gageRR (version 0.1.0)

d2_integral: d2 and c4 Constants for Gage R&R

Description

Functions to calculate the \(d_2\) constant (expected range of a normal subgroup), the chi-square bias correction factor \(c_4\), and a Minitab-style adjusted \(d_2\) that incorporates the number of subgroups.

Usage

d2_integral(m, rel.tol = .Machine$double.eps^0.5)
c4(n)
d2_minitab_df(m, g)

Value

• d2_integral() returns a numeric scalar (expected range for subgroup size m).

• c4() returns a numeric scalar (bias correction factor).

• d2_minitab_df() returns a numeric scalar (adjusted constant).

Arguments

m

Integer. Subgroup size (must be \(\ge 2\)).

rel.tol

Relative tolerance for integration (passed to integrate()).

n

Integer. Degrees of freedom argument for c4.

g

Integer. Number of subgroups (must be \(\ge 1\)).

Details

• d2_integral(m) computes the exact \(d_2(m)\) by numerical integration.

• c4(n) computes the chi-square bias correction factor \(c_4(n)\).

• d2_minitab_df(m, g) computes a finite-sample adjusted constant \(d_2^{adj}(m,g) = d_2(m) / c_4(df)\), with \(df = g \times (m-1)\) degrees of freedom, consistent with Minitab/AIAG tables.

See Also

integrate, gamma

Examples

# Exact d2 for subgroup size 5
d2_integral(5)

# Chi-square bias correction for df = 8
c4(8)

# Minitab-style adjusted constant for m = 5, g = 2
d2_minitab_df(5, 2)