PH1ARMA {PH1XBAR}

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, 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 = "Matrix",
  standardize = TRUE,
  verbose = FALSE
)

Arguments

X

input and it must be a vector

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 model

plot.option

- 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

phi.vec

vector of autoregressive coefficient(s). When case = 'K', the vector needs to be provided with the length same as the first value in the order. If autoregressive coefficents does not present, phi needs to be NULL

theta.vec

vector of moving-average coefficient(s). When case = 'K', the vector needs to be provided with the length same as the third value in the order. If moving-average coefficents does not present, theta needs to be 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 coeficients.

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 large enough, the simulated process is assumed to be in the stable stage.

sim.type

type of simulation. When sim.type = 'Matrix', the simulation is generated using matrix computation. When sim.type = 'Recursive', the simulation is based on a recursion.

standardize

Output standardized data instead of raw data

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')