evaluate_control_chart_two_groups {DySS}

Evaluate Control Charts

Description

The function evaluate_control_chart_two_groups evaluates control charts when the in-control (IC) and out-of-control (OC) charting statistics are supplied separately in two matrices chart_matrix_IC and chart_matrix_OC.

Usage

evaluate_control_chart_two_groups(
  chart_matrix_IC,
  time_matrix_IC,
  nobs_IC,
  starttime_IC,
  endtime_IC,
  chart_matrix_OC,
  time_matrix_OC,
  nobs_OC,
  starttime_OC,
  endtime_OC,
  design_interval,
  n_time_units,
  time_unit,
  no_signal_action = "omit"
)

Arguments

chart_matrix_IC, chart_matrix_OC

charting statistics arranged as a numeric matrix.
chart_matrix_IC[i,j] is the jth charting statistic of the ith IC subject.
chart_matrix_OC[i,j] is the jth charting statistic of the ith OC subject.

time_matrix_IC, time_matrix_OC

observation times arranged as a numeric matrix.
time_matrix_IC[i,j] is the jth observation time of the ith IC subject.
time_matrix_OC[i,j] is the jth observation time of the ith OC subject.
chart_matrix_IC[i,j] is the charting statistic of the ith IC subject at time_matrix[i,j].
chart_matrix_OC[i,j] is the charting statistic of the ith OC subject at time_matrix[i,j].

nobs_IC, nobs_OC

number of observations arranged as an integer vector.
nobs_IC[i] is the number of observations for the ith subject.
nobs_OC[i] is the number of observations for the ith subject.

starttime_IC, starttime_OC

a numeric vector that gives the start times.
starttime_IC[i] is the time that the ith IC subject starts to be monitored.
starttime_OC[i] is the time that the ith OC subject starts to be monitored.

endtime_IC, endtime_OC

a numeric vector that gives the end times.
endtime_IC[i] is the time that the ith IC subject is lost to be monitored.
endtime_OC[i] is the time that the ith OC subject is lost to be monitored.

design_interval

a numeric vector of length two that gives the left- and right- limits of the design interval. By default, design_interval=range(time_matrix,na.rm=TRUE).

n_time_units

an integer value that gives the number of basic time units in the design time interval.
The design interval will be discretized to seq(design_interval[1],design_interval[2],length.out=n_time_units)

time_unit

an optional numeric value of basic time unit. Only used when n_time_units is missing.
The design interval will be discretized to seq(design_interval[1],design_interval[2],by=time_unit)

no_signal_action

a character value specifying how to set signal times when processes with no signals.
If no_signal_action=="omit", the signal time is set to be missing.
If no_signal_action=="maxtime", the signal time is set to be the time from start time to the end of the design interval.
If no_signal_action=="endtime", the signal time is set to be the time from start time to the end time.

Details

Evaluate Control Charts

Value

an list that stores the evaluation measures.

$thres

A numeric vector. Threshold values for control limits.

$FPR

A numeric vector. False positive rates.

$TPR

A numeric vector. True positive rates.

$ATS0

A numeric vector. In-control ATS.

$ATS1

A numeric vector. Out-of-control ATS.

References

Qiu, P. and Xiang, D. (2014). Univariate dynamic screening system: an approach for identifying individuals with irregular longitudinal behavior. Technometrics, 56:248-260.
Qiu, P., Xia, Z., and You, L. (2020). Process monitoring ROC curve for evaluating dynamic screening methods. Technometrics, 62(2).

Examples

pattern<-estimate_pattern_long_1d(
  data_matrix=data_example_long_1d$data_matrix_IC,
  time_matrix=data_example_long_1d$time_matrix_IC,
  nobs=data_example_long_1d$nobs_IC,
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  estimation_method="meanvar",
  smoothing_method="local linear",
  bw_mean=0.1,
  bw_var=0.1)

chart_IC_output<-monitor_long_1d(
  data_example_long_1d$data_matrix_IC,
  data_example_long_1d$time_matrix_IC,
  data_example_long_1d$nobs_IC,
  pattern=pattern,side="upward",chart="CUSUM",
  method="standard",parameter=0.2)

chart_OC_output<-monitor_long_1d(
  data_example_long_1d$data_matrix_OC,
  data_example_long_1d$time_matrix_OC,
  data_example_long_1d$nobs_OC,
  pattern=pattern,side="upward",chart="CUSUM",
  method="standard",parameter=0.2)

output_evaluate<-evaluate_control_chart_two_groups(
  chart_matrix_IC=chart_IC_output$chart[1:50,],
  time_matrix_IC=data_example_long_1d$time_matrix_IC[1:50,],
  nobs_IC=data_example_long_1d$nobs_IC[1:50],
  starttime_IC=rep(0,50),
  endtime_IC=rep(1,50),
  chart_matrix_OC=chart_OC_output$chart[1:50,],
  time_matrix_OC=data_example_long_1d$time_matrix_OC[1:50,],
  nobs_OC=data_example_long_1d$nobs_OC[1:50],
  starttime_OC=rep(0,50),
  endtime_OC=rep(1,50),
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  no_signal_action="maxtime")