A Computational Framework for Censoring Design in Monitoring Lifetime Data from One-Dimensional Exponential Families

Monitoring product lifetimes is essential for ensuring quality and reliability, with control charts based on lifetime testing commonly used to assess whether the production process is in control. To ensure timely feedback, censoring is often applied in lifetime tests. However, the performance of the control chart can heavily depend on the choice of censoring time c. A small c may result in significant information loss, complicating the inference about the production process's state, while a large c prolongs the test duration, defeating the purpose of censoring. In this context, this study proposes a computational framework for evaluating the average time to signal (ATS) to facilitate the determination of optimal c when monitoring Type-I censored lifetimes from the one-dimensional exponential family. Our framework relates the monitored plotting statistics to sufficient statistics of censored lifetimes through two distribution-dependent functions, simplifying the ATS calculation to evaluate the cumulative distribution function (cdf) of the sufficient statistics. To ensure both the accuracy and computational efficiency of our framework, an efficient numerical tool, the recursive discrete convolution algorithm, is developed to approximate complex integrals when evaluating the cdf of the sum of truncated random variables. The flexibility of the proposed framework is demonstrated through its application to censored gamma and lognormal lifetimes. Numerical analysis reveals how ATS varies with c, offering guidance for selecting the optimal c. Two case studies further illustrate the potential of the proposed framework in lifetime test design, providing practical insights for balancing information retention and test duration in lifetime monitoring.