Double-Sampling np Chart: Average Run Length

Compute the average run length for the double-sampling np chart as the reciprocal of the signal probability at each supplied nonconforming proportion.

Usage

dsnp_arl(p, n1, n2, wl, ucl1, ucl2)

Arguments

p

Nonconforming proportion to evaluate, a finite numeric scalar or vector in \([0, 1]\).

n1

First-stage sample size, a positive integer.

n2

Second-stage sample size, a positive integer.

wl

Finite fractional warning limit.

ucl1

Finite fractional first-stage upper control limit greater than wl.

ucl2

Finite fractional combined upper control limit greater than wl.

Value

A list with arl, the average run length; pt, total acceptance probability; p_signal, signal probability; and the validated chart parameters n1, n2, wl, ucl1, and ucl2.

Details

For signal probability \(1 - P_T(p)\), the ARL is \(1 / (1 - P_T(p))\). It is infinite when the signal probability is zero.

References

Joekes, S., Smrekar, M. and Barbosa, E. P. (2015). Extending a double sampling control chart for non-conforming proportion in high quality processes to the case of small samples. Statistical Methodology, 23, 35–49.

See also

dsnp_prob_accept, dsnp_ass

Author

Daniela R. Recchia, Emanuel P. Barbosa

Examples

arl0 <- dsnp_arl(0.005, 34, 162, 1.5, 2.5, 4.5)$arl
arl1 <- dsnp_arl(0.0075, 34, 162, 1.5, 2.5, 4.5)$arl
c(arl0 = arl0, arl1 = arl1)
#>     arl0     arl1 
#> 803.4114 193.2229