ISO 22514-6:2013

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

• ISO 22514-1 (General principles and concepts)
• ISO 22514-2 (Time-dependent process models)
• ISO 22514-5 (Attribute characteristics)
• ISO 22514-7 (Capability of measurement processes)

Keywords: ISO 22514-6:2013, multivariate normal distribution, process capability, process performance, multivariate PCI, bivariate normal, tolerance region, capability index.