Robust online detection on highly censored data using a semi-parametric EWMA chart

For time and cost considerations, high censoring rate is quite common in life tests, which is a critical issue in lifetime monitoring. Conventional control charts designed for highly censored data are commonly based on the Weibull distribution. However, the distribution assumption may not be valid in practice, which brings challenges to the monitoring procedures. Motivated by this, a semi-parametric exponential weighted moving average (EWMA) control charting procedure is developed for highly censored lifetime data of any distribution. The control scheme uses the Kaplan-Meier estimator to construct the cumulative distribution function (CDF) and generalized Pareto distribution to improve the tail estimation. Then a Kolmogorov-Smirnov statistic defined by the differences between the in-control CDF and the empirical CDF is integrated into an EWMA charting scheme to monitor the Type I right-censored sample. We use simulation studies and a real-data analysis to show the efficiency of the proposed control chart.