getDeltaHL_up {LGCU}R Documentation

Estimation of the H_delta parameter with learning for upward detection in Gamma CUSUM control charts

Description

This function calculates the optimal value of H_delta using a dynamic learning scheme based on the ARL_Clplus function, iteratively adjusting H_delta to achieve an expected ARL with higher accuracy and adaptability.

Based on the methodology proposed by Madrid-Alvarez, García-Díaz, and Tercero-Gómez (2024), this function allows adjusting H_delta in different sample size scenarios, ensuring that the control chart progressively adapts to changes in the Gamma distribution.

Features:

Recommendations

Usage

getDeltaHL_up(
  n_I,
  alpha,
  beta,
  beta_ratio,
  H_plus,
  a,
  b,
  ARL_esp,
  replicates,
  N_init,
  N_final,
  known_alpha,
  K_l,
  delay,
  tau
)

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 posterior estimate.

H_plus

Initial 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.

replicates

Number of replications in the Monte Carlo simulation.

N_init

Number of initial iterations for adjustment.

N_final

Number of final iterations for averaging H_delta.

known_alpha

TRUE if alpha is fixed, FALSE if it should be estimated.

K_l

Secondary control threshold for parameter updating.

delay

Number of observations before updating beta0_est.

tau

Point in time where beta changes.

Value

A numeric value corresponding to the optimal H_delta estimated with learning for the upward CUSUM control chart.

Examples


getDeltaHL_up(
           n_I = 200, alpha = 1, beta = 1, beta_ratio = 2,
            H_plus = 6.8313, a = 0.1, b = 0.05, ARL_esp = 370,
             replicates = 100, N_init = 100, N_final = 500,
             known_alpha = TRUE, K_l = 2, delay = 25, tau = 1
            )
            



[Package LGCU version 0.1.5 Index]