D-Optimal Joint Best Linear Unbiased Predictors In Progressively Type-Ii Ordered Statistics

Reliability and life-testing experiments play a crucial role in understanding the longevity and performance of systems and components, particularly in high-stakes applications such as engineering, manufacturing, and quality control. In this thesis, we focus on the prediction of future unobserved failure times by employing joint predictors based on progressively Type-II censored data obtained from such life-testing experiments. Specifically, we derive explicit analytical expressions for the joint best linear unbiased predictors (BLUPs) of two future order statistics under the D-optimality criterion. The derivation involves minimizing the determinant of the variance-covariance matrix of the predictors within the context of progressively Type-II censored schemes. This approach ensures that the resulting joint predictors are D-optimal, establishing them as a highly efficient choice for predicting unobserved future data points. One of the primary contributions of this work is the detailed comparison between joint predictors and marginal predictors, which is accomplished by analyzing the design efficiency in various scenarios. By evaluating efficiency measures such as D-efficiency and Trace-efficiency, the analysis highlights the strengths of joint prediction approaches over marginal predictions in terms of gaining efficiency and thus improving reliability outcomes. This comparison provides valuable insights into the practical benefits of employing joint predictors when analyzing reliability data from life-testing experiments on progressively Type-II censored data. Additionally, the study also investigates the conditions under which joint BLUPs do not exist, demonstrating the inherent limitations and challenges of using such predictors under specific situations.