Products often operate in dynamic environments, and field failure data is frequently heavily censored, posing significant challenges in the assessment of product reliability. To enhance the accuracy of field reliability predictions, we introduce a novel joint modelling approach that combines accelerated life tests (ALT) and field failure data. We capture the stochastic influence of dynamic environmental factors on product aging using an exponential dispersion process and present a methodology for jointly modelling ALT and field failure data. Our approach is grounded in the cumulative exposure principle, providing a clear and intuitive physical interpretation. We offer point and interval estimates for model parameters and reliability using maximum likelihood and Bayesian methods, validating their effectiveness through comprehensive simulation studies. Finally, we demonstrate the performance and practical application of our proposed joint model through the analysis of a real dataset.
Xu et al. (Mon,) studied this question.