Statistical Monitoring of Censored Lifetime Data: Insights Into Two Special Alarm Phenomena

Monitoring lifetime variation of mass-produced products is a central objective of process quality control in industrial settings. Unlike classical quality-control problems, sequential monitoring of lifetime data poses a unique challenge because failure-time information must be obtained through life tests, which inevitably introduce time delays. This paper delves into the monitoring of type-I censored lifetime data, focusing on two previously underexplored alarm phenomena: competing alarms and predetermined alarms. They have distinct generation mechanisms: competing alarms exhibit a “later comes, first alarms” pattern, in which a sample drawn later may complete its life test earlier, and the earliest among all alarm-triggering samples ultimately determines the detection delay; predetermined alarms occur when an alarm can be anticipated before a sample’s life test is completed, serving as a proactive mechanism to expedite decision-making. We develop statistical models to characterize the underlying generation mechanisms of both phenomena. Through extensive Monte Carlo simulations, we evaluate their occurrence probabilities and effects on control-chart performance metrics. Our findings reveal that although incorporating these alarms is expected to reduce the out-of-control average time to signal, predetermined alarms yield notable improvements in certain cases, whereas competing alarms have no discernible effect on the optimal censoring time. Two industrial examples further illustrate the practical benefits of accounting for these alarms. Our research offers actionable insights for decision-making in the statistical monitoring of censored lifetime data.