ISO 22514-6-2013 PDF

Full title and description

Statistical methods in process management — Capability and performance — Part 6: Process capability statistics for characteristics following a multivariate normal distribution (ISO 22514-6:2013). This part of ISO 22514 specifies methods to calculate process performance and capability statistics when product or process characteristics must be treated jointly (multivariate), principally for variables that follow a multivariate normal distribution (commonly bivariate).

Abstract

ISO 22514-6:2013 defines multivariate process capability and performance indices and the associated calculation procedures. It gives guidance on when a multivariate assessment is appropriate, describes transformations of tolerance regions to elliptic (ellipsoidal) form where necessary, and presents formulas and statistical relations (including links to the F-distribution) to compute multivariate C and P indices using sample estimates of mean vector and covariance matrix. The document focuses on combining correlated characteristics into a single comprehensive capability statistic and provides practical recommendations (for example on sample size) for reliable estimation.

General information

• Status: Published — confirmed current after ISO review (confirmed 2024).
• Publication date: 15 February 2013.
• Publisher: International Organization for Standardization (ISO).
• ICS / categories: 03.120.30 (Application of statistical methods).
• Edition / version: Edition 1 (2013).
• Number of pages: 34.

Scope

This part of ISO 22514 provides definitions, calculation methods and practical guidance for assessing process capability and performance when the quality of interest is described by multiple, potentially correlated continuous characteristics that can be modelled by a multivariate normal distribution. It covers selection and computation of multivariate capability indices, required sample considerations, handling of tolerance regions that are not naturally elliptic, and how to convert these regions for elliptic-based index calculation. The standard is primarily intended for multivariate cases (typically bivariate) but includes principles applicable to higher dimensions.

Key topics and requirements

• Definition and computation of multivariate process capability (C) and performance (P) indices based on the multivariate normal model.
• Recommendation to centre distributions at target for certain index calculations and procedures to determine the largest contour ellipsoid contained within a tolerance region.
• Transformation of non-elliptic tolerance regions into equivalent elliptic/ellipsoidal regions for index computation.
• Use of the covariance matrix and mean vector to characterise multivariate dispersion and location.
• Statistical relations linking multivariate contour probabilities to the F-distribution for probability calculations.
• Guidance on sample-size considerations (practical recommendation: relatively large sample sizes — e.g., on the order of 125 or more — are preferred for reliable estimation of multivariate indices).
• Advice on when to prefer multivariate capability assessment (e.g., correlated characteristics, non-rectangular tolerance regions, or desire for a single comprehensive statistic).

Typical use and users

This standard is used by quality engineers, process statisticians, metrologists, manufacturing engineers and technical specialists who must evaluate process capability where multiple correlated characteristics determine product acceptability. Typical applications include geometric tolerances, dimensional chains, dynamic balancing metrics, material-property vectors, and other situations where separate univariate indices do not adequately represent the joint behaviour of quality characteristics.

Related standards

ISO 22514 is a multipart series on statistical methods in process management — capability and performance. Closely related parts include: ISO 22514-1 (General principles and concepts, 2014), ISO 22514-2 (Process capability and performance of time-dependent process models — later editions available), ISO 22514-3 (Machine performance studies; original 2008, later revised), ISO 22514-4 (Process capability estimates and performance measures, 2016), ISO 22514-5 (Attributive characteristics, 2019), ISO 22514-7 (Capability of measurement processes; newer edition published after 2012) and ISO 22514-8 (Machine performance of a multi-state production process, 2014). ISO/TC 69/SC 4 is the technical committee responsible for the series.

Keywords

process capability, multivariate normal distribution, capability index, performance index, multivariate PCI, covariance matrix, ellipsoid, tolerance region, F-distribution, statistical methods, ISO 22514, process performance, quality control.

FAQ

Q: What is this standard?

A: ISO 22514-6:2013 specifies statistical methods to calculate process capability and performance measures when characteristics are multivariate and can be modelled by a multivariate normal distribution.

Q: What does it cover?

A: It covers definitions and calculation procedures for multivariate capability (C) and performance (P) indices, transformation of tolerance regions to elliptic/ellipsoidal form, use of the mean vector and covariance matrix, probability calculations related to contour ellipsoids (via the F-distribution relation), and guidance on sample-size and applicability.

Q: Who typically uses it?

A: Quality and process engineers, statisticians, metrologists and manufacturing specialists who need to assess capability for multiple correlated product or process characteristics.

Q: Is it current or superseded?

A: ISO 22514-6:2013 is published and was reviewed and confirmed by ISO in 2024; the 2013 edition remains current. Note that other parts of the ISO 22514 series have been revised at different times—users should check the latest editions of related parts when applying the series.

Q: Is it part of a series?

A: Yes. ISO 22514-6 is part of the ISO 22514 series (Statistical methods in process management — Capability and performance), which includes multiple parts addressing general principles, time-dependent models, machine performance, attribute characteristics, measurement process capability and multi-state processes.

Q: What are the key keywords?

A: Process capability, multivariate normal, capability index, performance index, covariance matrix, ellipsoid, tolerance region, statistical process assessment.