Overview
ISO 7870-9:2020 - "Control charts - Part 9: Control charts for stationary processes" provides guidance on constructing and applying statistical process control (SPC) charts when process data exhibit autocorrelation but are in statistical equilibrium (stationary). The standard outlines practical charting approaches for monitoring process means and variability when the fundamental i.i.d. assumption of traditional SPC charts does not hold.
Key topics and technical scope
- Scope: Construction and application of control charts for stationary autocorrelated processes.
- Core concepts covered: autocovariance, autocorrelation function (ACF), stationarity, AR(1) models, average run length (ARL).
- Main charting approaches:
- Residual charts: fit a time‑series or mathematical model, compute residuals (R_t = x_t − x̂_t) and apply traditional X, CUSUM or EWMA charts to residuals. Advantages and limitations are discussed (modelling required; residuals assumed uncorrelated).
- Traditional charts with adjusted limits: modify control limits to account for autocorrelation rather than modelling; includes EWMAST (EWMA for stationary processes) and modified CUSUM variants. The EWMA statistic is expressed in the standard as Z_t = (1 − λ)Z_{t−1} + λ X_t, with variance adjustments that incorporate the process autocorrelations.
- Monitoring variability: techniques for tracking process variance under stationarity.
- Other approaches: additional methods to handle autocorrelation and comparisons among charts.
- Supporting material: informative annexes on stochastic processes/time series (Annex A) and performance of traditional charts with autocorrelated data (Annex B). Normative linkage to ISO 3534‑2 (statistics vocabulary).
Practical applications
- Monitoring continuous-production processes where measurements are temporally correlated (chemical, process, petrochemical industries).
- Quality control in manufacturing contexts with short sampling intervals that induce positive autocorrelation.
- Biomedical and biological process monitoring where random bursts cause sustained autocorrelated effects.
- Use cases illustrated include viscosity monitoring in rolling mills and typical SPC implementations where modelling or limit adjustments are required.
Who should use this standard
- Quality engineers and SPC practitioners adapting control charts for autocorrelated data.
- Process statisticians and data scientists implementing residual‑based SPC or modified EWMA/CUSUM charts.
- Operations and process control teams in continuous industries, laboratories, and regulated sectors where time dependence is present.
Related standards and references
- ISO 7870 series (other parts on control charts)
- ISO 3534‑2 (Statistics - vocabulary and symbols - applied statistics)
Keywords: ISO 7870-9:2020, control charts, stationary processes, autocorrelation, SPC, EWMAST, residual charts, modified CUSUM, process monitoring, quality control, time series.
