Overview
ISO 22514-6:2013 - Statistical methods in process management - Capability and performance - Part 6 - defines methods for calculating process capability and process performance statistics when product or process characteristics are best treated as a multivariate quantity. The standard focuses mainly on bivariate normal distributions (two-dimensional) but is applicable in principle to higher-dimensional multivariate normal cases. It provides definitions and calculation approaches (extensions of classical C and Cpk indices) for assessing capability where features are correlated or tolerance regions are non-rectangular.
Key topics and requirements
- Multivariate quantity and tolerance region: Treats feature vectors (e.g., x, y coordinates) and tolerance regions such as ellipses, circles or other multivariate shapes rather than independent univariate limits.
- Index types: Introduces different index families (notably Type I - probability-based - and Type II - geometry/area-based) and further variants (e.g., Ic, IIc) for capability/performance measurement.
- Calculation formulas: Provides formulae for capability and performance indices for multivariate normal data; derivations and informative examples are included in annexes.
- Assumptions and prerequisites:
- Data are assumed to follow a multivariate normal distribution (primarily bivariate).
- The measuring system’s capability should be demonstrated prior to process capability assessment.
- Recommended minimum sample size to estimate PCI is preferably at least 125.
- Scope limitation: The standard defines and describes methods but does not evaluate which method is preferable for specific situations - selection is left to the user’s judgement.
Practical applications
ISO 22514-6 is practical for cases where treating features jointly gives a more accurate assessment than separate univariate analyses:
- Geometric tolerances (e.g., 2D or 3D hole position, slot dimensions)
- Dynamic magnitudes such as shaft imbalance
- Correlated material properties or chemical parameters
- Approval of production processes, supplier comparisons, contract compliance, complaint and damage analyses
Benefits include a single comprehensive statistic for correlated features, correct handling of non-rectangular tolerance regions (ellipsoids, circles), and more realistic capability/performance assessment where interdependencies matter.
Who should use this standard
- Quality engineers and process engineers assessing multivariate product features
- Metrologists and statisticians implementing capability studies
- Suppliers and customers defining multivariate capability limits in contracts
- R&D and manufacturing teams dealing with correlated dimensional or functional characteristics
Related standards
Keywords: ISO 22514-6:2013, multivariate normal distribution, process capability, process performance, multivariate PCI, bivariate normal, tolerance region, capability index.
