Evaluating Actuarial Present Values in Continuous Annuities Under the Hossian Assumption: A Case Study of Main Transformers

The lifespan of grid equipment plays a pivotal role in determining equipment renewal strategies. In calculating the actuarial present value, adopting a segmented lifespan hypothesis becomes essential for accuracy. It is evident that the validity of this Hypothesis significantly enhances the precision in forecasting grid equipment lifespan. When compared with other conventional assumption, the segmented lifespan approach enables a more thorough integration of failure data drawn from life tables. Moreover, this Hypothesis facilitates a continuous failure rate estimation across the entire lifecycle of grid equipment, while also offering additional beneficial geometric properties. In this study, the Hossion Hypothesis is utilized to assess the reliability of segmented lifespan failure rate estimations. Drawing on the Hossion Hypothesis, this work delves into the actuarial present value computations for two distinct categories of continuous service lives. Furthermore, this study employs life tables from key equipment of the China Southern Power Grid (2020–2023, main transformer) to conduct numerical analyses, followed by a comparison with the Balducci Hypothesis results. Through this comparative analysis, the study illustrates the advantages of the Hossion Hypothesis in actuarial present value estimation, and substantiates its potential to improve the precision of failure rate predictions.