Double-Sampling np Chart: Average Sample Size

Compute the average sample size for the double-sampling np chart under complete inspection of every second-stage sample that is requested.

Usage

dsnp_ass(p, n1, n2, wl, ucl1)

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.

Value

A list with ass, the average sample size; p_second, the probability that the second sample is required; and the validated chart parameters n1, n2, wl, and ucl1.

Details

If a decision is reached at the first stage, $n_1$ items are inspected; otherwise all $n_2$ additional items are inspected. Therefore $$ASS(p) = n_1 + n_2 P_p(\text{second stage}).$$ This function does not use curtailed inspection within the second sample.

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.

Author

Daniela R. Recchia, Emanuel P. Barbosa

Examples

dsnp_ass(0.005, 34, 162, 1.5, 2.5)$ass
#> [1] 35.93534