Type-II progressive censoring with GLM-based random removal mechanism dependent on the experimental conditions

This article presents a novel stochastic removal mechanism under Type-II progressive random censoring in which removal probabilities are allowed to be dependent on the lifetime conditions through Generalized Linear Models (GLM). These conditions potentially include failure distances (the time required to observe the next failure) or other covariate information available in the experiment. The proposed GLM-based random removal mechanism includes a set of tuning parameters that are determined by the researcher according to the possible failure distance category. These parameters allow flexible determination of the removal probabilities leading to necessary experimental cost and time reductions. To establish the proposed mechanism, the Proportional Hazard Rate (PHR) family of distributions is considered. Also, the maximum likelihood estimators of parameters and their asymptotic variances are derived for the Weibull distributed lifetime data. A simple simulation algorithm for generating Type-II progressive censoring samples with GLM-based dependent removal probabilities is also presented. The expected experiment time required to complete the life test under this censoring scheme is also investigated using the Monte Carlo integration method. Several simulation studies are conducted to evaluate and compare the performance of the proposed mechanism. A sensitivity analysis is also considered to study the effect of misspecification of removal mechanism coefficients. Finally, two real data sets are analyzed for illustrative purposes.

Automated summary

This article presents a novel stochastic removal mechanism using Generalized Linear Models (GLM) with dependent removal probabilities based on lifetime conditions. It investigates the parameter estimation and variance estimation for the Weibull distributed removal mechanism under Type-II progressive random censoring. A simulation algorithm for generating samples with GLM-based removal probabilities is also provided, and the expected experiment time is analyzed using Monte Carlo integration method. The performance of the proposed mechanism is evaluated through simulation studies and real data analysis, and the sensitivity analysis is considered.