Search Control Limit
Given a chart matrix, the function search_CL searches the control limit (CL) so that the specified average time to signals (ATS) can be attained.
search_CL( chart_matrix, time_matrix, nobs, starttime, endtime, design_interval, n_time_units, time_unit, ATS_nominal, CL_lower, CL_step, CL_upper, no_signal_action = "omit", ATS_tol, CL_tol )
chart_matrix: charting statistics arranged as a numeric matrix.
chart_matrix[i,j] is the jth charting statistic of the ith subject.
time_matrix: observation times arranged as a numeric matrix.
time_matrix[i,j] is the jth observation time of the ith subject, corresponding to the time the charting statistic chart_matrix[i,j] is computed.
nobs: number of observations arranged as an integer vector.
nobs[i] is the number of observations for the ith subject.
starttime: a vector of times from the start of monitoring.
starttime[i] is the time that the ith subject starts to be monitored.
endtime: a vector of times from the start of monitoring.
endtime[i] is the time that the ith 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)
ATS_nominal: a numeric value.
ATS_nominal is the nominal (or say targeted) ATS that is intended to achieve.
CL_lower, CL_step, CL_upper: three numeric values.
The control limit will be searched within the interval [CL_lower,CL_upper].
When applying grid search, the algorithm will use a step size of CL_step.
(Namely, the algorithm will start with CL_lower, and search through the sequences CL_lower, CL_lower+CL_step, CL_lower+2*CL_step, ... until CL_upper.)
no_signal_action: a character specifying the method to use when a signal is not given to a process. If no_signal_action="omit" take averages by omitting the processes with no signals, namely, average only the processes with signals.
If no_signal_action="maxtime" impute the signal times by the maximum time, which is the right limit of design time interval.
If no_signal_action="endtime" impute the signal times by the end times.
ATS_tol: a numeric value.
Error tolerance for ATS.
CL_tol: a numeric value.
Error tolerance for control limit.
a numeric value, the control limit that gives the desired ATS.
Search Control Limit
result_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$n_time_units, estimation_method="meanvar", smoothing_method="local linear", bw_mean=0.1, bw_var=0.1) result_monitoring<-monitor_long_1d( data_matrix_new=data_example_long_1d$data_matrix_IC, time_matrix_new=data_example_long_1d$time_matrix_IC, nobs_new=data_example_long_1d$nobs_IC, pattern=result_pattern, side="upward", chart="CUSUM", method="standard", parameter=0.5) CL<-search_CL( chart_matrix=result_monitoring$chart, time_matrix=data_example_long_1d$time_matrix_IC, nobs=data_example_long_1d$nobs_IC, starttime=rep(0,nrow(data_example_long_1d$time_matrix_IC)), endtime=rep(1,nrow(data_example_long_1d$time_matrix_IC)), design_interval=data_example_long_1d$design_interval, n_time_units=data_example_long_1d$n_time_units, ATS_nominal=200,CL_lower=0,CL_upper=5)
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