Double-Sampling np Chart: Complete Design Search

Perform a joint discrete search over first-stage sample size (n1), second-stage sample size (n2), and DS-np control limits to find optimal chart designs. This function performs an exhaustive search over the Cartesian product of n1_range and n2_range, calling dsnp_limits for each pair and collecting the best feasible candidates across all pairs.

Usage

dsnp_design(
  p0,
  p1,
  n1_range,
  n2_range,
  arl0_min = 200,
  alpha = NULL,
  objective = c("arl1", "ass0", "weighted"),
  weights = c(arl1 = 1, ass0 = 1),
  allow_empty_warning = FALSE,
  max_results = 20,
  progress = FALSE,
  ass0_max = NULL
)

# S3 method for class 'dsnp_design'
print(x, ...)

Arguments

p0: In-control nonconforming proportion. Scalar in (0, 1).
p1: Out-of-control nonconforming proportion. Scalar in (0, 1). Must be greater than p0.
n1_range: Integer vector of first-stage sample sizes to evaluate. Positive integers, no duplicates, no NAs.
n2_range: Integer vector of second-stage sample sizes to evaluate. Positive integers, no duplicates, no NAs.
arl0_min: Minimum acceptable in-control ARL. Scalar greater than 1, or NULL if alpha is supplied.
alpha: Maximum acceptable false alarm probability. Scalar in (0, 1), or NULL if arl0_min is supplied. When both are provided, candidates must satisfy both constraints.
objective: Optimization objective. One of "arl1" (minimize out-of-control ARL), "ass0" (minimize in-control ASS), or "weighted" (minimize a weighted combination of normalized ARL1 and ASS0).
weights: Named numeric vector with elements arl1 and ass0. Both must be non-negative and at least one must be positive. Only used when objective = "weighted".
allow_empty_warning: Logical. If FALSE (default), discard candidates with no integer in the warning zone.
max_results: Maximum number of feasible candidates to return. Positive integer.
progress: Logical. If TRUE, print progress messages during the search.
ass0_max: Optional maximum in-control average sample size. When supplied, it must be a finite positive scalar and candidates must satisfy ass0 <= ass0_max. The current ASS calculation follows equation (15) of Joekes et al. (2015) and assumes complete inspection of the second sample whenever the first-stage count is in the warning region.
x: An object of class "dsnp_design".
...: Additional arguments (ignored).

Value

An object of class "dsnp_design" with the following elements:

best: The top-ranked feasible candidate (a one-row data.frame).
candidates: Up to max_results feasible candidates, sorted by the chosen objective.
parameters: A list of the input parameters.
search: A list with search summary counts:
failures: A data.frame of failed pairs with columns n1, n2, and message. Empty if no failures occurred.

Details

The search is discrete and exhaustive within the supplied ranges; it is not a continuous optimization. The cost grows with the number of (n1, n2) pairs and the number of limit candidates evaluated per pair. This function does not implement curtailed inspection.

When alpha is NULL and arl0_min is provided, an effective alpha of 1 / arl0_min is used to guide dsnp_limits(), but final feasibility is checked against the explicit arl0 >= arl0_min condition.

The published design problem minimizes out-of-control ARL subject to ass0 <= ass0_max and arl0 >= arl0_min. Setting ass0_max = NULL omits only the ASS constraint and preserves the behavior of earlier IQCC versions. The argument is appended to the function signature so existing positional calls retain their meaning.

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. doi:10.1016/j.stamet.2014.09.003 .

Author

Daniela R. Recchia, Emanuel P. Barbosa

Examples


# Small example for fast execution
res <- dsnp_design(
    p0 = 0.05, p1 = 0.10,
    n1_range = 5:6, n2_range = 8:10,
    arl0_min = 50, objective = "arl1"
)
res$best[, c("n1", "n2", "wl", "ucl1", "ucl2", "arl0", "arl1")]
#>   n1 n2  wl ucl1 ucl2     arl0     arl1
#> 1  6 10 1.5  2.5  2.5 69.03209 12.50785