getDeltaH_down {LGCU}R Documentation

Estimation of the Optimal H_delta Value to Guarantee Performance in the Downward CUSUM Control Chart

Description

This function calculates the optimal value of H_delta that guarantees a specific performance in the Gamma CUSUM control chart for downward detection. It employs a Monte Carlo simulation approach and an iterative adjustment process to determine the appropriate value.

Following the methodology presented by Madrid‐Alvarez, García‐Díaz, and Tercero‐Gómez (2024), this function allows adjusting H_delta for different sample size configurations, ensuring that the control chart maintains the desired performance in terms of expected ARL.

Features:

Recommendations

Usage

getDeltaH_down(
  n_I,
  alpha,
  beta,
  beta_ratio,
  H_minus,
  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_minus

Initial lower 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 should be estimated (FALSE).

Value

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

Examples


getDeltaH_down(n_I = 100, alpha = 1, beta = 1, beta_ratio = 1/2,
               H_minus = -4.1497, 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]