ISO 7870-7:2020

Overview

ISO 7870-7:2020 - Control charts - Part 7: Multivariate control charts specifies how to construct and use multivariate control charts within statistical process control (SPC). The standard presents practical, state-of-the-art methods for monitoring several related quality characteristics simultaneously (multivariate statistical process control, MSPC). It focuses on control-chart design, limits and interpretation for vector-valued measurements (mean vector and covariance matrix), and gives worked examples and estimation guidance. Note: the use of PCA and PLS for MSPC is explicitly excluded from this document.

Key topics and technical requirements

• Purpose and applying conditions for multivariate control charts, including when variables are correlated and why univariate charts can be misleading.
• Classification of multivariate charts and guidance for selecting an appropriate charting method.
• Charts for monitoring the process mean:
  • Procedures for subgroup size n > 1 and n = 1.
  • χ control charts (when pre-specified parameter values are known).
  • T control charts (when pre-specified parameter values are unknown).
• Multivariate EWMA / MEWMA (multivariate exponential weighted moving average) methods and selection of weighting parameters.
• Control charts for process dispersion and tests for assignable causes.
• Interpretation of out-of-control signals and recommended follow-up actions.
• Annexes with practical examples (MSPC example, MEWMA example) and an annex on estimation of μ (mean vector) and Σ (covariance matrix).
• Definitions, symbols and abbreviations (SPC, MSPC, EWMA, MEWMA, UCL/LCL, ARL) and normative reference to ISO 3534-2 (statistics vocabulary).

Practical applications

• Monitoring processes where multiple correlated quality characteristics must be controlled simultaneously (e.g., chemical processes, semiconductor manufacturing, multi-attribute inspection).
• Detecting multivariate mean shifts and dispersion changes while accounting for covariance between variables to reduce false alarms.
• Implementing MSPC modules in SPC software and quality management systems.
• Supporting process capability assessments for multivariate distributions (in conjunction with related standards).

Who should use this standard

• Quality engineers, process engineers and statisticians implementing SPC for multidimensional measurements.
• Software developers and data scientists building MSPC tools and dashboards.
• Auditors and compliance professionals assessing multivariate control procedures in manufacturing and process industries.

Related standards

• ISO 3534-2: vocabulary and symbols for applied statistics (normative reference).
• ISO 22514-6: methods for capability statistics for multivariate distributions (complementary guidance).

Keywords: ISO 7870-7, multivariate control charts, statistical process control, MSPC, MEWMA, EWMA, T control chart, χ control chart, covariance matrix, process monitoring, quality control.