Closed-Form Solutions for the Weibull Distribution Parameters and Performance Lifetime Index with Interval-Censored Data

In lifetime testing, reliably assessing the life performance index of the Weibull distribution under Type I interval-censored data is a critical task. Although maximum likelihood estimation (MLE) is a conventional approach for parameter estimation, closed-form solutions are unavailable for this data type. To address this limitation, four least-squares estimation methods based on data transformation are developed. The proposed estimations can provide closed-form solutions for the Weibull distribution and life performance index. The asymptotic unbiasedness and normality of the proposed estimators are rigorously established. Their effectiveness is further supported by simulation studies. Moreover, the practical relevance of the methods is illustrated with two real-data applications.