  Rapidly detecting problems in the quality of care is of utmost importance for
the well-being of patients. Without proper inspection schemes, such problems
can go undetected for years. Cumulative sum (CUSUM) charts have proven to be
useful for quality control, yet available methodology for survival outcomes is
limited. The few available continuous time inspection charts usually require
the researcher to specify an expected increase in the failure rate in advance,
thereby requiring prior knowledge about the problem at hand. Misspecifying
parameters can lead to false positive alerts and large detection delays. To
solve this problem, we take a more general approach to derive the new
Continuous time Generalized Rapid response CUSUM (CGR-CUSUM) chart. We find an
expression for the approximate average run length (average time to detection)
and illustrate the possible gain in detection speed by using the CGR-CUSUM over
other commonly used monitoring schemes on a real life data set from the Dutch
Arthroplasty Register as well as in simulation studies. Besides the inspection
of medical procedures, the CGR-CUSUM can also be used for other real time
inspection schemes such as industrial production lines and quality control of
services.
