d₂ constant

range to sigma conversion

σ ≈ R̄ / d₂

d₂ is the expected range of n values from a standard normal distribution: 1.128 for n = 2, 1.693 for n = 3, 2.059 for n = 4, 2.326 for n = 5. Dividing the average range by d₂ estimates the standard deviation. Related constants A₂, D₃ and D₄ give the control limits of X-bar and R charts.

Calculate it

Process Capability & Control Charts: Cp, Cpk, Pp, Ppk, PPM and confidence intervals with X-bar/R, X-bar/S or I-MR charts and all 8 Nelson rules.

Related terms

• Sigma within: short-term standard deviation