Overview
ISO 7870-6:2016 - Control charts - Part 6: EWMA control charts defines the use of Exponentially Weighted Moving Average (EWMA) control charts as a statistical process control (SPC) technique to detect small to moderate shifts in a process mean. The standard explains how to compute and plot the EWMA statistic (a geometrically weighted average of current and all prior sample means), how to set control limits that depend on the smoothing parameter (λ) and confidence factor L, and practical recommendations for implementation and interpretation.
Key topics and technical requirements
- EWMA statistic definition: each plotted value z_i is a weighted combination of the current sample mean and the previous EWMA value. The most recent samples receive the largest weight; weights decline geometrically with age.
- Smoothing parameter (λ): 0 < λ < 1 controls memory - small λ gives strong smoothing (sensitive to small shifts), large λ makes EWMA behave more like a Shewhart X̄ chart.
- Control limits: limits are set as the center line (process target μ0) ± L × σ_z(i), where σ_z(i) is the EWMA standard deviation at sample i. The standard emphasizes using the exact transient limits early in monitoring and notes that limits approach steady‑state values after many samples.
- Rational subgroups: for subgroup size n > 1, replace x_i with the subgroup mean x̄_i and use σ_x = σ/√n in calculations.
- Initialization: recommended starting value z0 is the process target μ0 (or an average of preliminary data).
- Performance metrics: Average Run Length (ARL), MAXRL and control chart effectiveness are addressed; annexes provide examples and combined-chart strategies.
- Variants and annexes: normative annexes cover combined Shewhart–EWMA charts, EWMA charts for proportions and counts, multiple nonconformities, trend analysis, and robustness to non‑normality.
Practical applications and who should use it
ISO 7870-6 is designed for quality and process professionals who need early detection of small, gradual shifts in process average. Typical users and applications:
- Quality engineers and statisticians implementing SPC in manufacturing, chemical processing, pharmaceuticals, food, and other continuous processes.
- Process engineers monitoring equipment wear, drift or slow deterioration where early warning is critical.
- Operations with low production rate or costly inspection (n = 1 situations) where subgroup sampling is difficult or expensive.
- Service and administrative processes (e.g., monthly complaint counts, automated inspection systems) where individual observations or aggregated counts are charted.
- Use cases include combining EWMA with Shewhart charts to capture both small and large shifts and applying EWMA variants for proportions or counts.
Related standards
- ISO 7870-1: General guidelines for control charts
- ISO 7870-2: Shewhart control charts
- ISO 7870-4: Cumulative sum (CUSUM) charts - alternative for small-shift detection
Keywords: ISO 7870-6:2016, EWMA control charts, exponentially weighted moving average, statistical process control, smoothing parameter lambda, control limits, ARL, Shewhart, CUSUM, rational subgroups.