A Hybrid Approach to Weibull Renewal Approximation with Increasing Failure Rate  
Author Tongdan Jin

 
Co-Author(s) Fei Sun; Heidi Taboada; Jose Espiritu

 
Abstract When the inter-renewal times follow the Weibull distribution, the closed-form renewal equation mathematically is intractable. In this paper, a hybrid method that combines numerical computation with a quantitative model is proposed to approximate the Weibull renewal function. The approximation function has a simple analytical structure that virtually involves one parameter to be estimated. The method is applicable to Weibull distributions where the shape parameter is larger than one. When the shape parameter exceeds 1.5, sinc function is adopted to characterize the dynamics of transient renewal during its initial phase. We compare the approximation model with the actual renewal data under different Weibull distributions. The result shows that the approximation model is quite accurate for a wide range of shape parameter.

 
Keywords Sinc function; Renewal theory; Weibull distribution; transient renewal
   
    Article #:  20248
 
Proceedings of the 20th ISSAT International Conference on Reliability and Quality in Design
August 7-9, 2014 - Seattle, Washington, U.S.A.