units of inspection to be more sensitive than its competitors, but not necessarily twice larger. The CUSUM version of the ACS Poisson chart also proved to be more efficient than the bivariate Poisson CUSUM chart. Similar results were also observed with the monitoring of trivariate Poisson processes.