Skip to contents

Double-Sampling np Chart: Limit Search

Source: R/dsnp_limits.R
dsnp_limits.Rd

Search for feasible fractional control limits for the double-sampling np chart by enumerating integer threshold combinations and evaluating each candidate with the shared numerical core used by dsnp_prob_accept(), dsnp_arl(), and dsnp_ass(). This function searches limits for fixed sample sizes; it does not optimize the complete sampling design.

Usage

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

Arguments

p0

In-control nonconforming proportion, a finite scalar in \([0, 1]\).

n1

First-stage sample size, a positive integer.

n2

Second-stage sample size, a positive integer.

alpha

Maximum desired false-alarm probability, a finite scalar in \((0, 1)\).

p1

Optional out-of-control proportion, a finite scalar in \([0, 1]\). When supplied, ARL1 is the primary performance ranking.

conservative

Logical. If TRUE, candidates satisfying p_signal0 <= alpha are ranked before infeasible candidates.

allow_empty_warning

Logical. If FALSE, discard candidates with no integer count in the warning zone.

max_results

Positive integer maximum number of ranked candidates to retain.

Value

A list with the following elements:

best

The first row of candidates, retained as a data frame.

candidates

A data frame containing up to max_results ranked candidates. Columns are wl, ucl1, ucl2, wl_accept, ucl1_reject, ucl2_accept, pt0, p_signal0, arl0, ass0, and feasible; when p1 is supplied, pt1, p_signal1, arl1, and ass1 are also included.

p0, p1, n1, n2, alpha

The validated input parameters.

conservative, allow_empty_warning

The validated input flags.

Details

The function enumerates valid combinations of wl_accept, ucl1_reject, and ucl2_accept, then converts them to fractional limits. A candidate is feasible when its in-control signal probability is no greater than alpha.

With p1, candidates are ranked by feasibility when conservative = TRUE, then by increasing ARL1, ASS0, and distance from alpha. Without p1, they are ranked by feasibility, distance from alpha, ASS0, and ARL0. Setting conservative = FALSE removes feasibility from the front of the corresponding ordering.

When ucl1_reject = wl_accept + 1, the warning zone is empty and the chart degenerates to a single-sample scheme. Such candidates are excluded by default; when allowed, their probabilities are computed directly with stats::pbinom().

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_arl, dsnp_ass

Author

Daniela R. Recchia, Emanuel P. Barbosa

Examples

limits0 <- dsnp_limits(0.05, 5, 10, alpha = 0.05)
limits0$best
#>    wl ucl1 ucl2 wl_accept ucl1_reject ucl2_accept       pt0  p_signal0     arl0
#> 1 0.5  1.5  2.5         0           2           2 0.9598674 0.04013256 24.91743
#>       ass0 feasible
#> 1 7.036266     TRUE
nrow(limits0$candidates)
#> [1] 20

limits1 <- dsnp_limits(0.05, 5, 10, alpha = 0.05, p1 = 0.10)
limits1$best[, c("wl", "ucl1", "ucl2", "arl0", "arl1", "ass0")]
#>    wl ucl1 ucl2     arl0     arl1     ass0
#> 1 0.5  1.5  2.5 24.91743 5.951221 7.036266