Control Charts

Rare-Event Control Charts (g, t)

g chart (Benneyan) and t chart (Nelson 1/3.6 transform) for rare events.

Statusvalidated

Version1.0.0

Minitab equivalentStat > Control Charts > Rare Event Charts (G, T)

Description

g chart: count of opportunities between consecutive events. Geometric distribution; limits via Benneyan: CL=ḡ, UCL/LCL = ḡ ± 3·√(ḡ·(ḡ+1)). t chart: time between events, exponentially distributed. Nelson transform y = t^(1/3.6) brings the series closer to normal; I-MR limits computed on y, results back-transformed for display.

Formulas

g chart

CL = \overset{g}{ˉ}, UCL/LCL = \overset{g}{ˉ} \pm 3 \overset{g}{ˉ} (\overset{g}{ˉ} + 1)

Benneyan 1999

t chart (transformed)

y_{i} = t_{i}^{1/3.6}, UCL/LCL = \overset{y}{ˉ} \pm 3 \overline{MR}_{y} / d_{2}

Nelson 1994 — I-MR on y

References

Benneyan, J. C. (1999), Geometric-based g-Type Statistical Control Charts
Nelson, L. S. (1994), A Control Chart for Parts-per-Million Nonconforming Items