Function g_chart 

pub fn g_chart(inter_event_counts: &[f64]) -> Option<GChart>

Compute the G chart from inter-event conforming counts.

Formulas

• ḡ = mean(gᵢ)
• UCL = ḡ + 3·√(ḡ·(ḡ+1))
• LCL = max(0, ḡ − 3·√(ḡ·(ḡ+1)))

The spread term √(ḡ·(ḡ+1)) follows directly from the variance of the geometric distribution: Var(G) = (1−p)/p² ≈ ḡ·(ḡ+1) when p is small.

Returns

None if fewer than 3 observations or any count is negative.

References

• Kaminsky, F.C. et al. (1992). “Statistical control charts based on a geometric distribution”, Journal of Quality Technology 24(2), pp. 63-69.
• Benneyan, J.C. (2001). “Number-Between g-Type Statistical Quality Control Charts for Healthcare Applications”, Health Care Management Science 4(4), pp. 305-318.
• Woodall, W.H. (2006). “The Use of Control Charts in Health-Care and Public-Health Surveillance”, Journal of Quality Technology 38(2), pp. 89-104.