EWMA Chart

Time-weighted control chart — each point is an exponentially weighted average; sensitive to small persistent shifts.

Also known as: EWMA, Exponentially Weighted Moving Average

The EWMA chart (Exponentially Weighted Moving Average, Roberts 1959) integrates information across successive observations and detects small persistent shifts (0.5σ–1.5σ) much faster than classical Shewhart charts.

z_{i} = λ x_{i} + (1 - λ) z_{i - 1}, 0 < λ \leq 1

λ (smoothing) — small λ (0.05–0.10) → long "memory", very sensitive to 1σ shifts; large λ (0.3–0.4) → Shewhart-like behaviour
Control limits UCL/LCL = $\overset{x}{ˉ} \pm L \overset{σ}{^} λ / (2 - λ)$ ; typical $L = 3$ , at small λ $L = 2.7$
Starting value $z_{0} = \overset{x}{ˉ}$ from the baseline

Used in

Control Chart (Time-Weighted)

In the Algorithm Lab

control-charts/time-weighted-chart

Sources

Roberts, S. W. — Control Chart Tests Based on Geometric Moving Averages, Technometrics, 1(3), 1959
Montgomery, D. C. — Introduction to Statistical Quality Control, 8th Edition, Chapter 9
Lucas, J. M. & Saccucci, M. S. — Exponentially Weighted Moving Average Control Schemes, Technometrics, 32(1), 1990

EWMA Chart

See also

Used in

In the Algorithm Lab

Sources