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.
