Monitoring time-between-events for health management

In the history of health management, control chart techniques have been applied to monitor different types of systems, e.g. human health, equipment health, or healthcare systems. However, with the development of modern technology, the traditional control charts, which monitor the number or the proportion of events occurring in a certain sampling interval, are facing more and more obstacles for high quality process monitoring where the defect rate is low. The time-between-events (TBE) chart which monitors the time between successive occurrences of events is especially suitable for this type of data. The word ¿time¿ is used to represent the attribute or variable data observed between consecutive events of concern. Based on the characteristic of interest, the TBE charts could be classified into attribute charts and variable charts. Original attribute TBE charts which monitor the number of conforming items observed before a nonconforming item appears are based on the geometric distribution, while original variable TBE charts which monitor the time between failures are based on exponential distributions. Starting from these, various TBE charts have been developed for different health applications based on assumptions like the Weibull distribution, the gamma distribution, the Poisson distribution and so on. Moreover, the simultaneous monitoring or control of two or more related quality-process characteristics is necessary in system health management. Thus the study of multivariate TBE charts has also become an interesting topic in recent years. In this paper, we review the current development trends of TBE charts and the related applications in health monitoring. Numerical examples are given to illustrate the performance of some TBE charts.