calculate_ATS function

Calculate ATS

The function calculate_ATS calculates the average time to signals (ATS) given a control chart matrix and a specified control limit (CL). ATS is defined as the average time from the start of process monitoring to signal times.

calculate_ATS(
  chart_matrix,
  time_matrix,
  nobs,
  starttime,
  endtime,
  design_interval,
  n_time_units,
  time_unit,
  CL,
  no_signal_action = "omit"
)

Arguments

• chart_matrix: charting statistic values 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 numeric vector that gives the start times.

  starttime[i] is the time that the ith subject starts to be monitored.

• endtime: a numeric vector that gives the end times.

  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)

• CL: a numeric value specifying the control limit.

  CL is the control limit, signals will be given if charting statistics are greater than the control limit.

• 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.

Returns

a numeric value, the ATS given the charting statistics and the control limit.

Details

Calculate ATS

Examples

data("data_example_long_1d")

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$data_matrix_OC,
  time_matrix_new=data_example_long_1d$time_matrix_OC,
  nobs_new=data_example_long_1d$nobs_OC,
  pattern=result_pattern,
  side="upward",
  chart="CUSUM",
  method="standard",
  parameter=0.5)

result_ATS<-calculate_ATS(
  chart_matrix=result_monitoring$chart,
  time_matrix=data_example_long_1d$time_matrix_OC,
  nobs=data_example_long_1d$nobs_OC,
  starttime=rep(0,nrow(data_example_long_1d$time_matrix_OC)),
  endtime=rep(1,nrow(data_example_long_1d$time_matrix_OC)),
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  CL=2.0)

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).