cl_sacf

Notedocblock 
cl_sacf(sp_dgp::ICSTS, lam, L0, cl_init, d1::Int, d2::Int;
        reps_final, reps_bracket, bracket_step,
        arl_truncation_factor, verbose, cl_tol, seed)

Compute the critical limit cl for an EWMA control chart based on the spatial autocorrelation function (SACF) such that the in-control ARL equals L0.

The search proceeds in two phases:

  1. Bracketing: A coarse Monte Carlo estimate (using reps_bracket replications) steps away from cl_init in increments of bracket_step until an interval [a, b] is found where the ARL crosses L0.
  2. Refinement: The ITP root-finding algorithm narrows the bracket to within cl_tol using full Monte Carlo estimates (reps_final replications). Using a fixed seed ensures the ARL function behaves smoothly across evaluations within a single call. With large reps_final, the result is accurate regardless of which seed is used. Pass seed=nothing (default) for independent results across calls, or fix the seed for reproducibility.

Arguments

  • sp_dgp::ICSTS: Data-generating process under the in-control distribution.
  • lam: EWMA smoothing parameter λ ∈ (0, 1].
  • L0: Target in-control ARL.
  • cl_init: Initial guess for the critical limit.
  • d1::Int: The first (row) delay for the spatial process.
  • d2::Int: The second (column) delay for the spatial process.

Keyword Arguments

  • reps_final=10_000: Replications used during the ITP refinement phase.
  • reps_bracket=1_000: Replications used during the bracketing phase.
  • bracket_step=0.01: Step size for the bracketing search.
  • arl_truncation_factor=50: Individual simulation runs are capped at arl_truncation_factor * L0 steps during bracketing.
  • cl_tol=1e-4: Absolute convergence tolerance on cl for the ITP phase.
  • seed=nothing: Random seed for reproducibility.
  • verbose=false: If true, prints progress information at each evaluation.

Returns

  • cl::Float64: The critical limit achieving an in-control ARL of L0.

Example

sp_dgp = ICSTS(20, 20, Normal(0, 1))
cl = cl_sacf(sp_dgp, 0.1, 370.0, 0.5, 1, 1; reps_final=50_000, seed=42)