PH1ARMA: Build Phase I individual control chart with an ARMA model...

In bolus123/PH1XBAR: Phase I Shewhart X-Bar Chart

Build Phase I individual control chart with an ARMA model using a corrected charting constant

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 = 0.1
	,order = NULL
	,plot.option = TRUE
	,interval = c(1, 4)
	,case = 'U'
	,method = 'Method 3'
	,nsim.coefs = 100
	,nsim.process = 1000
	,burn.in = 50
	,sim.type = 'Matrix'
	,logliktol = 1e-2
	,verbose = FALSE
	,max.p=1
	,max.q=0
	,max.d=0
  ,standardize=TRUE
)

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	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
method	estimation method for the control chart. When method = 'Method 3' is maximum likehood estimations plus method of moments. Other options are 'Method 1' which is pure MLE and 'Method 2' 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 ECM gets involved. When burn.in is large enough, the ACM gets involved.
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.
logliktol	convergence tolerance for the log likelihood
verbose	print diagnostic information about fap0 and the charting constant during the simulations for the exact method
max.p	max.p for auto.arima
max.q	max.q for auto.arima
max.d	max.d for auto.arima
standardize	Output z-scores instead of raw data

Value

Object of type list. A named list with the following objects:

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

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')

bolus123/PH1XBAR documentation built on Nov. 12, 2023, 6:21 a.m.