Evaluate Control Charts
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.
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" )
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.
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.
$ATS1: A numeric vector. Out-of-control ATS.
Evaluate Control Charts
pattern<-estimate_pattern_long_1d( data_matrix=data_example_long_1d$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")
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).
Useful links