Analytical Solution for Parameter Estimation of Weibull Distributions with Interval-Censored Data

Abstract

This paper addresses the challenge of parameter estimation for Weibull distributions with continuous interval-censored data, a critical issue in reliability engineering where failures are observed only at predetermined inspection intervals. Traditional estimation methods often struggle with the uncertainty of failure times, leading to suboptimal results. To overcome this limitation, we propose a novel analytical approach that directly fits the probability density function to the frequency histogram, offering an alternative to conventional numerical algorithms. This method not only improves estimation accuracy but also enhances computational efficiency. Theoretical validation is established using the dual least squares method, and extensive Monte Carlo simulations further confirm its robustness. Comparative analysis with existing approaches highlights the superiority of our method in terms of both precision and stability. To demonstrate its practical applicability, we apply the proposed approach to Hong Kong casualty data from the World Health Organization, effectively estimating the age distribution of unidentified casualties. The results underscore the method’s potential for broader applications in reliability analysis and risk assessment.

Received: 27 October 2024 | Revised: 12 March 2025 | Accepted: 3 April 2025 

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

The data that support the findings of this study are openly available in World Health Organization at https://platform.who.int/mortality/themes/theme-details/mdb/injuries.

Author Contribution Statement

Yang Yu: Conceptualization, Methodology, Software, Validation, Formal analysis, Data curation, Writing – original draft, Writing – review & editing, Visualization. Jianguo Gong: Resources, Funding acquisition. Kunping Zhu: Conceptualization, Methodology, Investigation, Supervision, Project administration.