offlinem: Offline monitoring

Description

Offline T2.var and W.var control charts for monitoring batch processes based on VAR model. This approach is fully described in "Marcondes Filho, D., & Valk, M. (2020). Dynamic VAR Model-Based Control Charts for Batch Process Monitoring. European Journal of Operational Research."

Usage

offlinem(
  data,
  size,
  newdata = NULL,
  confidence.level = 0.99,
  type = "T2.var",
  covvar = "empirical",
  plot = TRUE,
  var.estimates = FALSE
)

Arguments

data

dataframe of reference dataset. For each batch, variables are arranged in lines and columns are time-instants. The different batches are combined in a single dataset through rbind

size

number of variables

newdata

dataframe of one or more new batches for monitoring (each with same number of variables and time instants of data). Different batches are combined in a single dataset through rbind

confidence.level

H0 probability to be consider to define the quantile (default is 0.99)

type

"T2.var" for Hotelling chart (default) and "W.var" for Generalized Variance chart

covvar

"empirical" for sample covariance of coefficients (default) and "theoretical" for estimated theoretical covariance

plot

TRUE shows the charts plots (default TRUE)

var.estimates

TRUE show informations about the VAR modeling phase (default FALSE)

Value

beyond.limits: returns the batches that the T2.var (or W.var) scores are above the control limit

LimT2 (or LimW): T2.var (or W.var) control limit

perc: perc_ref (and perc_new) returns the rate of reference batches (and new batches) above the control limit (perc_ref= g_ref/I and perc_new= g_new/Inew, where I (Inew) is the overall number of reference batches (new batches) and g_ref (g_new) is the number of reference batches (new batches) above the control limit)

arl: arl_ref (and arl_new) returns the mean number of reference batches (and new batches) before a signal is given by the charts (arl_ref=1/perc_ref and arl_new=1/perc_new)

varest: If var.estimates=TRUE, it returns the matrices (vec.phis and vec.phis.new) in which each row contains the estimated VAR(1) phis for each reference batches and new batches, respectively; the matrices (vec.cov.theoretical and vec.cov.empirical) with the theoretical and empirical estimated phis covariances from the reference batches, respectively; the lists (cov.B1 and cov.B1new) of the theoretical estimated phis covariances of the reference and new batches, respectively; the number (I) of reference batches; the number (Inew) of new batches; and the number (n) of time-instants

Details

#' The maximum number of variables is five.

All batches must have the same number of time-instants.

The dataset of batches in "data" are considered to be in control

Examples

Run this code

# NOT RUN {
# Example 1: Monitoring considering two variables and Inew= 10 in control batches

   mydata=simoff()
   T2.var=offlinem(data=mydata$data,size=2)
   T2.var.new=offlinem(data=mydata$data,size=2,newdata=mydata$newdata)
   W.var=offlinem(data=mydata$data,size=2,type="W.var")
   W.var.new=offlinem(data=mydata$data,size=2,type="W.var",newdata=mydata$newdata)


# Example 2: Monitoring considering three variables and Inew=50 out of control batches

   B1=matrix(c(-0.3,0,0.4,0,0.2,0,0,-0.1,0.5),3,byrow=TRUE)
   B1new=matrix(c(0.7,0,0.4,0,0.5,0,0,-0.1,0.5),3,byrow=TRUE)
   mydata2=simoff(n=100,I=100,size=3,Inew=50,B1,varcov=diag(3),B1new)
   T2.var=offlinem(data=mydata2$data,size=3)
   T2.var.new=offlinem(data=mydata2$data,size=3,newdata=mydata2$newdata)
   W.var=offlinem(data=mydata2$data,size=3,type="W.var")
   W.var.new=offlinem(data=mydata2$data,size=3,type="W.var",newdata=mydata2$newdata)

# }