getDeltaH_up {LGCU}R Documentation

Estimation of the optimal H_delta value to guarantee performance in the upward CUSUM control chart

Description

This function calculates the optimal H_delta value that ensures specific performance in the Gamma CUSUM control chart for upward detection. It relies on Monte Carlo simulations and an iterative adjustment process to determine the appropriate value.

Following the methodology proposed by Madrid-Alvarez, Garcia-Diaz, and Tercero-Gomez (2024), this function allows adjusting H_delta for different sample size scenarios, ensuring that the control chart maintains the expected performance in terms of ARL.

Features:

Recommendations

Usage

getDeltaH_up(
  n_I,
  alpha,
  beta,
  beta_ratio,
  H_plus,
  a,
  b,
  ARL_esp,
  m,
  N_init,
  N_final,
  known_alpha
)

Arguments

n_I

Sample size in Phase I.

alpha

Shape parameter of the Gamma distribution.

beta

Scale parameter of the Gamma distribution.

beta_ratio

Ratio between beta and its estimate.

H_plus

Initial upper limit of the CUSUM chart.

a

Tolerance level for the expected ARL (0 <= a < 1).

b

Tolerance level for the expected ARL (0 < b < 1).

ARL_esp

Desired expected ARL value.

m

Number of states in the Markov matrix.

N_init

Number of initial iterations.

N_final

Number of final iterations.

known_alpha

Indicates whether alpha is known (TRUE) or needs to be estimated (FALSE).

Value

A numeric value corresponding to the optimal H_delta for the upward CUSUM control chart, ensuring the expected performance.

Examples


getDeltaH_up(n_I = 100, alpha = 1, beta = 1, beta_ratio = 2, H_plus = 6.8313,
             a = 0.1, b = 0.05, ARL_esp = 370, m = 100,
             N_init = 10, N_final = 1000, known_alpha = TRUE)
             


[Package LGCU version 0.1.5 Index]