Robustness and Efficiency Considerations When Testing Process Reliability with a Limit of Detection

Processes in biotechnology are considered reliable if they produce samples satisfying regulatory benchmarks. For example, laboratories may be required to show that levels of an undesirable analyte rarely (e.g., in less than 5% of samples) exceed a tolerance threshold. This can be challenging when measurement systems feature a lower limit of detection, rendering some observations left-censored. We investigate the implications of detection limits on location-scale model-based inference in reliability studies, including their impact on large and finite sample properties of various estimators and the sensitivity of results to model misspecification. To address the need for robust methods, we introduce a flexible weakly parametric model in which the right tail of the response distribution is approximated using a piecewise-constant hazard model. Simulation studies are reported that investigate the performance of the established and proposed methods, and an illustrative application is given to a study of drinking can weights. We conclude with a discussion of areas warranting future work.