Control Chart (Rare Events)

Control Charts for Rare Events

For rare events (accidents, tool breaks, low-rate defects) Shewhart and attribute charts are useless — they would show zeros for days then one isolated jump that looks like an outlier. Specialised charts handle the underlying distribution properly.

g chart (opportunities between events): Plots the number of units or days between two consecutive events. Geometric distribution. Limits per Benneyan: CL = ḡ, UCL/LCL = ḡ ± 3·√(ḡ·(ḡ+1)).

t chart (time between events): Plots the time between events (continuous, exponentially distributed). The time axis is transformed: y = t^(1/3.6) (Nelson 1994). I-MR limits are computed on y; the KPI strip back-transforms them to the original scale.

Both charts typically have an LCL near zero. The actionable signals are upward jumps (a long quiet stretch is rarely as useful as a sudden cluster).

Pitfalls

Wrong data type: The g chart needs counts between events; the t chart needs actual time durations. Mixing them yields nonsense limits.

Too few events: With fewer than ~20 observations ḡ fluctuates strongly and the limits are unreliable. Classic 25–30-point SPC rule applies here too.

Non-stationary rate: Both charts assume the event rate is constant. With a clearly increasing rate (e.g. after tool wear) split the data first and run separate charts.

Examples

This module ships with the following example datasets — load any of them in the app with a single click.

Available in the following cycles

• DMAIC: Control
• DMADV: Verify
• 8D: D6 — Implementation