Modeling Medical and Reliability Data Sets Using a Novel Reciprocal Weibull Distribution: Estimation Methods and Sequential Sampling Plan Based on Truncated Life Testing

Abstract

An extended version of the reciprocal Weibull model is proposed and thoroughly analyzed. Key statistical properties of the model are derived, and various estimation techniques are employed to estimate the unknownparameters. A simulation study is conducted to evaluate the performance of these methods. Additionally, two real-world datasets are utilized to compare the effectiveness of the competing estimation methods. The significance of the proposed model is highlighted through these applications, demonstrating its superior performance over other competing models in fitting the datasets. A sequential sampling plan based on truncated life testing is introduced, leveraging a newly developed probabilistic model to enhance quality control decisions. The plan determines the acceptance or rejection of a lot based on life test outcomes within a specified truncation time, optimizing inspection efforts. A series of numerical experiments are conducted to validate the proposed approach, demonstrating its effectiveness in minimizing sample sizes while maintaining desired risk levels. The results highlight the impact of key parameters on the sampling process, ensuring a balance between producer and consumer risks.