cl_sop

Notedocblock 
cl_sop(sop_dgp, lam, L0, cl_init, d1, d2;
       reps_final, reps_bracket, bracket_step,
       arl_truncation_factor, chart_choice, refinement,
       verbose, cl_tol, seed)

Compute the critical limit cl for a EWMA control chart such that the in-control Average Run Length (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, which is required for the root finder to work reliably. 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

  • sop_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. Does not need to be precise — a rough value in the right ballpark is sufficient.
  • d1, d2: Integer parameters passed to the ARL simulation.

Keyword Arguments

  • reps_final=10_000: Replications used during the ITP refinement phase. Increase for a more accurate result.
  • reps_bracket=1_000: Replications used during the bracketing phase. Fewer replications are sufficient here since only the sign of ARL - L0 matters.
  • 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. Prevents excessive compute when cl is far from the root during bracketing.
  • chart_choice=TauTilde(): Control chart statistic to use.
  • refinement=OrdinaryType(): SOP classification; a RefinedType applies a refined chart computation.
  • cl_tol=1e-4: Absolute convergence tolerance on cl for the ITP phase.
  • seed=nothing: Random seed for reproducibility. If nothing, a fresh seed is drawn each call. Fix to an integer (e.g. seed=42) to get the same result across runs.
  • verbose=false: If true, prints cl and ARL at each function evaluation.

Returns

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

Example

cl = cl_sop(dgp, 0.1, 370.0, 2.5, 3, 5; reps_final=50_000, seed=42)