Statistical process control (SPC) for double-bounded information: Choosing wisely the parametric family for unit data

Abstract

This article presents a Statistical Process Control (SPC) framework considering the response process as a unit variable, which demands special treatment. This study designed a Shiny app related to data visualization and inferential estimation adopting SPC charts and Extreme Value Theory. We also proposed a new flexible unit probabilistic model (named FlexShape), which is simple yet overcomes skew information and bimodality in historical data, as part of the complex learning task. Results showed that the proposed framework enables it to handle unit data sets. As an example, we presented data storytelling from the water particle monitoring (relative humidity) from one Atacama Desert station, known to be one of the driest areas on Earth, across hidden patterns such as inundation and microweather. Finally, the developed framework makes possible any research on the univariate unit data decision-making, enabling the database import and adjusting some parametric models, and enabling the comparison of different units’ distribution goodness-of-fit.

Keywords:

• asymmetry data
• bimodal unit distribution
• iterative analysis
• rates and proportions monitoring
• R shiny

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was funded by Universidad de Atacama grant number ATA1956 – CC88433. This study was partially supported by the Vicerrectoría de Investigación y Postgrado (VRIP) and Dirección de Postgrado of the Universidad de Atacama (UDA). The author David Elal-Olivero was supported by the DIUDA REGULAR project No. 22409 from the Universidad de Atacama, Chile. Paulo H. Ferreira acknowledges support from the Brazilian National Council for Scientific and Technological Development [CNPq, grant No. 307221/2022-9].

Notes on contributors

Diego C. Nascimento

Diego C. Nascimento is an Associate Professor at Universidad de Atacama, Copiapó, Chile. He holds a Ph.D. degree in Statistics from the Federal University of São Carlos/University of São Paulo (UFSCar/USP), a M.Sc. degree in Business Management from the Federal University of Pernambuco (UFPE), and a B.Sc. degree in Statistics from the Federal University of Rio Grande do Norte (UFRN). He works mainly on the following topics: statistical learning, data visualization and analytics.

Oilson A. Gonzatto Junior

Oilson A. Gonzatto Junior is a Professor of Statistics at University of São Paulo (USP), São Carlos, São Paulo, Brazil. He received his Ph.D. degree in Statistics in 2021 from UFSCar/USP, his M.Sc degree in Biostatistics in 2017 and B.Sc degree in Statistics in 2016 both from State University of Maringá (UEM), Maringá, Paraná, Brazil, and his licentiate degree in Mathematics in 2014 from State University of Paraná (UNESPAR). He also has a Postdoctoral training at the University of São Paulo (USP), Brazil, in 2021–2023. Currently researches in survival and reliability analysis.

David Elal-Olivero

David Elal-Olivero is a Full Professor at Universidad de Atacama, Copiapó, Chile. He received his Ph.D. degree in Ciencias Matemáticas in 1987 from the Universidad Complutense de Madrid, Spain. His main research interests include distribution theory.

Estefania Bonnail

Estefania Bonnail is an Associate Professor at Universidad de Atacama, Copiapó, Chile. She received her Ph.D. degree in Marine and Coastal Management (Erasmus Mundus Ph.D. program) in 2016 from the Universidad de Cádiz, Spain. She has done intensive research in the field of ecotoxicology.

Paulo H. Ferreira

Paulo H. Ferreira is a Professor of Statistics at the Institute of Mathematics and Statistics, Federal University of Bahia (UFBA), Brazil. He received his Ph.D., M.Sc. and B.Sc. degrees in Statistics all from the Federal University of São Carlos (UFSCar), Brazil. He also has a Postdoctoral training at the University of São Paulo (USP), Brazil. His main research interests include survival and reliability analysis, data mining and statistical process control.