Double-Sampling np Chart: Limit Search

Search for feasible fractional control limits for the double-sampling np chart by enumerating integer threshold combinations and evaluating each candidate using the numeric core functions dsnp_prob_accept, dsnp_arl, and dsnp_ass.

dsnp_limits(
  p0,
  n1,
  n2,
  alpha = 0.0027,
  p1 = NULL,
  conservative = TRUE,
  allow_empty_warning = FALSE,
  max_results = 20
)

Arguments

p0: The in-control nonconforming proportion. Must be in [0, 1].
n1: The first-stage sample size (positive integer).
n2: The second-stage sample size (positive integer).
alpha: The maximum desired false alarm probability at p0. Must be in (0, 1). When conservative = TRUE, candidates with p_signal0 <= alpha are preferred.
p1: Optional out-of-control proportion. When provided, candidates are ranked by ARL1 (lower is better).
conservative: Logical. If TRUE (default), feasible candidates (p_signal0 <= alpha) are ranked first. If FALSE, all candidates are returned ordered by proximity to alpha.
allow_empty_warning: Logical. If FALSE (default), discard candidates with no integer in the warning zone (ucl1_reject <= wl_accept + 1). This avoids single-sample disguised as DS-np.
max_results: Maximum number of candidates to return. Must be a positive integer.

Value

A list with the following elements:

best: The first row of candidates (a data.frame row).
candidates: A data.frame with all evaluated candidates, sorted by the ranking criteria. Columns include wl, ucl1, ucl2, wl_accept, ucl1_reject, ucl2_accept, pt0, p_signal0, arl0, ass0, feasible, and (if p1 is provided) pt1, p_signal1, arl1, ass1.
p0, p1, n1, n2, alpha: The input parameters.
conservative, allow_empty_warning: The input flags.

Details

The function enumerates all valid combinations of integer thresholds (wl_accept, ucl1_reject, ucl2_accept), converts them to fractional limits compatible with dsnp_prob_accept, and evaluates each candidate's performance at the in-control proportion p0. When p1 is supplied, out-of-control metrics are also computed and used for ranking.

When the warning zone is empty (ucl1_reject = wl_accept + 1), the chart degenerates to a single-sample scheme and probabilities are computed directly via pbinom without calling the core functions.

References

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

Author

Daniela R. Recchia, Emanuel P. Barbosa

Examples


# Small example for fast execution
res <- dsnp_limits(p0 = 0.05, n1 = 5, n2 = 10, alpha = 0.05)
res$best
#>    wl ucl1 ucl2 wl_accept ucl1_reject ucl2_accept       pt0  p_signal0     arl0
#> 1 0.5  1.5  2.5         0           2           2 0.9598674 0.04013256 24.91743
#>       ass0 feasible
#> 1 7.036266     TRUE
nrow(res$candidates)
#> [1] 20

# With out-of-control proportion for ranking
res <- dsnp_limits(p0 = 0.05, n1 = 5, n2 = 10, alpha = 0.05,
                   p1 = 0.10)
res$best[, c("wl", "ucl1", "ucl2", "arl0", "arl1", "ass0")]
#>    wl ucl1 ucl2 arl0        arl1     ass0
#> 1 0.5  5.5 15.5  Inf -4.5036e+15 7.262191