A Novel Approach for Parameter Estimation of Mixture oftwo Weibull Distributions in Failure Data Modeling

Abstract The mixture of two 2-parameter Weibull distributions (MixW), as a specialized variant of the mixtureof Weibull distributions, serves as an ideal model for heterogeneous data sets within the realms ofreliability studies and survival analysis. A principal challenge in dealing with MixW lies in the estima-tion of parameters. Inspired by the exemplary efficacy of the quasi-Monte Carlo method in Quantileestimation, this paper introduces an innovative approach, which employs the Harrell-Davis and threeSfakianakis and Verginis quantile estimators to enhance the representativeness of the sample, therebyimproving the accuracy of parameter estimation. Given the difficulty in deriving analytical expres-sions for the parameters of MixW and their propensity for convergence to local maxima, this paperadopts the sequential number-theoretic (SNTO) algorithm for the numerical resolution of parameterestimation. The initial optimization region for SNTO is determined via the graphical method of theWeibull Probability Plot (WPP). Simulation studies have demonstrated that our proposed methodsignificantly enhances estimation precision and reduces dependence on the “quality” of the sample.Furthermore, this methodology has been applied to two real data sets, showcasing the effectiveness ofour proposed approach.