A max-operator-based multivariate process capability analysis approach with application to a gear grinding process

Multivariate process capability analysis aims to assess the ability of a manufacturing process that meets the specification limits of multiple quality characteristics (QCs). Most of the existing multivariate process capability analysis approaches rely on modifications of tolerance or process region and/or restrictive assumptions, are computationally intensive and provide few cues for process improvement. This paper aims to address these issues by proposing a max-operator-based capability analysis approach for a process with multiple QCs. The proposed approach first transforms the measurement data into dimensionless data with a common upper specification limit one, and then aggregates the transformed QCs into an overall performance indicator using the max-operator aggregation model, which ensures that all the specification limits are exactly met and considerably simplifies the analysis. The overall performance indicator is modelled by an appropriate distribution, and the process capability is assessed from the fitted right-tail distribution. When the process is deemed to be incapable, a root cause analysis is carried out to provide the information useful for process improvement. A real dataset is analyzed and a case study on gear grinding is included to illustrate the appropriateness and usefulness of the proposed approach.