On Censoring Time in Statistical Monitoring of Lifetime Data

Life tests for highly reliable products often take a long time even using accelerated life testing with censoring. When the production process is monitored by control charts with the product lifetime as the key quality characteristic, the time spent on life testing could incur significant delays for practitioners to make decisions after sampling. However, shortening the test duration, that results in excessive right-censored observations, inevitably degrades the test power for anomaly detection. This study pays close attention to the determination of censoring time in life tests when monitoring lifetime data with the likelihood-based control charts. To interpret the optimal censoring time, the performance metric—out-of-control average time to signal (OC ATS), is deconstructed into two parts: the original OC ATS and the delay caused by life testing. Finite-sample analytical and large-sample asymptotic expressions of ATS metrics are derived for Type-I censored exponential lifetimes. Similar analytical expressions are also derived for the Weibull case. For general distributions, a Monte Carlo simulation procedure is developed for obtaining approximate results. Our numerical investigation uncovers the 2-fold impact of censoring time on the actual performance of control charts under various scenarios and provides useful references for practitioners to set more sensible censoring times in life testing.