PH1ARMA: Phase I individual control chart with an ARMA model

In PH1XBAR: Phase I Shewhart X-Bar Chart

Phase I individual control chart with an ARMA model

Description

Build a Phase I individual control chart for the ARMA models. The charting constant is corrected by this approach.

Usage

PH1ARMA(
  X,
  cc = NULL,
  fap0 = 0.05,
  order = c(1, 0),
  plot.option = TRUE,
  interval = c(1, 4),
  case = "U",
  phi.vec = NULL,
  theta.vec = NULL,
  mu0 = NULL,
  sigma0 = NULL,
  method = "MLE+MOM",
  nsim.coefs = 100,
  nsim.process = 1000,
  burn.in = 50,
  sim.type = "Recursive",
  transform = "none",
  lambda = 1,
  standardize = FALSE,
  verbose = FALSE
)

Arguments

X	input and it must be a vector (m by 1)
cc	nominal Phase I charting constant. If this is given, the function will not re-compute the charting constant.
fap0	nominal false Alarm Probabilty in Phase I
order	order for ARMA(p, q) model
plot.option	- draw a plot for the process; TRUE - Draw a plot for the process, FALSE - Not draw a plot for the process
interval	searching range of charting constants for the exact method
case	known or unknown case. When case = 'U', the parameters are estimated, when case = 'K', the parameters need to be input
phi.vec	a vector of length p containing autoregressive coefficient(s). When case = 'K', the vector must have a length equal to the first value in the order. If no autoregressive coefficent presents, set phi.vec = NULL
theta.vec	a vector of length q containing moving-average coefficient(s). When case = 'K', the vector must have a length equal to the first value in the order. If no moving-average coefficent presents, set theta.vec = NULL
mu0	value of the IC process mean. When case = 'K', the value needs to be provided.
sigma0	value of the IC process standard deviation. When case = 'K', the value needs to be provided.
method	estimation method for the control chart. When method = 'MLE+MOM' is maximum likehood estimations plus method of moments. Other options are 'MLE' which is pure MLE and 'CSS' which is pure CSS.
nsim.coefs	number of simulation for coefficients.
nsim.process	number of simulation for ARMA processes
burn.in	number of burn-ins. When burn.in = 0, the simulated process is assumed to be in the initial stage. When burn.in is sufficiently large (e.g., the default value of 50), the simulated process is assumed to have reached a stable state.
sim.type	type of simulation. When sim.type = 'Recursive', the simulation is generated recursively, as in the ARMA model. When sim.type = 'Matrix', the simulation is generated using the covariance matrix among observations, derived from the relationship between the ARMA coefficient(s) and the partial autocorrelation(s). Note that sim.type = 'Matrix' is primarily used as a proof of concept and is not recommended for practical use due to its high computational cost.
transform	type of transformation. When transform = 'none', no transformation is performed. When transform = 'boxcox', the Box-Cox transformation is used. When transform = 'yeojohnson', the Yeo-Johnson transformation is used.
lambda	parameter used in the Box-Cox or Yeo-Johnson transformation.
standardize	Output standardized charting statistics instead of raw ones. When standardize = TRUE, the standardization is used. When standardize = FALSE, the standardization is not performed.
verbose	print diagnostic information about fap0 and the charting constant during the simulations for the exact method

Value

CL Object type double - central line

gamma Object type double - process variance estimate

cc Object type double - charting constant

order Object type integer - order for ARMA model

phi.vec Object type integer - values of autoregressors

theta.vec Object type integer - values of moving averages

LCL Object type double - lower charting limit

UCL Object type double - upper charting limit

CS Object type double - charting statistic

References

Yao, Y., Chakraborti, S., Yang, X., Parton, J., Lewis Jr, D., and Hudnall, M. (2023). Phase I control chart for individual autocorrelated data: application to prescription opioid monitoring. Journal of Quality Technology, 55(3), 302-317.

Examples

# load the data in the package as an example
data(preston_data)

# set number of simulations
nsim.process <- 10
nsim.coefs <- 10

# An example using the default setting whose fap0 = 0.1
PH1ARMA(preston_data, nsim.process = nsim.process, nsim.coefs = nsim.coefs)

# When users get an error message about the size of matrix,
# the function needs to use the alternative simulation type as follows
PH1ARMA(preston_data, fap0 = 0.05, 
	nsim.process = nsim.process, nsim.coefs = nsim.coefs, sim.type = 'Recursive')

PH1XBAR documentation built on June 19, 2025, 5:07 p.m.