DySS (version 1.0)

search_CL: Search Control Limit

Description

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.

Usage

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
)

Value

a numeric value, the control limit that gives the desired ATS.

Arguments

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.

Details

Search Control Limit

Examples

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)